spath3 (23jan21)

git-svn-id: svn://tug.org/texlive/trunk@57504 c570f23f-e606-0410-a88d-b1316a301751

18 files changed, 11052 insertions, 5703 deletions

diff --git a/Master/texmf-dist/doc/latex/spath3/README b/Master/texmf-dist/doc/latex/spath3/README
index a9d1fe62103..dad3e28a92f 100644
--- a/Master/texmf-dist/doc/latex/spath3/README
+++ b/Master/texmf-dist/doc/latex/spath3/README
@@ -1,6 +1,6 @@
 ----------------------------------------------------------------
 spath3 --- LaTeX3 functions for manipulating PGF soft paths
-E-mail: stacey@math.ntnu.no
+E-mail: loopspace@mathforge.org
 Released under the LaTeX Project Public License v1.3c or later
 See http://www.latex-project.org/lppl.txt
 ----------------------------------------------------------------
diff --git a/Master/texmf-dist/doc/latex/spath3/README.txt b/Master/texmf-dist/doc/latex/spath3/README.txt
index a9d1fe62103..dad3e28a92f 100644
--- a/Master/texmf-dist/doc/latex/spath3/README.txt
+++ b/Master/texmf-dist/doc/latex/spath3/README.txt
@@ -1,6 +1,6 @@
 ----------------------------------------------------------------
 spath3 --- LaTeX3 functions for manipulating PGF soft paths
-E-mail: stacey@math.ntnu.no
+E-mail: loopspace@mathforge.org
 Released under the LaTeX Project Public License v1.3c or later
 See http://www.latex-project.org/lppl.txt
 ----------------------------------------------------------------
diff --git a/Master/texmf-dist/doc/latex/spath3/calligraphy.pdf b/Master/texmf-dist/doc/latex/spath3/calligraphy.pdf
new file mode 100644
index 00000000000..f2852f4d1ba
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/spath3/calligraphy.pdf
diff --git a/Master/texmf-dist/doc/latex/spath3/calligraphy_doc.tex b/Master/texmf-dist/doc/latex/spath3/calligraphy.tex
index c1b88c9e8e7..7690e5c5b73 100644
--- a/Master/texmf-dist/doc/latex/spath3/calligraphy_doc.tex
+++ b/Master/texmf-dist/doc/latex/spath3/calligraphy.tex
@@ -1,4 +1,4 @@
-\immediate\write18{tex spath3.dtx}
+\immediate\write18{tex spath3_doc.dtx}
 \documentclass{ltxdoc}
 \usepackage[T1]{fontenc}
 \usepackage{trace}
@@ -11,7 +11,14 @@
  
 \usepackage{listings}
 \lstloadlanguages{[LaTeX]TeX}
-\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
+\lstset{
+  breakatwhitespace=true,
+  breaklines=true,
+  language=[LaTeX]TeX,
+  basicstyle=\small\ttfamily,
+  keepspaces=true,
+  columns=fullflexible
+}
  
 \usepackage{fancyvrb}
 
@@ -22,7 +29,6 @@
    \begin{center}
    \setlength{\parindent}{0pt}
    \fbox{\begin{minipage}{.9\linewidth}
-     \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
      \lstinputlisting[]{example.out}
    \end{minipage}}
 
@@ -36,13 +42,20 @@
 \GetFileInfo{spath3.sty}
 
 \title{The \textsf{calligraphy} Package: Documentation}
-\author{Andrew Stacey \\ \url{stacey@math.ntnu.no}}
+\author{Andrew Stacey \\ \url{loopspace@mathforge.org}}
 \date{\fileversion~from \filedate}
 
 \begin{document}
 
 \maketitle
-% \section{Introduction}
+
+  \section{Pre-Introduction}
+  This library is built on top of a package for manipulating PGF's \emph{soft paths} called \texttt{spath3}.
+  Version 2.0 of \texttt{spath3} involved considerable reorganisation of the code.
+  I tried to ensure that this didn't affect this library but it is extremely likely that I wasn't fully successful.
+  If something that used to work no longer does, please do let me know either by opening an issue on github (\url{https://github.com/loopspace/spath3}) or at the above email.
+
+  \section{Introduction}
 The \Verb+calligraphy+ TikZ library is designed to enable calligraphic style drawings in TikZ.
 The idea is to be able to ``stroke'' a line with a ``pen''.
 As a simple example, compare the two lines in the following picture.
@@ -255,4 +268,4 @@ The following pens are predefined:
 \end{example}
 \end{itemize}
 
-\end{document}
\ No newline at end of file
+\end{document}
diff --git a/Master/texmf-dist/doc/latex/spath3/calligraphy_doc.pdf b/Master/texmf-dist/doc/latex/spath3/calligraphy_doc.pdf
deleted file mode 100644
index 12a0313d8ad..00000000000
--- a/Master/texmf-dist/doc/latex/spath3/calligraphy_doc.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/spath3/knots.pdf b/Master/texmf-dist/doc/latex/spath3/knots.pdf
new file mode 100644
index 00000000000..b1962a3c4c4
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/spath3/knots.pdf
diff --git a/Master/texmf-dist/doc/latex/spath3/knots_doc.tex b/Master/texmf-dist/doc/latex/spath3/knots.tex
index 67c23ca1287..20859a1d4ec 100644
--- a/Master/texmf-dist/doc/latex/spath3/knots_doc.tex
+++ b/Master/texmf-dist/doc/latex/spath3/knots.tex
@@ -1,17 +1,24 @@
-\immediate\write18{tex spath3.dtx}
+\immediate\write18{tex spath3_code.dtx}
 \documentclass{ltxdoc}
 \usepackage[T1]{fontenc}
 \usepackage{trace}
 \usepackage{lmodern}
 \usepackage{morefloats}
 \usepackage{tikz}
-\usetikzlibrary{knots}
+\usetikzlibrary{knots,spath3,hobby}
 \usepackage[numbered]{hypdoc}
 \definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} 
  
 \usepackage{listings}
 \lstloadlanguages{[LaTeX]TeX}
-\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
+\lstset{
+  breakatwhitespace=true,
+  breaklines=true,
+  language=[LaTeX]TeX,
+  basicstyle=\small\ttfamily,
+  keepspaces=true,
+  columns=fullflexible
+}
  
 \usepackage{fancyvrb}
 
@@ -22,7 +29,6 @@
    \begin{center}
    \setlength{\parindent}{0pt}
    \fbox{\begin{minipage}{.9\linewidth}
-     \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
      \lstinputlisting[]{example.out}
    \end{minipage}}
 
@@ -37,15 +43,41 @@
 \GetFileInfo{spath3.sty}
 
 \title{The \textsf{knots} Package: Documentation}
-\author{Andrew Stacey \\ \url{stacey@math.ntnu.no}}
+\author{Andrew Stacey \\ \url{loopspace@mathforge.org}}
 \date{\fileversion~from \filedate}
 
 \begin{document}
 
 \maketitle
 
-\section{Introduction}
+\section{Pre-Introduction}
+
+This library is built on top of a package for manipulating PGF's \emph{soft paths} called \texttt{spath3}.
+  Version 2.0 of \texttt{spath3} involved considerable reorganisation of the code.
+  I tried to ensure that this didn't affect this library but it is extremely likely that I wasn't fully successful.
+  If something that used to work no longer does, please do let me know either by opening an issue on github (\url{https://github.com/loopspace/spath3}) or at the above email.
+
+  That version of \texttt{spath3} also introduced an alternative way of drawing knots which involves breaking the paths at their crossing points and introducing actual gaps.
+  This makes it easier to do things like have the knots on non-uniform backgrounds, and to style different parts of the knot differently such as illustrating a \(3\)--colouring.
+  To see how that works, look at the documentation of the \texttt{spath3} TikZ library.
+  Here's an example of how to draw a knot with that library.
+
+  \begin{example}
+\begin{tikzpicture}[
+    use Hobby shortcut,
+    every trefoil component/.style={ultra thick, draw},
+    trefoil component 1/.style={red},
+    trefoil component 2/.style={blue},
+    trefoil component 3/.style={green},
+]
+\path[spath/save=trefoil] ([closed]90:2) foreach \k in {1,...,3} { .. (-30+\k*240:.5) .. (90+\k*240:2) } (90:2);
+\tikzset{spath/knot={trefoil}{8pt}{1,3,5}}
+\end{tikzpicture}
+\end{example}
 
+
+\section{Introduction}
+  
 The \Verb+knots+ package is a TikZ library for drawing knot (and similar) diagrams.
 It provides a few useful styles and node shapes but its main contribution is the \Verb+knot+ environment.
 The \Verb+knot+ environment allows you to draw some strands of a knot (or braid or tangle or whatever -- we shall use the imprecise term ``knot'' to refer to any similar diagram) and then to modify the crossings via a simple interface.
diff --git a/Master/texmf-dist/doc/latex/spath3/knots_doc.pdf b/Master/texmf-dist/doc/latex/spath3/knots_doc.pdf
deleted file mode 100644
index d818161e21f..00000000000
--- a/Master/texmf-dist/doc/latex/spath3/knots_doc.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/spath3/spath3.pdf b/Master/texmf-dist/doc/latex/spath3/spath3.pdf
new file mode 100644
index 00000000000..bbc90be42e4
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/spath3/spath3.pdf
diff --git a/Master/texmf-dist/doc/latex/spath3/spath3.tex b/Master/texmf-dist/doc/latex/spath3/spath3.tex
new file mode 100644
index 00000000000..86f925ba9e7
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/spath3/spath3.tex
@@ -0,0 +1,650 @@
+\RequirePackage{shellesc}
+\immediate\write18{tex spath3_code.dtx}
+\documentclass{l3doc}
+\usepackage{tikz}
+\usetikzlibrary{
+  spath3,
+  hobby,
+  patterns,
+  intersections,
+  arrows.meta,
+}
+ 
+\usepackage{listings}
+\lstloadlanguages{[LaTeX]TeX}
+\lstset{
+  breakatwhitespace=true,
+  breaklines=true,
+  language=[LaTeX]TeX,
+  basicstyle=\small\ttfamily,
+  keepspaces=true,
+  columns=fullflexible
+}
+ 
+\usepackage{fancyvrb}
+
+\newenvironment{example}
+{\VerbatimEnvironment
+\begin{VerbatimOut}[gobble=0]{example.out}}
+{\end{VerbatimOut}
+   \begin{center}
+   \setlength{\parindent}{0pt}
+   \fbox{\begin{minipage}{.9\linewidth}
+     \lstinputlisting[]{example.out}
+   \end{minipage}}
+
+   \fbox{\begin{minipage}{.9\linewidth}
+     \centering
+     \input{example.out}
+   \end{minipage}}
+\end{center}
+}
+
+\providecommand*{\url}{\texttt}
+\GetFileInfo{spath3.sty}
+
+\title{The \textsf{spath3} Package: Documentation}
+\author{Andrew Stacey \\ \url{loopspace@mathforge.org}}
+  \date{\fileversion~from \filedate}
+
+  \begin{document}
+
+  \maketitle
+
+  \section{Introduction}
+
+  The \texttt{spath3} package was originally designed as a low-level package for manipulating the \emph{soft paths} defined by PGF/TikZ.
+  Soft paths form one stage of the stack of translations between what the author writes in the \texttt{tikzpicture} environments in their \LaTeX\ document and what is eventually written to the output file.
+  Most of the complicated processing has been done by the time a soft path is constructed, but it is still very definitely a \TeX\ object and there has not, for example, been any consideration as to what the eventual output file format is (such as PDF, DVI, or SVG).
+  So it is very amenable to being modified at this stage and this package provides a set of routines for doing so.
+
+  The original purpose was to provide a common core on which other packages would be built.
+  Indeed, the packages \texttt{calligraphy}, \texttt{knots}, and \texttt{penrose} all use this package.
+  However, over time I've found myself wanting to use the routines of this package at a higher level and so have designed some user-level interfaces.
+  This document documents those.
+
+  To clarify some terminology, paths are composed of \emph{segment} and \emph{components}.
+A \emph{segment} is a minimal drawing piece.
+Thus it might be a straight line or a B\'ezier curve.
+A \emph{component} is a minimal connected section of the path.
+So every component starts with a move command and continues until the next move command.
+For ease of implementation (and to enable a copperplate pen in the calligraphy package!), an isolated move is considered as a component.
+
+  
+  \section{TikZ Keys}
+
+\begin{lstlisting}
+\usetikzlibrary{spath3}
+\end{lstlisting}
+
+The \texttt{spath3} TikZ library defines a set of keys that can be issued to muck about with soft paths.
+These are all defined in the \texttt{spath} family, so all the following keys should be prefixed by \texttt{spath/}, or the key \texttt{spath/.cd} needs to be used beforehand.
+
+\subsection{Saving and Using Soft Paths}
+
+\begin{function}{save}
+\begin{syntax}
+|save=|\meta{name}
+\end{syntax}
+
+Saves the current path with name \texttt{<name>}.
+This delays until the path is fully constructed so can be issued in the options to the main command.
+
+Soft paths constructed this way are local to the group in which the path command is issued.
+
+The soft path is actually stored in a macro constructed from the name.
+There are a couple of reasons for using a \emph{name} rather than a macro directly.
+One is so that it is compatible with the \texttt{intersections} library -- by default both this package and that save their paths in the same underlying macro.
+The other is to provide a way to link a soft path with a set of TikZ styles (this is particularly useful when splitting the path into components).
+\end{function}
+
+\begin{function}{save global}
+\begin{syntax}
+|save global=|\meta{name}
+\end{syntax}
+
+Saves the current soft path globally.
+\end{function}
+
+\begin{function}{clone}
+\begin{syntax}
+|clone=|\marg{target}\marg{source}
+\end{syntax}
+
+Clones one soft path into another.
+\end{function}
+
+\begin{function}{restore}
+\begin{syntax}
+|restore=|\meta{name}
+\end{syntax}
+
+Restores a previously saved soft path to the current path.
+This happens immediately so can be issued in the options to the main command and then the path can be extended with normal drawing commands.
+Any keys that affect the soft path directly should be applied \emph{before} this one.
+
+One thing should be noted about transformations.
+By the time a soft path is built, all available transformations have been applied.
+This means that when re-inserting a soft path back into a high level command (such as |\draw|), the effect of existing transformations might produce some confusing effects.
+When restoring a path then the library tries to set the last point correctly, but depending on how this is used it can result in transformations being applied twice.
+\end{function}
+
+\begin{function}{append}
+\begin{syntax}
+|append=|\meta{name}
+\end{syntax}
+
+This inserts a soft path into the path at the current point, it is therefore more suited to being used part way through a path construction.
+In a sense, it is a little like a \texttt{pic} in that it enables the user to construct a path segment early to be reused at various places.
+
+The path is \emph{welded} on to the current path, meaning that it starts from the current point and there is no \texttt{move}.
+This is particularly useful for creating filled regions.
+\end{function}
+
+\begin{function}{reverse}
+\begin{syntax}
+|reverse=|\meta{name}
+\end{syntax}
+
+Reverses the path in the named spath object.
+This doesn't do any actually drawing.
+The effect is local, but if you want to work with both the original path and its reversal in the same path then use the \texttt{clone} key to copy it first.
+\end{function}
+
+\begin{function}{append reverse}
+\begin{syntax}
+|append reverse=|\meta{name}
+\end{syntax}
+
+Like \texttt{append} except that the inserted path is reversed first.
+\end{function}
+
+\begin{function}{insert}
+\begin{syntax}
+|insert=|\meta{name}
+\end{syntax}
+
+Like \texttt{append} except that it doesn't move the inserted path and there is a move between the current path and the inserted path.
+\end{function}
+
+\begin{function}{
+  shorten at end,
+shorten at start,
+shorten at both ends
+}
+\begin{syntax}
+|shorten at end=|\marg{name}\marg{dimen}
+\end{syntax}
+
+Shortens the soft path by the dimension from one or both ends.
+This shortens the soft path along its length so that it is guaranteed that the shorter path traces a subset of the original path.
+For B\'ezier curves, however, the amount of shortening is approximate and is better for shorter distances.
+If wanting to shorten by a large amount it is better to shorten by a small amount a number of times.
+\end{function}
+
+\begin{function}{translate}
+\begin{syntax}
+|translate=|\marg{name}\marg{x-dimen}\marg{y-dimen}
+\end{syntax}
+
+Translates the soft path by the given dimensions.
+\end{function}
+
+\begin{function}{transform}
+\begin{syntax}
+|transform=|\marg{name}\marg{transformations}
+\end{syntax}
+
+This applies the transformation to the soft path.
+The transformation is processed by TikZ so should consist of TikZ-level transformations such as |shift={(2,2)}|.
+\end{function}
+
+\subsection{Intersection Routines}
+
+To use these features you need to use the \texttt{intersections} library.
+
+\begin{function}{split at self intersections}
+\begin{syntax}
+|split at self intersections=|\meta{path}
+\end{syntax}
+
+This inserts breaks into the named soft path at the points where it intersects itself.
+\end{function}
+
+\begin{function}{split at intersections}
+\begin{syntax}
+|split at intersections=|\marg{first}\marg{second}
+\end{syntax}
+
+This inserts breaks into a pair of paths at their mutual intersections.
+\end{function}
+
+\subsection{Working with Components}
+
+\begin{function}{get components of}
+\begin{syntax}
+|get components of=|\marg{macro}\marg{path}
+\end{syntax}
+  
+This splits the path into a list of its components, which are stored in the macro.
+The macro can be used in a |\foreach|.
+\end{function}
+
+\begin{function}{render components}
+\begin{syntax}
+|render components=|\meta{path}
+\end{syntax}
+
+This renders the components of a given path as separate TikZ commands, so that each can be separately styled.
+It applies the following styles (in this order):
+
+\begin{enumerate}
+\item \texttt{every spath component}
+\item \texttt{spath component <number>}
+\item \texttt{spath component=<number>}
+\item \texttt{every <path> component}
+\item \texttt{<path> component <number>}
+\item \texttt{<path> component=<number>}
+\end{enumerate}
+\end{function}
+
+\begin{function}{insert gaps after components}
+\begin{syntax}
+|insert gaps after components=|\marg{path}\marg{gap}\marg{components}
+\end{syntax}
+
+This inserts a gap between components of a path by shortening the end of the specified component and start of the next one.
+The list of components is passed through a |\foreach| loop so that syntax like |2,4,...,16|.
+\end{function}
+
+\begin{function}{join components}
+\begin{syntax}
+|join components=|\marg{path}\marg{components}
+\end{syntax}
+
+This removes the \texttt{move} between the given component and the previous one.
+If the component is the first one then it is joined to the last component.
+\end{function}
+
+\begin{function}{spot weld}
+\begin{syntax}
+|spot weld=|\meta{path}
+\end{syntax}
+
+This removes the \texttt{move} between any two components of the path where the end point of one component is the same as the initial point of the next (the tolerance on error here is \(0.01\)pt).
+\end{function}
+
+\begin{function}{remove empty components}
+\begin{syntax}
+|remove empty components=|\meta{path}
+\end{syntax}
+
+This removes empty components of the path (which consist of simply a move).
+\end{function}
+
+\subsection{Shortening Paths}
+
+\begin{function}{
+shorten path at end,
+shorten path at start,
+shorten path at both ends
+}
+\begin{syntax}
+|shorten path at end=|\marg{path}\marg{length}
+\end{syntax}
+
+This shortens a path by the given amount from the specified end.
+The shortening is done so that it guarantees that it lies along the original path, but therefore the length is not completely guaranteed to be accurate.
+This is particularly true for B\'ezier paths and if there is a very short segment at the end.
+
+It uses the derivative at the end to work out how much to shorten by.
+\end{function}
+
+\subsection{Exporting Paths}
+
+There are two keys to export a path.
+
+\begin{function}{save to aux}
+\begin{syntax}
+|save to aux=|\meta{path}
+\end{syntax}
+
+This will save the path to the auxfile so that it is available again on the next run through.
+\end{function}
+
+\begin{function}{export to svg}
+\begin{syntax}
+|export to svg=|\meta{path}
+\end{syntax}
+
+Saves the path to the file \texttt{path.svg} as an SVG document.
+\end{function}
+
+\subsection{Knots}
+
+\begin{function}{knot}
+\begin{syntax}
+|knot=|\meta{path}\meta{gap}\meta{components}
+\end{syntax}
+
+This style combines various of the above to make it simpler to draw knots and links.
+It expands to:
+
+\begin{lstlisting}
+knot/.style n args={3}{
+  spath/.cd,
+  split at self intersections=#1,
+  insert gaps after components={#1}{#2}{#3},
+  maybe spot weld=#1,
+  render components=#1
+}
+\end{lstlisting}
+
+This splits a path at the points where it self-intersects and then inserts gaps between specified components.
+The key |maybe spot weld| does a |spot weld| depending on whether or not the key |draft mode| is set to |true| or |false|.
+The point here is that when designing the knot it is useful to not weld together components since that changes the component count.
+But once the gaps are inserted in the desired places, welding the remaining components produces a nicer diagram.
+
+The components can be styled using the keys as described in |render components|.
+\end{function}
+
+\subsection{Coordinates}
+
+Soft paths are not natural TikZ objects and so when replaced back into a TikZ path construction then they don't fully interact with other TikZ things, like placing nodes at points on the path.
+To make things a little easier there is defined a coordinate system which identifies a point at a certain location along a soft path and keys which apply a transformation.
+
+\begin{function}{spath cs}
+\begin{syntax}
+|(spath cs:|\marg{name} \marg{parameter}|)|
+\end{syntax}
+
+The location specification is a little technical.
+It is specified as a number from \(0\) to \(1\), but the parameter works as follows.
+Let \(n\) be the number of \emph{segments} on the path (these are the individual drawing elements that make up the path).
+The interval from \(\frac{k-1}{n}\) to \(\frac{k}{n}\) is assigned to the \(k\)th segment of the path.
+Then for a parameter in that interval, the location uses the natural parametrisation of that segment.
+For a straight line, it is simply the proportional position along but for a B\'ezier curve then it uses the B\'ezier parametrisation.
+
+The space is vital, so if the \texttt{name} is contained in a macro then a space has to be inserted somehow.
+One option is to wrap the macro in braces, as seen in the examples in the next section.
+\end{function}
+
+\begin{function}{transform to, upright transform to}
+\begin{syntax}
+|transform to=|\marg{path}\marg{parameter}
+|upright transform to=|\marg{path}\marg{parameter}
+\end{syntax}
+
+These keys (which are in the |spath| family) set the transformation so that the origin is at the specified point of the curve (as described above) and the \(x\)--axis is tangential to the curve.
+The transformation is \emph{orthogonal} in that it is achieved by a rotation and a translation.
+
+The first key aligns the axes so that the \(x\)--axis is in the forward direction of the path as that path was constructed.
+The second key aligns the axes so that the \(y\)--axis points up the page.
+The intention with the second key is that it is similar to what happens with the |sloped| key when a node is placed on a curve.
+\end{function}
+
+\section{Examples}
+
+\begin{enumerate}
+\item Saving, restoring, inserting, and appending.
+
+\begin{example}
+\begin{tikzpicture}
+\path[spath/save=rpath] (0,0) to[out=30,in=150] (1,1);
+\foreach \k in {1,...,9} {
+  \fill[green] (spath cs:rpath 0.\k) circle[radius=3pt];
+  \node[above left] at (spath cs:rpath 0.\k) {\(0.\k\)};
+}
+\fill[green] (2,2) circle[radius=3pt];
+\draw[blue, spath/transform={rpath}{shift={(2,2)}}, spath/restore=rpath] node[right] {transform};
+\draw[orange] (3,0) [spath/insert=rpath] node[right] {insert};
+\draw[red] (3,-1) -- +(0,2) [spath/append=rpath] node[above] {append};
+\draw[spath/restore=rpath] node[right] {restore};
+\end{tikzpicture}
+\end{example}
+
+\item Reversing.
+
+\begin{example}
+\begin{tikzpicture}
+\path[spath/save=apath] (0,0) to[out=0,in=180] (2,1) to[out=0,in=180] (4,0);
+\filldraw[
+  green,
+  draw=black,
+  ultra thick,
+  spath/restore=apath
+] -- ++(0,-4) [spath/append reverse=apath] -- cycle;
+\end{tikzpicture}
+\end{example}
+
+\item Transformations.
+
+\begin{example}
+\begin{tikzpicture}
+\draw[spath/save=tpath] (0,0) rectangle +(1,1);
+\draw[rotate=45, xscale=2, yscale=3, ultra thick, red] (0,0) rectangle +(1,1);
+\draw[
+  spath/transform={tpath}{rotate=45, xscale=2, yscale=3},
+  spath/restore={tpath}];
+\end{tikzpicture}
+\end{example}
+
+\begin{example}
+\begin{tikzpicture}
+\draw[spath/save=oval] (0,0) to[out=0,in=0] (0,2) to[out=180,in=180] (0,0);
+\foreach \k in {0,...,9} {
+  \node[transform shape, spath/transform to={oval}{0.\k}] {k};
+}
+\begin{scope}[xshift = 3cm]
+\draw[spath/save=soval] (0,0) to[out=0,in=0] (0,2) to[out=180,in=180] (0,0);
+\foreach \k in {0,...,9} {
+  \node[transform shape, spath/upright transform to={soval}{0.\k}] {k};
+}
+\end{scope}
+\end{tikzpicture}
+\end{example}
+
+\item Shortening.
+
+\begin{example}
+\begin{tikzpicture}
+\path[spath/save=apath] (0,0) foreach \k in {1,...,4} { -- ++(1,0) +(0,0)};
+\draw[
+  ultra thick,
+  red,
+  spath/.cd,
+  shorten at end={apath}{7pt},
+  shorten at start={apath}{9pt},
+  translate={apath}{0pt}{1pt},
+  restore=apath,
+];
+\draw (0,0) circle[radius=9pt] [spath/insert=apath] circle[radius=7pt];
+\end{tikzpicture}
+\end{example}
+
+
+\begin{example}
+\begin{tikzpicture}
+\path[spath/save=apath] (0,0) foreach \k in {1,...,4} { to[out=0,in=180] ++(1,0) +(0,0)};
+\draw[
+  ultra thick,
+  red,
+  spath/.cd,
+  shorten at end={apath}{7pt},
+  shorten at start={apath}{9pt},
+  translate={apath}{0pt}{1pt},
+  restore=apath,
+];
+\draw (0,0) circle[radius=9pt] [spath/insert=apath] circle[radius=7pt];
+\end{tikzpicture}
+\end{example}
+
+\begin{example}
+\begin{tikzpicture}
+\draw[spath/save=npath] (0,0) foreach \k in {1,...,4} { -- ++(1,0) +(0,0)};
+\draw[green] (0,0) -- +(0,-3pt) foreach \k in {1,...,4} { -- +(0,-3pt) ++(1,0)} -- +(0,-3pt);
+
+\tikzset{
+  spath/.cd,
+  insert gaps after components={npath}{10pt}{1,3},
+  get components of={npath}\components,
+}
+
+\tikzset{
+  path 1/.style={
+    red,
+  },
+}
+
+\foreach[count=\k] \cpt in \components {
+  \path[
+    draw,
+    path \k/.try,
+    spath/.cd,
+    translate=\cpt{0pt}{\k pt},
+    restore=\cpt,
+  ] +(0,3pt) -- +(0,-3pt);
+  \node[text=red] at (spath cs:{\cpt} .5) {\(\k\)};
+}
+\end{tikzpicture}
+\end{example}
+
+\item Intersections.
+
+One of the main motivations for implementing the intersection routines was to provide a different way of drawing knots and links and similar diagrams.
+
+\begin{enumerate}
+
+\item Define the two paths for the braid (usually these will be defined with |\path|).
+\begin{example}
+\begin{tikzpicture}[
+  use Hobby shortcut,
+]
+\draw[spath/save global=pathA] (0,0) to[out=0,in=180] ++(2,1) to[out=0,in=180] ++(2,-1)  to[out=0,in=180] ++(2,1)  to[out=0,in=180] ++(2,-1);
+\draw[spath/save global=pathB] (0,1) to[out=0,in=180] ++(2,-1) to[out=0,in=180] ++(2,1)  to[out=0,in=180] ++(2,-1)  to[out=0,in=180] ++(2,1);
+\end{tikzpicture}
+\end{example}
+
+\item Split the paths at their mutual intersections and render them with a count of the components.
+
+\begin{example}
+\begin{tikzpicture}
+\tikzset{
+  spath/.cd,
+  split at intersections={pathA}{pathB},
+  get components of={pathA}\pathAcomponents,
+  get components of={pathB}\pathBcomponents,
+}
+
+\foreach[count=\k] \cpt in \pathAcomponents {
+  \draw[spath/restore=\cpt,-Circle];
+  \node[fill=white, fill opacity=.5, circle, text opacity=1] at (spath cs:{\cpt} .5) {\(\k\)};
+}
+
+\foreach[count=\k] \cpt in \pathBcomponents {
+  \draw[spath/restore=\cpt,-Circle];
+  \node[fill=white, fill opacity=.5, circle, text opacity=1] at (spath cs:{\cpt} .5) {\(\k\)};
+}
+\end{tikzpicture}
+\end{example}
+
+\item Now we insert gaps after certain components in each path and then render the components.
+To show that the gaps are genuine, we use a patterned background.
+Although the paths were defined globally, the splitting in the previous example was local so we need to repeat it in this one.
+
+\begin{example}
+\begin{tikzpicture}
+\tikzset{
+  spath/.cd,
+  split at intersections={pathA}{pathB},
+  insert gaps after components={pathA}{5pt}{1,3},
+  join components={pathA}{3,5},
+  get components of={pathA}\pathAcomponents,
+  insert gaps after components={pathB}{5pt}{2,4},
+  join components={pathB}{2,4},
+  get components of={pathB}\pathBcomponents,
+}
+
+\fill[red!50!white] (-.5,-.5) rectangle (8.5,1.5);
+\fill[pattern=bricks, pattern color=white] (-.5,-.5) rectangle (8.5,1.5);
+
+\foreach[count=\k] \cpt in \pathAcomponents {
+  \draw[blue, line width=2pt,spath/restore=\cpt];
+  \node[fill=cyan, fill opacity=.5, circle, text opacity=1] at (spath cs:{\cpt} .3) {\(\k\)};
+}
+
+\foreach[count=\k] \cpt in \pathBcomponents {
+  \draw[green, line width=2pt,spath/restore=\cpt];
+  \node[fill=green!50, fill opacity=.5, circle, text opacity=1] at (spath cs:{\cpt} .3) {\(\k\)};
+}
+\end{tikzpicture}
+\end{example}
+\end{enumerate}
+
+\item This example is notable because many of the intersection points are where segments of the path end, showing that the algorithm works well even in this circumstance.
+
+\begin{enumerate}
+\item Here's the original path.
+\begin{example}
+\begin{tikzpicture}
+\draw[spath/save global=spiral] (5,0) -- (2.5,0) -- ++(0,-.25) -- ++(-2.5,0)
+arc[radius=2.25cm,start angle=180,end angle=90]
+arc[radius=2cm,start angle=90, delta angle=-180]
+arc[radius=1.75cm,start angle=-90, delta angle=-180]
+arc[radius=1.5cm,start angle=90, delta angle=-180]
+arc[radius=1.25cm,start angle=-90, delta angle=-180]
+arc[radius=1cm,start angle=90, delta angle=-180]
+arc[radius=.75cm,start angle=-90, delta angle=-180]
+arc[radius=.5cm,start angle=90, delta angle=-180]
+;
+\end{tikzpicture}
+\end{example}
+
+\item This renders labels on each component after splitting.
+\begin{example}
+\begin{tikzpicture}
+\tikzset{
+  spath/.cd,
+  split at self intersections=spiral,
+  get components of={spiral}\pathcomponents,
+}
+
+\foreach[count=\k] \cpt in \pathcomponents {
+  \draw[spath/restore=\cpt,-|];
+  \node[fill=white, fill opacity=.5, circle, text opacity=1] at (spath cs:{\cpt} .5) {\(\k\)};
+}
+\end{tikzpicture}
+\end{example}
+
+\item Finally, we put the gaps in where we want them.
+
+\begin{example}
+\begin{tikzpicture}
+\tikzset{
+  spath/.cd,
+  split at self intersections=spiral,
+  insert gaps after components={spiral}{10pt}{1,3,5,7,10,11,14},
+  spot weld=spiral,
+  get components of={spiral}\pathcomponents,
+}
+
+\foreach[count=\k] \cpt in \pathcomponents {
+  \draw[blue, line width=2pt,spath/restore=\cpt];
+}
+\end{tikzpicture}
+\end{example}
+\end{enumerate}
+
+\item Here's a trefoil knot, demonstrating the \texttt{knot} style that simplifies creating knots.
+\begin{example}
+\begin{tikzpicture}[
+  use Hobby shortcut,
+  every trefoil component/.style={ultra thick, draw, red},
+  trefoil component 1/.style={blue},
+]
+\path[spath/save=trefoil] ([closed]90:2) foreach \k in {1,...,3} { .. (-30+\k*240:.5) .. (90+\k*240:2) } (90:2);
+\tikzset{spath/knot={trefoil}{8pt}{1,3,5}}
+\end{tikzpicture}
+\end{example}
+\end{enumerate}
+  \end{document}
diff --git a/Master/texmf-dist/doc/latex/spath3/spath3_code.pdf b/Master/texmf-dist/doc/latex/spath3/spath3_code.pdf
index be1f2941bd8..77d3e3b723c 100644
--- a/Master/texmf-dist/doc/latex/spath3/spath3_code.pdf
+++ b/Master/texmf-dist/doc/latex/spath3/spath3_code.pdf
diff --git a/Master/texmf-dist/source/latex/spath3/spath3.dtx b/Master/texmf-dist/source/latex/spath3/spath3.dtx
deleted file mode 100644
index 9d6ae2825df..00000000000
--- a/Master/texmf-dist/source/latex/spath3/spath3.dtx
+++ /dev/null
@@ -1,4228 +0,0 @@
-% \iffalse meta-comment
-%<*internal>
-\iffalse
-%</internal>
-%<*readme>
-----------------------------------------------------------------
-spath3 --- LaTeX3 functions for manipulating PGF soft paths
-E-mail: stacey@math.ntnu.no
-Released under the LaTeX Project Public License v1.3c or later
-See http://www.latex-project.org/lppl.txt
-----------------------------------------------------------------
-
-This package defines some functions used to manipulate PGFs soft paths.
-As applications of its use, included are a package for drawing calligraphic paths and a package for drawing knot diagrams.
-%</readme>
-%<*internal>
-\fi
-\def\nameofplainTeX{plain}
-\ifx\fmtname\nameofplainTeX\else
-  \expandafter\begingroup
-\fi
-%</internal>
-%<*install>
-\input docstrip.tex
-\keepsilent
-\askforoverwritefalse
-\preamble
-----------------------------------------------------------------
-spath3 --- Functions for manipulating PGF soft paths
-E-mail: stacey@math.ntnu.no
-Released under the LaTeX Project Public License v1.3c or later
-See http://www.latex-project.org/lppl.txt
-----------------------------------------------------------------
-
-\endpreamble
-\postamble
-
-Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
-
-This work may be distributed and/or modified under the
-conditions of the LaTeX Project Public License (LPPL), either
-version 1.3c of this license or (at your option) any later
-version.  The latest version of this license is in the file:
-
-http://www.latex-project.org/lppl.txt
-
-This work is "maintained" (as per LPPL maintenance status) by
-Andrew Stacey.
-
-This work consists of the files  spath3.dtx
-                                 calligraphy_doc.tex
-                                 knots_doc.tex
-and the derived files            spath3.ins,
-                                 spath3_code.pdf,
-                                 spath3.sty,
-                                 tikzlibrarycalligraphy.code.tex
-                                 tikzlibraryknots.code.tex
-                                 calligraphy.pdf
-                                 knots.pdf
-                                 README
-
-\endpostamble
-\usedir{tex/latex/spath3}
-\generate{
-  \file{\jobname.sty}{\from{\jobname.dtx}{spath3}}
-}
-\generate{
-  \file{tikzlibrarycalligraphy.code.tex}{\from{\jobname.dtx}{calligraphy}}
-}
-\generate{
-  \file{tikzlibraryknots.code.tex}{\from{\jobname.dtx}{knots}}
-}
-%</install>
-%<install>\endbatchfile
-%<*internal>
-\usedir{source/latex/spath3}
-\generate{
-  \file{\jobname.ins}{\from{\jobname.dtx}{install}}
-}
-\nopreamble\nopostamble
-\usedir{doc/latex/demopkg}
-\generate{
-  \file{README.txt}{\from{\jobname.dtx}{readme}}
-}
-\ifx\fmtname\nameofplainTeX
-  \expandafter\endbatchfile
-\else
-  \expandafter\endgroup
-\fi
-%</internal>
-%<*driver>
-\documentclass[full]{l3doc}
-\usepackage[T1]{fontenc}
-\usepackage{lmodern}
-%\usepackage{morefloats}
-\usepackage{tikz}
-\usepackage{trace}
-\usepackage{spath3}
-%\traceoff
-%\usepackage[numbered]{hypdoc}
-\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} 
- 
-\usepackage{listings}
-\lstloadlanguages{[LaTeX]TeX}
-\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
- 
-\usepackage{fancyvrb}
-
-\newenvironment{example}
-  {\VerbatimEnvironment
-   \begin{VerbatimOut}[gobble=2]{example.out}}
-  {\end{VerbatimOut}
-   \begin{center}
-%   \setlength{\parindent}{0pt}
-   \fbox{\begin{minipage}{.9\linewidth}
-     \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
-     \lstinputlisting[]{example.out}
-   \end{minipage}}
-
-   \fbox{\begin{minipage}{.9\linewidth}
-     \input{example.out}
-   \end{minipage}}
-\end{center}
-}
-\EnableCrossrefs
-\CodelineIndex
-\RecordChanges
-\begin{document}
-  \DocInput{\jobname.dtx}
-\end{document}
-%</driver>
-% \fi
-%
-% \CheckSum{4488}
-%
-% \CharacterTable
-%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
-%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
-%   Digits        \0\1\2\3\4\5\6\7\8\9
-%   Exclamation   \!     Double quote  \"     Hash (number) \#
-%   Dollar        \$     Percent       \%     Ampersand     \&
-%   Acute accent  \'     Left paren    \(     Right paren   \)
-%   Asterisk      \*     Plus          \+     Comma         \,
-%   Minus         \-     Point         \.     Solidus       \/
-%   Colon         \:     Semicolon     \;     Less than     \<
-%   Equals        \=     Greater than  \>     Question mark \?
-%   Commercial at \@     Left bracket  \[     Backslash     \\
-%   Right bracket \]     Circumflex    \^     Underscore    \_
-%   Grave accent  \`     Left brace    \{     Vertical bar  \|
-%   Right brace   \}     Tilde         \~}
-%
-%
-% \changes{1.0}{2011/05/03}{Converted to DTX file}
-% \changes{1.1}{2016/02/19}{Fixes due to changes in LaTeX3}
-% \changes{1.2}{2019/02/12}{More fixes due to changes in LaTeX3}
-%
-% \DoNotIndex{\newcommand,\newenvironment}
-%
-% \providecommand*{\url}{\texttt}
-% \GetFileInfo{spath3.sty}
-% \title{The \textsf{spath3} package}
-% \author{Andrew Stacey \\ \url{stacey@math.ntnu.no}}
-% \date{\fileversion~from \filedate}
-%
-%
-% \maketitle
-%
-% 
-% \section{Introduction}
-%
-% The \Verb+spath3+ package is intended as a library for manipulating PGF's \emph{soft paths}.
-% In between defining a path and using it, PGF stores a path as a \emph{soft path} where all the defining structure has been resolved into the basic operations but these have not yet been written to the output file.
-% They can therefore still be manipulated by \TeX, and as they have a very rigid form (and limited vocabulary), they are relatively easy to modify.
-% This package provides some methods for working with these paths.
-% It is not really intended for use by end users but as a foundation on which other packages can be built.
-% As examples, the \Verb+calligraphy+ package and the \Verb+knot+ package are included.
-% The first of these simulates a calligraphic pen stroking a path.
-% The second can be used to draw knot (and similar) diagrams.
-%
-% The format of a soft path is a sequence of triples of the form \Verb+\macro {dimension}{dimension}+.
-% The macro is one of a short list, the dimensions are coordinates in points.
-% There are certain further restrictions, particularly that every path must begin with a \Verb+move to+, and B\'ezier curves consist of three triples.
-%
-% \StopEventually{}
-%
-% \section{Implementation}
-%
-% \iffalse
-%<*spath3>
-% \fi
-% \subsection{Initialisation}
-%
-% Load the \LaTeX3 foundation and register us as a \LaTeX3\ package.
-%    \begin{macrocode}
-\NeedsTeXFormat{LaTeX2e}
-\RequirePackage{expl3}
-\RequirePackage{pgf}
-\ProvidesExplPackage {spath3} {2019/02/12} {1.2} {Functions for
-manipulating PGF soft paths}
-\RequirePackage{xparse}
-%    \end{macrocode}
-%
-% We need a slew of temporary variables.
-%    \begin{macrocode}
-\tl_new:N \l__spath_tmpa_tl
-\tl_new:N \l__spath_tmpb_tl
-\tl_new:N \l__spath_tmpc_tl
-\tl_new:N \l__spath_tmpd_tl
-\tl_new:N \l__spath_smuggle_tl
-\dim_new:N \l__spath_tmpa_dim
-\dim_new:N \l__spath_tmpb_dim
-\fp_new:N \l__spath_tmpa_fp
-\fp_new:N \l__spath_tmpb_fp
-\int_new:N \l__spath_tmpa_int
-\int_new:N \g__spath_map_int
-%    \end{macrocode}
-%
-% We need to be able to compare against the macros that can occur in  a soft path so these token lists contain them.
-%    \begin{macrocode}
-\tl_new:N \g__spath_moveto_tl
-\tl_new:N \g__spath_lineto_tl
-\tl_new:N \g__spath_curveto_tl
-\tl_new:N \g__spath_curvetoa_tl
-\tl_new:N \g__spath_curvetob_tl
-\tl_new:N \g__spath_closepath_tl
-\tl_set:Nn \g__spath_moveto_tl {\pgfsyssoftpath@movetotoken}
-\tl_set:Nn \g__spath_lineto_tl {\pgfsyssoftpath@linetotoken}
-\tl_set:Nn \g__spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
-\tl_set:Nn \g__spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
-\tl_set:Nn \g__spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
-\tl_set:Nn \g__spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
-%    \end{macrocode}
-%
-% \subsection{Basic Structure and Methods}
-%
-% A soft path is a \Verb+prop+.
-% These are lists of the attributes that we define.
-% The first consists of all attributes, the second of those that are ``moveable'' in the sense that they change if we transform the path, the third are the ones that contain actual paths.
-%
-% Note that if using these attributes outside an \Verb+expl3+ context, the spaces should be omitted.
-%    \begin{macrocode}
-\tl_new:N \g__spath_attributes
-\tl_new:N \g__spath_moveable_attributes
-\tl_new:N \g__spath_path_attributes
-\tl_set:Nn \g__spath_attributes {
-  {path}
-  {reverse path}
-  {length}
-  {real length}
-  {number of components}
-  {initial point}
-  {final point}
-  {initial action}
-  {final action}
-  {min bb}
-  {max bb}
-}
-\tl_set:Nn \g__spath_moveable_attributes {
-  {initial point}
-  {final point}
-  {min bb}
-  {max bb}
-}
-\tl_set:Nn \g__spath_path_attributes {
-  {path}
-  {reverse path}
-}
-%    \end{macrocode}
-%
-% An \Verb+spath+ object is actually a \Verb+prop+.
-% The following functions are wrappers around the underlying \Verb+prop+ functions.
-% We prefix the names to avoid clashing with other \Verb+prop+s that might be lying around, this is why all the \Verb+spath+ methods take argument \Verb+:n+ and not \Verb+:N+.
-% Given that \Verb+spath+ objects might be created inside a group but used outside it, we work globally throughout.
-% \begin{macro}{\spath_new:n}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_new:n #1
-{
-  \prop_new:c {l__spath_#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_clear:n}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_clear:n #1
-{
-  \prop_gclear:c {l__spath_#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_clear_new:n}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_clear_new:n #1
-{
-  \prop_gclear_new:c {l__spath_#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_show:n}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_show:n #1
-{
-  \prop_show:c {l__spath_#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_put:nnn}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_put:nnn #1#2#3
-{
-  \prop_gput:cnn {l__spath_#1} {#2} {#3}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_remove:nn}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_remove:nn #1#2
-{
-  \prop_gremove:cn {l__spath_#1} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\__spath_get:nn}
-% This function is an internal one since the real \Verb+get+ function will generate its data if it does not already exist.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \__spath_get:nn #1#2
-{
-  \prop_item:cn {l__spath_#1} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\__spath_get:nnN}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \__spath_get:nnN #1#2#3
-{
-  \prop_get:cnN {l__spath_#1} {#2} #3
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_if_in:nn}
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \spath_if_in:nn #1#2 {p, T, F, TF}
-{
-  \prop_if_in:cnTF {l__spath_#1} {#2}
-  { \prg_return_true: }
-  { \prg_return_false: }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\__spath_get:nnN}
-%    \begin{macrocode}
-\cs_generate_variant:Nn \__prop_split:NnTF {cnTF}
-\prg_new_protected_conditional:Npnn \__spath_get:nnN #1#2#3 {T, F, TF}
-{
-  \__prop_split:cnTF {l__spath_#1} {#2}
-  {
-    \tl_set:Nn #3 {##2}
-    \prg_return_true:
-  }
-  { \prg_return_false: }
-}
-\cs_generate_variant:Nn \spath_put:nnn {nnV, nnx, nno}
-\cs_generate_variant:Nn \__spath_get:nn {Vn}
-\cs_generate_variant:Nn \__spath_get:nnN {VnN}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_if_exist:n}
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \spath_if_exist:n #1 {p,T,F,TF}
-{
-  \prop_if_exist:cTF {l__spath_#1}
-  {
-    \prg_return_true:
-  }
-  {
-    \prg_return_false:
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_clone:nn}
-% Clones an \Verb+spath+.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_clone:nn #1 #2
-{
-  \spath_clear_new:n {#2}
-  \tl_map_inline:Nn \g__spath_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \spath_put:nnV {#2} {##1} \l__spath_tmpa_tl
-    }
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_get_current_path:n}
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \spath_get_current_path:n #1
-{
-  \pgfsyssoftpath@getcurrentpath\l__spath_tmpa_tl
-  \spath_clear_new:n {#1}
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_set_current_path:n}
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
-{
-  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \pgfsyssoftpath@setcurrentpath\l__spath_tmpa_tl
-  \pgfsyssoftpath@flushcurrentpath
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_use_path:nn}
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
-{
-  \spath_set_current_path:n {#1}
-  \pgfusepath{#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_protocol_path:n}
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
-{
-  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_tikz_path:nn}
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
-{
-  \path[#1] \pgfextra{
-    \spath_get:nnN {#2} {path} \l__spath_tmpa_tl
-    \pgfsyssoftpath@setcurrentpath \l__spath_tmpa_tl
-  };
-}
-\cs_generate_variant:Nn \spath_tikz_path:nn {Vn}
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Computing Information}
-%
-% \begin{macro}{\spath_get:nn}
-% The information that we store along with a soft path can be computed from it, but computing it every time is wasteful.
-% So this is the real \Verb+\spath_get:nn+ function which checks to see if we have already computed it and then either retrieves it or computes it. 
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_get:nn #1#2
-{
-  \spath_if_in:nnF {#1} {#2}
-  {
-    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
-  }
-  \__spath_get:nn {#1} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_get:nnN}
-% As above but leaves the result in a token list rather than in the stream.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_get:nnN #1#2#3
-{
-  \spath_if_in:nnF {#1} {#2}
-  {
-    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
-  }
-  \__spath_get:nnN {#1} {#2} #3
-}
-\cs_generate_variant:Nn \spath_get:nnN {VnN}
-%    \end{macrocode}
-% \end{macro}
-%
-% The next slew of functions generate data from the original path, storing it in the \Verb+prop+ for further retrieval.
-% \begin{macro}{\spath_generate_length:n}
-% Counts the number of triples in the path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_length:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \spath_put:nnx {#1} {length} {\int_eval:n {\tl_count:N \l__spath_tmpa_tl /3 }}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_reallength:n}
-% The real length of a path is the number of triples that actually draw something (that is, the number of lines and curves).
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_reallength:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \int_set:Nn \l__spath_tmpa_int {0}
-  \tl_map_inline:Nn \l__spath_tmpa_tl {
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@linetotoken}
-    {
-      \int_incr:N \l__spath_tmpa_int
-    }
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@curvetotoken}
-    {
-      \int_incr:N \l__spath_tmpa_int
-    }
-  }
-  \spath_put:nnx {#1} {real length} {\int_use:N \l__spath_tmpa_int}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_numberofcomponents:n}
-% A component is a continuous segment of the path, separated by moves.
-% Successive moves are not collapsed, and zero length moves count.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_numberofcomponents:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \int_set:Nn \l__spath_tmpa_int {0}
-  \tl_map_inline:Nn \l__spath_tmpa_tl {
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@movetotoken}
-    {
-      \int_incr:N \l__spath_tmpa_int
-    }
-  }
-  \spath_put:nnx {#1} {number of components} {\int_use:N \l__spath_tmpa_int}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_initialpoint:n}
-% The starting point of the path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_initialpoint:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  \spath_put:nnV {#1} {initial point} \l__spath_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_finalpoint:n}
-% The final point of the path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_finalpoint:n #1
-{
-  \tl_clear:N \l__spath_tmpb_tl
-  \spath_if_in:nnTF {#1} {reverse path}
-  {
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  }
-  {
-    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \tl_reverse:N \l__spath_tmpa_tl
-    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  }
-  \spath_put:nnV {#1} {final point} \l__spath_tmpb_tl    
-}
-\cs_generate_variant:Nn \spath_generate_finalpoint:n {V}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_reversepath:n}
-% This computes the reverse of the path.
-% TODO: handle closed paths, possibly rectangles.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_reversepath:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_left:Nx \l__spath_tmpb_tl
-  {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
-  }
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
-  }
-  {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nn \l__spath_tmpd_tl {}
-    \tl_case:NnF \l__spath_tmpc_tl
-    {
-      \g__spath_moveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl }
-      \g__spath_lineto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl }
-      \g__spath_curveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl }
-      \g__spath_curvetoa_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl }
-      \g__spath_curvetob_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl }
-    }
-    {
-      \tl_show:N \l__spath_tmpc_tl
-    }
-    \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_left:Nx \l__spath_tmpb_tl
-    {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
-    }
-  }
-  \tl_put_left:NV \l__spath_tmpb_tl \g__spath_moveto_tl
-  \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_initialaction:n}
-% This is the first thing that the path does (after the initial move).
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_initialaction:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_if_empty:NF \l__spath_tmpa_tl {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-  }
-  \spath_put:nnV {#1} {initial action} \l__spath_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_final action:n}
-% This is the last thing that the path does.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_finalaction:n #1
-{
-  \tl_clear:N \l__spath_tmpb_tl
-  \spath_if_in:nnTF {#1} {reverse path}
-  {
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  }
-  {
-    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \tl_reverse:N \l__spath_tmpa_tl
-  }
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_if_empty:NF \l__spath_tmpa_tl {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-  }
-  \tl_if_eq:NNT \l__spath_tmpa_tl \g__spath_curvetoa_tl
-  {
-    \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_curveto_tl
-  }
-  \spath_put:nnV {#1} {final action} \l__spath_tmpb_tl    
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_minbb:n}
-% This computes the minimum (bottom left) of the bounding box of the path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_minbb:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
-  }
-  {
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  }
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
-  {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
-  }
-  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_max bb:n}
-% This computes the maximum (top right) of the bounding box of the path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_generate_maxbb:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
-  }
-  {
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  }
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
-  {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
-  }
-  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_generate_all:n}
-% This function generates all of the data in one fell swoop.
-% By traversing the path just once it is quicker than doing each one individually.
-% However, it does need to store a lot of data as it goes.
-% \begin{itemize}
-% \item \Verb+\l__spath_rp_tl+ will hold the reversed path
-% \item \Verb+\l__spath_l_int+ will hold the length
-% \item \Verb+\l__spath_rl_int+ will hold the real length
-% \item \Verb+\l__spath_nc_int+ will hold the number of components
-% \item \Verb+\l__spath_ip_tl+ will hold the initial point
-% \item \Verb+\l__spath_fp_tl+ will hold the final point
-% \item \Verb+\l__spath_ia_tl+ will hold the initial action
-% \item \Verb+\l__spath_fa_tl+ will hold the final action
-% \item \Verb+\l__spath_minx_dim+ will hold the min x bb
-% \item \Verb+\l__spath_miny_dim+ will hold the min y bb
-% \item \Verb+\l__spath_maxx_dim+ will hold the max x bb
-% \item \Verb+\l__spath_maxy_dim+ will hold the max y bb
-% \end{itemize}
-%    \begin{macrocode}
-\tl_new:N \l__spath_rp_tl
-\int_new:N \l__spath_l_int
-\int_new:N \l__spath_rl_int
-\int_new:N \l__spath_nc_int
-\tl_new:N \l__spath_ip_tl
-\tl_new:N \l__spath_fp_tl
-\tl_new:N \l__spath_ia_tl
-\tl_new:N \l__spath_fa_tl
-\dim_new:N \l__spath_minx_dim
-\dim_new:N \l__spath_miny_dim
-\dim_new:N \l__spath_maxx_dim
-\dim_new:N \l__spath_maxy_dim
-
-\cs_new_nopar:Npn \spath_generate_all:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-
-  \tl_clear:N \l__spath_rp_tl
-  \int_set:Nn \l__spath_l_int {1}
-  \int_zero:N \l__spath_rl_int
-  \int_set:Nn \l__spath_nc_int {1}
-  \tl_clear:N \l__spath_ip_tl
-  \tl_clear:N \l__spath_fp_tl
-  \tl_clear:N \l__spath_ia_tl
-  \tl_clear:N \l__spath_fa_tl
-  \dim_zero:N \l__spath_minx_dim
-  \dim_zero:N \l__spath_miny_dim
-  \dim_zero:N \l__spath_maxx_dim
-  \dim_zero:N \l__spath_maxy_dim
-
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-  \tl_clear:N \l__spath_ip_tl
-  \tl_put_right:Nx \l__spath_ip_tl
-  {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
-  }
-
-  \dim_set_eq:NN \l__spath_minx_dim \l__spath_tmpa_dim
-  \dim_set_eq:NN \l__spath_miny_dim \l__spath_tmpb_dim
-  \dim_set_eq:NN \l__spath_maxx_dim \l__spath_tmpa_dim
-  \dim_set_eq:NN \l__spath_maxy_dim \l__spath_tmpb_dim
-
-  \tl_put_left:Nx \l__spath_rp_tl
-  {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
-  }
-
-  \tl_set:Nx \l__spath_ia_tl {\tl_head:N \l__spath_tmpa_tl}
-
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
-  }
-  {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nn \l__spath_tmpd_tl {}
-    \tl_set_eq:NN \l__spath_fa_tl \l__spath_tmpc_tl
-    \int_incr:N \l__spath_l_int
-
-    \tl_case:NnF \l__spath_tmpc_tl
-    {
-      \g__spath_moveto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl
-        \int_incr:N \l__spath_nc_int
-      }
-      \g__spath_lineto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl
-        \int_incr:N \l__spath_rl_int
-      }
-      \g__spath_curveto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl
-        \int_incr:N \l__spath_rl_int
-      }
-      \g__spath_curvetoa_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl
-      }
-      \g__spath_curvetob_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl
-      }
-    }
-    {
-      \tl_show:N \l__spath_tmpc_tl
-    }
-    \tl_put_left:NV \l__spath_rp_tl \l__spath_tmpd_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-    \dim_set:Nn \l__spath_minx_dim {\dim_min:nn { \l__spath_minx_dim} {\l__spath_tmpa_dim}}
-    \dim_set:Nn \l__spath_miny_dim {\dim_min:nn { \l__spath_miny_dim} {\l__spath_tmpb_dim}}
-    \dim_set:Nn \l__spath_maxx_dim {\dim_max:nn { \l__spath_maxx_dim} {\l__spath_tmpa_dim}}
-    \dim_set:Nn \l__spath_maxy_dim {\dim_max:nn { \l__spath_maxy_dim} {\l__spath_tmpb_dim}}
-
-    \tl_put_left:Nx \l__spath_rp_tl
-    {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
-    }
-
-    \tl_set:Nx \l__spath_fp_tl
-    {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
-    }
-
-  }
-
-  \tl_put_left:NV \l__spath_rp_tl \g__spath_moveto_tl
-
-  \spath_put:nnV {#1} {reverse path} \l__spath_rp_tl
-  \spath_put:nnV {#1} {length} \l__spath_l_int
-  \spath_put:nnV {#1} {real length} \l__spath_rl_int
-  \spath_put:nnV {#1} {number of components} \l__spath_nc_int
-  \spath_put:nnV {#1} {initial point} \l__spath_ip_tl
-  \spath_put:nnV {#1} {final point} \l__spath_fp_tl
-  \spath_put:nnV {#1} {initial action} \l__spath_ia_tl
-  \spath_put:nnV {#1} {final action} \l__spath_fa_tl
-
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
-  {
-    {\dim_use:N \l__spath_minx_dim}
-    {\dim_use:N \l__spath_miny_dim}
-  }
-  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
-
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
-  {
-    {\dim_use:N \l__spath_maxx_dim}
-    {\dim_use:N \l__spath_maxy_dim}
-  }
-  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
-
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Path Manipulation}
-%
-% \begin{macro}{\spath_translate:nnn}
-% Translates a path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_translate:nnn #1#2#3
-{
-  \tl_map_inline:Nn \g__spath_moveable_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
-  }
-  \tl_map_inline:Nn \g__spath_path_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
-      {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
-  }
-}
-
-\cs_generate_variant:Nn \spath_translate:nnn {nxx}
-%    \end{macrocode}
-%
-% This variant allows for passing the coordinates as a single braced group as it strips off the outer braces of the second argument.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_translate:nn #1#2
-{
-  \spath_translate:nnn {#1} #2
-}
-
-\cs_generate_variant:Nn \spath_translate:nn {nV}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_scale:nnn}
-% Scale a path.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_scale:nnn #1#2#3
-{
-  \tl_map_inline:Nn \g__spath_moveable_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-
-      \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\fp_to_dim:N \l__spath_tmpa_fp}
-        {\fp_to_dim:N \l__spath_tmpb_fp}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
-  }
-  \tl_map_inline:Nn \g__spath_path_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
-      {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        
-        \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\fp_to_dim:N \l__spath_tmpa_fp}
-          {\fp_to_dim:N \l__spath_tmpb_fp}
-        }
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
-  }
-}
-\cs_generate_variant:Nn \spath_scale:nnn {nxx}
-%    \end{macrocode}
-%
-% This variant allows for passing the coordinates as a single braced group as it strips off the outer braces of the second argument.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_scale:nn #1#2
-{
-  \spath_scale:nnn {#1} #2
-}
-
-\cs_generate_variant:Nn \spath_scale:nn {nV}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_transform:nnnnnnn}
-% Applies an affine (matrix and vector) transformation to path.
-% The matrix is specified in rows first.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_transform:nnnnnnn #1#2#3#4#5#6#7
-{
-  \tl_map_inline:Nn \g__spath_moveable_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
-      \fp_set:Nn \l__spath_tmpa_fp {\l__spath_tmpa_tl * #2 + \l__spath_tmpb_tl * #3 + #6}
-      \fp_set:Nn \l__spath_tmpb_fp {\l__spath_tmpa_tl * #4 + \l__spath_tmpb_tl * #5 + #7}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\fp_to_dim:N \l__spath_tmpa_fp}
-        {\fp_to_dim:N \l__spath_tmpb_fp}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
-  }
-  \tl_map_inline:Nn \g__spath_path_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
-      {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \fp_set:Nn \l__spath_tmpa_fp {\l_tmpa_tl * #2 + \l_tmpb_tl * #3 + #6}
-        \fp_set:Nn \l__spath_tmpb_fp {\l_tmpa_tl * #4 + \l_tmpb_tl * #5 + #7}
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\fp_to_dim:N \l__spath_tmpa_fp}
-          {\fp_to_dim:N \l__spath_tmpb_fp}
-        }
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
-  }
-}
-
-\cs_generate_variant:Nn \spath_transform:nnnnnnn {nxxxxxx}
-%    \end{macrocode}
-%
-% This variant allows for passing the coordinates as a single braced group as it strips off the outer braces of the second argument.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_transform:nn #1#2
-{
-  \spath_transform:nnnnnnn {#1} #2
-}
-
-\cs_generate_variant:Nn \spath_transform:nn {nV}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_reverse:n}
-% This reverses a path.
-% As a lot of the data is invariant under reversing, there isn't a lot to do.
-%     \begin{macrocode}
-\cs_new_nopar:Npn \spath_reverse:n #1
-{
-  \spath_if_in:nnF {#1} {reverse path} {
-    \use:c {spath_generate_reverse path:n} {#1}
-  }
-  \spath_swap:nnn {#1} {path} {reverse path}
-  \spath_swap:nnn {#1} {initial point} {final point}
-  \spath_swap:nnn {#1} {initial action} {final action}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_swap:nnn}
-% Swaps two entries, being careful to ensure that their existence (or otherwise) is preserved.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_swap:nnn #1#2#3
-{
-  \__spath_get:nnNF {#1} {#2} \l__spath_tmpa_tl {\tl_clear:N \l__spath_tmpa_tl}
-  \__spath_get:nnNF {#1} {#3} \l__spath_tmpb_tl {\tl_clear:N \l__spath_tmpb_tl}
-  \tl_if_empty:NTF \l__spath_tmpb_tl
-  {\spath_remove:nn {#1} {#2}}
-  {\spath_put:nnV {#1} {#2} \l__spath_tmpb_tl}
-  \tl_if_empty:NTF \l__spath_tmpa_tl
-  {\spath_remove:nn {#1} {#3}}
-  {\spath_put:nnV {#1} {#3} \l__spath_tmpa_tl}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_weld:nn}
-% This welds one path to another, moving the second so that it's initial point coincides with the first's final point.
-% It is called a \emph{weld} because the initial move of the second path is removed.
-% The first path is updated, the second is not modified.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_weld:nn #1#2
-{
-  \spath_clone:nn {#2} {tmp_path}
-  \spath_get:nnN {#1} {final point} \l__spath_tmpa_tl
-
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-  \spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
-
-  \dim_sub:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_sub:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-  \spath_translate:nxx {tmp_path} {\dim_use:N \l__spath_tmpa_dim} {\dim_use:N \l__spath_tmpb_dim}
-
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \__spath_get:nnN {tmp_path} {path} \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-
-  \__spath_get:nnNTF {tmp_path} {final point} \l__spath_tmpa_tl
-  {
-    \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
-  }
-  {
-    \spath_remove:nn {#1} {final point}
-  }
-
-  \__spath_get:nnNTF {tmp_path} {final action} \l__spath_tmpa_tl
-  {
-    \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
-  }
-  {
-    \spath_remove:nn {#1} {final action}
-  }
-
-  \__spath_get:nnNT {tmp_path} {min bb} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {min bb} \l__spath_tmpb_tl
-    {
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}
-      
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
-    }
-  }
-
-  \__spath_get:nnNT {tmp_path} {max bb} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {max bb} \l__spath_tmpb_tl
-    {
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}
-      
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
-    }
-  }
-  
-  \__spath_get:nnNT {tmp_path} {reverse path} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {reverse path} \l__spath_tmpb_tl
-    {
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
-    }
-  }
-
-  \__spath_get:nnNT {tmp_path} {length} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {length} \l__spath_tmpb_tl
-    {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
-      \spath_put:nnV {#1} {length} \l__spath_tmpa_int
-    }
-  }
-
-  \__spath_get:nnNT {tmp_path} {real length} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {real length} \l__spath_tmpb_tl
-    {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl}
-      \spath_put:nnV {#1} {real length} \l__spath_tmpa_int
-    }
-  }
-
-  \__spath_get:nnNT {tmp_path} {number of components} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {number of components} \l__spath_tmpb_tl
-    {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
-      \spath_put:nnV {#1} {number of components} \l__spath_tmpa_int
-    }
-  }
-  
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_prepend_no_move:nn}
-% Prepend the path from the second \Verb+spath+ to the first, removing
-% the adjoining move.  
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_prepend_no_move:nn #1#2
-{
-  \spath_if_exist:nT {#2}
-  {
-    \__spath_get:nnN {#2} {path} \l__spath_tmpa_tl
-    \__spath_get:nnN {#1} {path} \l__spath_tmpb_tl
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-
-    \spath_if_in:nnTF {#2} {initial point}
-    {
-      \__spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {initial point} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {initial point}
-    }
-
-    \spath_if_in:nnTF {#2} {initial action}
-    {
-      \__spath_get:nnN {#2} {initial action} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {initial action} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {initial action}
-    }
-
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {length}
-      &&
-      \spath_if_in_p:nn {#2} {length}
-    }
-    {
-      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
-    }
-    {
-      \spath_remove:nn {#1} {length}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {real length}
-      &&
-      \spath_if_in_p:nn {#2} {real length}
-    }
-    {
-      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl }}
-    }
-    {
-      \spath_remove:nn {#1} {real length}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {number of components}
-      &&
-      \spath_if_in_p:nn {#2} {number of components}
-    }
-    {
-      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
-    }
-    {
-      \spath_remove:nn {#1} {number of components}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {min bb}
-      &&
-      \spath_if_in_p:nn {#2} {min bb}
-    }
-    {
-      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {min bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-    }
-    {
-      \spath_remove:nn {#1} {min bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {max bb}
-      &&
-      \spath_if_in_p:nn {#2} {max bb}
-    }
-    {
-      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {max bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-    }
-    {
-      \spath_remove:nn {#1} {max bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {reverse path}
-      &&
-      \spath_if_in_p:nn {#2} {reverse path}
-    }
-    {
-      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpb_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
-    }
-    {
-      \spath_remove:nn {#1} {reverse path}
-    }
-
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_append_no_move:nn}
-% Append the path from the second \Verb+spath+ to the first, removing
-% the adjoining move.  
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_append_no_move:nn #1#2
-{
-  \spath_if_exist:nT {#2}
-  {
-    \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \spath_get:nnN {#2} {path} \l__spath_tmpb_tl
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-    \spath_if_in:nnTF {#2} {final point}
-    {
-      \__spath_get:nnN {#2} {final point} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {final point}
-    }
-    \spath_if_in:nnTF {#2} {final action}
-    {
-      \__spath_get:nnN {#2} {final action} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {final action}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {length}
-      &&
-      \spath_if_in_p:nn {#2} {length}
-    }
-    {
-      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
-    }
-    {
-      \spath_remove:nn {#1} {length}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {real length}
-      &&
-      \spath_if_in_p:nn {#2} {real length}
-    }
-    {
-      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl }}
-    }
-    {
-      \spath_remove:nn {#1} {real length}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {number of components}
-      &&
-      \spath_if_in_p:nn {#2} {number of components}
-    }
-    {
-      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
-    }
-    {
-      \spath_remove:nn {#1} {number of components}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {min bb}
-      &&
-      \spath_if_in_p:nn {#2} {min bb}
-    }
-    {
-      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {min bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-    }
-    {
-      \spath_remove:nn {#1} {min bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {max bb}
-      &&
-      \spath_if_in_p:nn {#2} {max bb}
-    }
-    {
-      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {max bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-    }
-    {
-      \spath_remove:nn {#1} {max bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {reverse path}
-      &&
-      \spath_if_in_p:nn {#2} {reverse path}
-    }
-    {
-      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpa_tl
-      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpb_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
-    }
-    {
-      \spath_remove:nn {#1} {reverse path}
-    }
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_bake_round:n}
-% Ought to clear the reverse path, if set.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_bake_round:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \pgf@@processround\l__spath_tmpa_tl\l__spath_tmpb_tl
-  \spath_put:nnV {#1} {path} \l__spath_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_close_path:n}
-% Appends a close path to the end of the path, and to the end of the reverse path.
-% For now, the point is the initial or final point (respectively).
-% To be future proof, it ought to be the point of the adjacent move to.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_close_path:n #1
-{
-  \spath_get:nnN {#1} {initial point} \l__spath_tmpb_tl
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-  \spath_if_in:nnT {#1} {reverse path}
-  {
-    \spath_get:nnN {#1} {final point} \l__spath_tmpb_tl
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Iteration Functions}
-%
-% \begin{macro}{\spath_map_component:Nn}
-% This iterates through the components of a path, applying the inline function to each.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_map_component:Nn #1#2
-{
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 {#2}
-  \tl_set:NV \l__spath_tmpa_tl #1
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
-  }
-  {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_if_eq:NNT \l__spath_tmpc_tl \g__spath_moveto_tl
-    {
-      \exp_args:NnV \use:c { __spath_map_ \int_use:N \g__spath_map_int :w } \l__spath_tmpb_tl
-\tl_clear:N \l__spath_tmpb_tl
-    }
-    \tl_if_single:NTF \l__spath_tmpc_tl
-    {
-      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
-    }
-    {
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\l__spath_tmpc_tl}}
-    }
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_map_segment_inline:Nn}
-% This iterates through the segments of the path, applying the inline function to each.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_map_segment_inline:Nn #1#2
-{
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 ##2 {#2}
-  \spath_map_segment_function:Nc #1 { __spath_map_ \int_use:N \g__spath_map_int :w }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_map_segment_inline:nn}
-% This iterates through the segments of the path of the \Verb+spath+ object, applying the inline function to each.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_map_segment_inline:nn #1#2
-{
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 ##2 {#2}
-  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
-  \spath_map_segment_function:Nc \l__spath_tmpd_tl { __spath_map_ \int_use:N \g__spath_map_int :w }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\spath_map_segment_function:nN}
-% This iterates through the segments of the path of the \Verb+spath+ object, applying the specified function to each.
-% The specified function should take two \Verb+N+ type arguments.
-% The first is a token representing the type of path segment, the second is the path segment itself.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_map_segment_function:nN #1#2
-{
-  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
-  \spath_map_segment_function:NN \l__spath_tmpd_tl #2
-}
-%    \end{macrocode}
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_map_segment_function:NN #1#2
-{
-  \tl_set_eq:NN \l__spath_tmpa_tl #1
-  \tl_clear:N \l__spath_tmpb_tl
-  \dim_zero:N \l__spath_tmpa_dim
-  \dim_zero:N \l__spath_tmpb_dim
-
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
-  }
-  {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_case:NnF \l__spath_tmpc_tl
-    {
-      \g__spath_lineto_tl
-      {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl
-
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-      }
-
-      \g__spath_curvetoa_tl
-      {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_curvetoa_tl
-
-        \prg_replicate:nn {2} {
-          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N               \l__spath_tmpa_tl}}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-          \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N             \l__spath_tmpa_tl}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        }
-
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-      }
-
-      \g__spath_closepath_tl
-      {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl
-
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-      }
-      
-    }    
-    {
-
-      \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpc_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      
-    }
-
-    #2 \l__spath_tmpc_tl \l__spath_tmpb_tl
-    \tl_clear:N \l__spath_tmpb_tl
-
-  }
-}
-\cs_generate_variant:Nn \spath_map_segment_function:NN {Nc}
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Public Commands}
-%
-% The next functions are more ``public'' than the previous lot.
-% That said, they aren't intended for direct use in a normal document.
-%
-% Most are just wrappers around internal functions.
-%
-% \begin{macro}{\MakeSPath}
-% Constructs an \Verb+spath+ object out of the given name and path.
-%    \begin{macrocode}
-\NewDocumentCommand \MakeSPath { m m }
-{
-  \spath_clear_new:n {#1}
-  \spath_put:nno {#1} {path} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\MakeSPathList}
-% This constructs a list of \Verb+spath+ objects from a single path by splitting it into components.
-%    \begin{macrocode}
-\NewDocumentCommand \MakeSPathList { m m }
-{
-  \tl_gclear_new:c {l__spath_list_#1}
-  \int_zero:N \l__spath_tmpa_int
-  \spath_map_component:Nn #2 {
-    \spath_clear_new:n {#1 _ \int_use:N \l__spath_tmpa_int}
-    \spath_put:nnn  {#1 _ \int_use:N \l__spath_tmpa_int} {path} {##1}
-    \tl_gput_right:cx {l__spath_list_#1} {{#1 _ \int_use:N \l__spath_tmpa_int}}
-    \int_incr:N \l__spath_tmpa_int
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\CloneSPath}
-%    \begin{macrocode}
-\NewDocumentCommand \CloneSPath { m m }
-{
-  \spath_clone:nn {#1} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathInfo}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathInfo { m m }
-{
-  \spath_get:nn {#1} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathPrepare}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathPrepare { m }
-{
-  \spath_generate_all:n {#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathListPrepare}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathListPrepare { m }
-{
-  \tl_map_inline:cn {l__spath_list_#1}
-  {
-    \spath_generate_all:n {##1}
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathInfoInto}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathInfoInto { m m m }
-{
-  \tl_clear_new:N #3
-  \spath_get:nnN {#1} {#2} #3
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathShow}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathShow { m }
-{
-  \spath_show:n {#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathTranslate}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathTranslate { m m m }
-{
-  \spath_translate:nnn {#1} {#2} {#3}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathTranslateInto}
-% Clones the path before translating it.
-%    \begin{macrocode}
-\NewDocumentCommand \SPathTranslateInto { m m m m }
-{
-  \spath_clone:nn {#1} {#2}
-  \spath_translate:nnn {#2} {#3} {#4}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathScale}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathScale { m m m }
-{
-  \spath_scale:nnn {#1} {#2} {#3}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathScaleInto}
-% Clones the path first.
-%    \begin{macrocode}
-\NewDocumentCommand \SPathScaleInto { m m m m }
-{
-  \spath_clone:nn {#1} {#2}
-  \spath_scale:nnn {#2} {#3} {#4}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathWeld}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathWeld { m m }
-{
-  \spath_weld:nn {#1} {#2}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\SPathWeldInto}
-%    \begin{macrocode}
-\NewDocumentCommand \SPathWeldInto { m m m }
-{
-  \spath_clone:nn {#1} {#2}
-  \spath_weld:nn {#2} {#3}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% Interfaces via TikZ keys.
-%     \begin{macrocode}
-\tikzset{
-  save~spath/.code={
-    \tikz@addmode{
-      \spath_get_current_path:n {#1}
-    }
-  },
-  restore~spath/.code={
-    \spath_set_current_path:n {#1}
-  }
-}
-%    \end{macrocode}
-% \subsection{Miscellaneous Commands}
-%
-% \begin{macro}{\spath_split_curve:nnNN}
-% Splits a Bezier cubic into pieces.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \spath_split_curve:nnNN #1#2#3#4
-{
-  \group_begin:
-  \tl_gclear:N \l__spath_smuggle_tl
-  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl {
-    {\tl_item:nn {#2} {2}}
-    {\tl_item:nn {#2} {3}}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {2} + (#1) * \tl_item:nn {#2} {5}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {3} + (#1) * \tl_item:nn {#2} {6}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {2} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {5} + (#1)^2 * \tl_item:nn {#2} {8}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {3} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {6} + (#1)^2 * \tl_item:nn {#2} {9}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
-      {
-      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
-    }}
-  }
-  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
-  \group_end:
-  \tl_set_eq:NN #3 \l__spath_smuggle_tl
-  \group_begin:
-  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
-      {
-      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {5} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {8} + (#1)^2 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {6} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {9} + (#1)^2 * \tl_item:nn {#2} {12}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {8} + (#1) * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {9} + (#1) * \tl_item:nn {#2} {12}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl {
-    {\tl_item:nn {#2} {11}}
-    {\tl_item:nn {#2} {12}}
-  }
-  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
-  \group_end:
-  \tl_set_eq:NN #4 \l__spath_smuggle_tl
-}
-
-\cs_generate_variant:Nn \spath_split_curve:nnNN {nVNN, VVNN}
-%    \end{macrocode}
-% \end{macro}
-% \iffalse
-%</spath3>
-% \fi
-%
-% \iffalse
-%<*calligraphy>
-% \fi
-%
-% \section{The Calligraphy Package}
-%
-% \subsection{Initialisation}
-%    \begin{macrocode}
-\RequirePackage{spath3}
-\ExplSyntaxOn
-
-\tl_new:N \l__cal_tmpa_tl
-\tl_new:N \l__cal_tmpb_tl
-\int_new:N \l__cal_tmpa_int
-\int_new:N \l__cal_tmpb_int
-\int_new:N \l__cal_path_component_int
-\int_new:N \l__cal_label_int
-\dim_new:N \l__cal_tmpa_dim
-\dim_new:N \l__cal_tmpb_dim
-\dim_new:N \l__cal_tmpc_dim
-\dim_new:N \l__cal_tmpd_dim
-\dim_new:N \l__cal_tmpe_dim
-\dim_new:N \l__cal_tmpf_dim
-\dim_new:N \l__cal_tmpg_dim
-\dim_new:N \l__cal_tmph_dim
-\bool_new:N \l__cal_annotate_bool
-\bool_new:N \l__cal_taper_start_bool
-\bool_new:N \l__cal_taper_end_bool
-\bool_new:N \l__cal_taperable_bool
-\dim_new:N \l__cal_taper_width_dim
-\dim_new:N \l__cal_line_width_dim
-
-\bool_set_true:N \l__cal_taper_start_bool
-\bool_set_true:N \l__cal_taper_end_bool
-
-\cs_generate_variant:Nn \tl_put_right:Nn {Nv}
-%    \end{macrocode}
-%
-% \subsection{TikZ Keys}
-%
-% The public interface to this package is through TikZ keys and styles.
-%    \begin{macrocode}
-\tikzset{
-  define~pen/.code={
-    \tikzset{pen~name=#1}
-    \pgf@relevantforpicturesizefalse
-    \tikz@addmode{
-      \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
-      \MakeSPathList{calligraphy pen \pgfkeysvalueof{/tikz/pen~name}}{\l__cal_tmpa_tl}
-      \SPathListPrepare{calligraphy pen \pgfkeysvalueof{/tikz/pen~name}}
-      \pgfusepath{discard}%
-    }
-  },
-  define~pen/.default={default},
-  use~pen/.code={
-    \tikzset{pen~name=#1}
-    \int_gzero:N \l__cal_path_component_int
-    \cs_set_eq:NN \pgfpathmoveto \cal_moveto:n
-    \tikz@addmode{
-      \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
-      \MakeSPathList{calligraphy path}{\l__cal_tmpa_tl}
-      \SPathListPrepare{calligraphy path}
-      \CalligraphyPathCreate{calligraphy path}{\pgfkeysvalueof{/tikz/pen~name}}
-    }
-  },
-  use~pen/.default={default},
-  pen~name/.initial={default},
-  copperplate/.style={pen~name=copperplate},
-  pen~colour/.initial={black},
-  weight/.is~choice,
-  weight/heavy/.style={
-    line~width=\pgfkeysvalueof{/tikz/heavy~line~width},
-    taper~width=\pgfkeysvalueof{/tikz/light~line~width},
-  },
-  weight/light/.style={
-    line~width=\pgfkeysvalueof{/tikz/light~line~width},
-    taper~width=0pt,
-  },
-  heavy/.style={
-    weight=heavy
-  },
-  light/.style={
-    weight=light
-  },
-  heavy~line~width/.initial=2pt,
-  light~line~width/.initial=1pt,
-  taper/.is~choice,
-  taper/.default=both,
-  taper/none/.style={
-    taper~start=false,
-    taper~end=false,
-  },
-  taper/both/.style={
-    taper~start=true,
-    taper~end=true,
-  },
-  taper/start/.style={
-    taper~start=true,
-    taper~end=false,
-  },
-  taper/end/.style={
-    taper~start=false,
-    taper~end=true,
-  },
-  taper~start/.code={
-    \tl_if_eq:nnTF {#1} {true}
-    {
-      \bool_set_true:N \l__cal_taper_start_bool
-    }
-    {
-      \bool_set_false:N \l__cal_taper_start_bool
-    }
-  },
-  taper~start/.default={true},
-  taper~end/.code={
-    \tl_if_eq:nnTF {#1} {true}
-    {
-      \bool_set_true:N \l__cal_taper_end_bool
-    }
-    {
-      \bool_set_false:N \l__cal_taper_end_bool
-    }
-  },
-  taper~end/.default={true},
-  taper~width/.code={\dim_set:Nn \l__cal_taper_width_dim {#1}},
-  nib~style/.code~2~args={
-    \tl_clear_new:c {l__cal_nib_style_#1}
-    \tl_set:cn {l__cal_nib_style_#1} {#2}
-  },
-  stroke~style/.code~2~args={
-    \tl_clear_new:c {l__cal_stroke_style_#1}
-    \tl_set:cn {l__cal_stroke_style_#1} {#2}
-  },
-  this~stroke~style/.code={
-    \tl_clear_new:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_path_component_int}
-    \tl_set:cn {l__cal_stroke_inline_style_ \int_use:N \l__cal_path_component_int} {#1}
-  },
-  annotate/.style={
-    annotate~if,
-    annotate~reset,
-    annotation~style/.update~value={#1},
-  },
-  annotate~if/.default={true},
-  annotate~if/.code={
-    \tl_if_eq:nnTF {#1} {true}
-    {
-      \bool_set_true:N \l__cal_annotate_bool
-    }
-    {
-      \bool_set_false:N \l__cal_annotate_bool
-    }
-  },
-  annotate~reset/.code={
-    \int_gzero:N \l__cal_label_int
-  },
-  annotation~style/.initial={draw,->},
-  annotation~shift/.initial={(0,1ex)},
-  every~annotation~node/.initial={anchor=south~west},
-  annotation~node~style/.code~2~args={
-    \tl_set:cn {l__cal_annotation_style_ #1 _tl}{#2}
-  },
-  tl~use:N/.code={
-    \exp_args:NV \pgfkeysalso #1
-  },
-  tl~use:c/.code={
-    \tl_if_exist:cT {#1}
-    {
-      \exp_args:Nv \pgfkeysalso {#1}
-    }
-  },
-  /handlers/.update~style/.code={
-    \tl_if_eq:nnF {#1} {\pgfkeysnovalue}
-    {
-      \pgfkeys{\pgfkeyscurrentpath/.code=\pgfkeysalso{#1}}
-    }
-  },
-  /handlers/.update~value/.code={
-    \tl_if_eq:nnF {#1} {\pgfkeysnovalue}
-    {
-      \pgfkeyssetvalue{\pgfkeyscurrentpath}{#1}
-    }
-  }
-}
-%    \end{macrocode}
-%
-% Some wrappers around the TikZ keys.
-%    \begin{macrocode}
-\NewDocumentCommand \pen { O{} }
-{
-  \path[define~ pen,every~ calligraphy~ pen/.try,#1]
-}
-
-\NewDocumentCommand \definepen { O{} }
-{
-  \tikz \path[define~ pen,every~ calligraphy~ pen/.try,#1]
-}
-
-\NewDocumentCommand \calligraphy { O{} }
-{
-  \path[use~ pen,every~ calligraphy/.try,#1]
-}
-%    \end{macrocode}
-%
-% \subsection{The Path Creation}
-%
-% \begin{macro}{\CalligraphyPathCreate}
-% This is the main command for creating the calligraphic paths.
-%    \begin{macrocode}
-\NewDocumentCommand \CalligraphyPathCreate { m m }
-{
-  \int_zero:N \l__cal_tmpa_int
-  \tl_map_inline:cn {l__spath_list_#1}
-  {
-    \int_incr:N \l__cal_tmpa_int
-    \int_zero:N \l__cal_tmpb_int
-    \tl_map_inline:cn {l__spath_list_calligraphy pen #2}
-    {
-      \int_incr:N \l__cal_tmpb_int
-      \group_begin:
-      \pgfsys@beginscope
-
-      \cal_apply_style:c {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-      \cal_apply_style:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-      \cal_apply_style:c {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-
-      \spath_clone:nn {##1} {calligraphy temp path}
-
-      \__spath_get:nnN {####1} {initial point} \l__cal_tmpa_tl
-      \spath_translate:nV {calligraphy temp path} \l__cal_tmpa_tl
-
-      \__spath_get:nnN {####1} {length} \l__cal_tmpa_tl
-      
-      \int_compare:nTF {\l__cal_tmpa_tl = 1}
-      {
-        \cal_at_least_three:n {calligraphy temp path}
-
-        \spath_protocol_path:n {calligraphy temp path}
-
-        \__spath_get:nnN {calligraphy temp path} {path} \l__cal_tmpa_tl
-
-        \tikz@options
-        \dim_set:Nn \l__cal_line_width_dim {\pgflinewidth}
-        \cal_maybe_taper:N \l__cal_tmpa_tl
-      }
-      {
-
-        \spath_weld:nn {calligraphy temp path} {####1}
-        \spath_reverse:n {##1}
-        \spath_reverse:n {####1}
-        \spath_weld:nn {calligraphy temp path} {##1}
-        \spath_weld:nn {calligraphy temp path} {####1}
-        \spath_reverse:n {##1}
-        \spath_reverse:n {####1}
-
-        \tl_clear:N \l__cal_tmpa_tl
-        \tl_set:Nn \l__cal_tmpa_tl {fill=\pgfkeysvalueof{/tikz/pen~colour},draw=none}
-        \tl_if_exist:cT  {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-        {
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-        }
-        \tl_if_exist:cT  {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-        {
-          \tl_put_right:Nn \l__cal_tmpa_tl {,}
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-        }
-        \tl_if_exist:cT  {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-        {
-          \tl_put_right:Nn \l__cal_tmpa_tl {,}
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-        }
-        \spath_tikz_path:Vn \l__cal_tmpa_tl {calligraphy temp path}
-
-      }
-      \pgfsys@endscope
-      \group_end:
-    }
-    \bool_if:NT \l__cal_annotate_bool
-    {
-      \spath_clone:nn {##1} {calligraphy temp path}
-      \tl_set_eq:Nc \l_tmpa_tl {l__spath_list_calligraphy pen #2}
-      \tl_reverse:N \l_tmpa_tl
-      \tl_set:Nx \l_tmpa_tl {\tl_head:N \l_tmpa_tl}
-      \spath_generate_finalpoint:V \l_tmpa_tl
-      \spath_get:VnN \l_tmpa_tl {final point} \l_tmpa_tl
-      \spath_translate:nV {calligraphy temp path} \l_tmpa_tl
-      \tikz@scan@one@point\pgfutil@firstofone\pgfkeysvalueof{/tikz/annotation~shift}
-      \spath_translate:nnn {calligraphy temp path} {\pgf@x} {\pgf@y}
-      
-      \pgfkeysgetvalue{/tikz/annotation~style}{\l_tmpa_tl}
-      \spath_tikz_path:Vn \l_tmpa_tl {calligraphy temp path}
-      \spath_get:nnN {calligraphy temp path} {final point} \l_tmpa_tl
-      \exp_last_unbraced:NV \pgfqpoint \l_tmpa_tl
-      \begin{scope}[reset~ cm]
-      \node[every~annotation~node/.try,tl~use:c =  {l__cal_annotation_style_ \int_use:N \l__cal_tmpa_int _tl}] at (\pgf@x,\pgf@y) {\int_use:N \l__cal_tmpa_int};
-      \end{scope}
-    }
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_moveto:n}
-% When creating the path, we need to keep track of the number of components so that we can apply styles accordingly.
-%    \begin{macrocode}
-\cs_new_eq:NN \cal_orig_moveto:n \pgfpathmoveto
-\cs_new_nopar:Npn \cal_moveto:n #1
-{
-  \int_gincr:N \l__cal_path_component_int
-  \cal_orig_moveto:n {#1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_apply_style:N}
-% Interface for applying \Verb+\tikzset+ to a token list.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_apply_style:N #1
-{
-  \tl_if_exist:NT #1 {
-    \exp_args:NV \tikzset #1
-  }
-}
-\cs_generate_variant:Nn \cal_apply_style:N {c}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_at_least_three:n}
-% A tapered path has to have at least three components.
-% This figures out if it is necessary and sets up the splitting.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_at_least_three:n #1
-{
-  \spath_get:nnN {#1} {real length} \l__cal_tmpa_tl
-  \tl_clear:N \l__cal_tmpb_tl
-  \int_compare:nTF {\l__cal_tmpa_tl = 1}
-  {
-    \spath_get:nnN {#1} {path} \l__cal_tmpa_tl
-    \spath_map_segment_inline:Nn \l__cal_tmpa_tl
-    {
-      \tl_case:NnF ##1 {
-        \g__spath_lineto_tl {
-          \cal_split_line_in_three:NN \l__cal_tmpb_tl ##2
-        }
-        \g__spath_curvetoa_tl {
-          \cal_split_curve_in_three:NN \l__cal_tmpb_tl ##2
-        }
-      }
-      {
-        \tl_put_right:NV \l__cal_tmpb_tl ##2
-      }
-    }
-    \spath_put:nnV {#1} {path} \l__cal_tmpb_tl
-  }
-  {
-    \int_compare:nT {\l__cal_tmpa_tl = 2}
-    {
-      \spath_get:nnN {#1} {path} \l__cal_tmpa_tl
-      \spath_map_segment_inline:Nn \l__cal_tmpa_tl
-      {
-        \tl_case:NnF ##1 {
-          \g__spath_lineto_tl {
-            \cal_split_line_in_two:NN \l__cal_tmpb_tl ##2
-          }
-          \g__spath_curvetoa_tl {
-            \cal_split_curve_in_two:NN \l__cal_tmpb_tl ##2
-          }
-        }
-        {
-          \tl_put_right:NV \l__cal_tmpb_tl ##2
-        }
-      }
-      \spath_put:nnV {#1} {path} \l__cal_tmpb_tl
-    }
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_split_line_in_two:NN}
-% Splits a line in two, adding the splits to the first token list.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_split_line_in_two:NN #1#2
-{
-  \tl_set_eq:NN \l__cal_tmpc_tl #2
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpa_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpb_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpc_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-  \dim_set:Nn \l__cal_tmpd_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(\l__cal_tmpa_dim + \l__cal_tmpc_dim)/2}}
-    {\dim_eval:n {(\l__cal_tmpb_dim + \l__cal_tmpd_dim)/2}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-  \tl_put_right:Nx #1 {
-    {\dim_use:N \l__cal_tmpc_dim}
-    {\dim_use:N \l__cal_tmpd_dim}
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_split_line_in_three:NN}
-% Splits a line in three, adding the splits to the first token list.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_split_line_in_three:NN #1#2
-{
-  \tl_set_eq:NN \l__cal_tmpc_tl #2
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpa_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpb_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpc_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-  \dim_set:Nn \l__cal_tmpd_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(2\l__cal_tmpa_dim + \l__cal_tmpc_dim)/3}}
-    {\dim_eval:n {(2\l__cal_tmpb_dim + \l__cal_tmpd_dim)/3}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(\l__cal_tmpa_dim + 2\l__cal_tmpc_dim)/3}}
-    {\dim_eval:n {(\l__cal_tmpb_dim + 2\l__cal_tmpd_dim)/3}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-  \tl_put_right:Nx #1 {
-    {\dim_use:N \l__cal_tmpc_dim}
-    {\dim_use:N \l__cal_tmpd_dim}
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_split_curve_in_two:NN}
-% Splits a curve in two, adding the splits to the first token list.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_split_curve_in_two:NN #1#2
-{
-  \spath_split_curve:nVNN {.5} #2 \l_tmpa_tl \l_tmpb_tl
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-  \tl_put_right:NV #1 \l_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_split_curve_in_three:NN}
-% Splits a curve in three, adding the splits to the first token list.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_split_curve_in_three:NN #1#2
-{
-  \spath_split_curve:nVNN {1/3} #2 \l_tmpa_tl \l_tmpb_tl
-
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-
-  \spath_split_curve:nVNN {.5} \l_tmpb_tl \l_tmpa_tl \l_tmpb_tl
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-  \tl_put_right:NV #1 \l_tmpb_tl
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\cal_maybe_taper:N}
-% Possibly tapers the path, depending on the booleans.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cal_maybe_taper:N #1
-{
-  \tl_set_eq:NN \l__cal_tmpa_tl #1
-
-  \bool_if:NT \l__cal_taper_start_bool
-  {
-
-    \dim_set:Nn \l__cal_tmpa_dim {\tl_item:Nn \l__cal_tmpa_tl {2}}
-    \dim_set:Nn \l__cal_tmpb_dim {\tl_item:Nn \l__cal_tmpa_tl {3}}
-    \tl_set:Nx \l__cal_tmpb_tl {\tl_item:Nn \l__cal_tmpa_tl {4}}
-
-    \tl_case:NnF \l__cal_tmpb_tl
-    {
-      \g__spath_lineto_tl
-      {
-
-        \bool_set_true:N \l__cal_taperable_bool
-        \dim_set:Nn \l__cal_tmpg_dim {\tl_item:Nn \l__cal_tmpa_tl {5}}
-        \dim_set:Nn \l__cal_tmph_dim {\tl_item:Nn \l__cal_tmpa_tl {6}}
-        \dim_set:Nn \l__cal_tmpc_dim {(2\l__cal_tmpa_dim + \l__cal_tmpg_dim)/3}
-        \dim_set:Nn \l__cal_tmpd_dim {(2\l__cal_tmpb_dim + \l__cal_tmph_dim)/3}
-        \dim_set:Nn \l__cal_tmpe_dim {(\l__cal_tmpa_dim + 2\l__cal_tmpg_dim)/3}
-        \dim_set:Nn \l__cal_tmpf_dim {(\l__cal_tmpb_dim + 2\l__cal_tmph_dim)/3}
-        \prg_replicate:nn {4}
-        {
-          \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
-        }
-        \tl_put_left:NV \l__cal_tmpa_tl \g__spath_moveto_tl
-      }
-      \g__spath_curvetoa_tl
-      {
-        \bool_set_true:N \l__cal_taperable_bool
-        \dim_set:Nn \l__cal_tmpc_dim {\tl_item:Nn \l__cal_tmpa_tl {5}}
-        \dim_set:Nn \l__cal_tmpd_dim {\tl_item:Nn \l__cal_tmpa_tl {6}}
-        \dim_set:Nn \l__cal_tmpe_dim {\tl_item:Nn \l__cal_tmpa_tl {8}}
-        \dim_set:Nn \l__cal_tmpf_dim {\tl_item:Nn \l__cal_tmpa_tl {9}}
-        \dim_set:Nn \l__cal_tmpg_dim {\tl_item:Nn \l__cal_tmpa_tl {11}}
-        \dim_set:Nn \l__cal_tmph_dim {\tl_item:Nn \l__cal_tmpa_tl {12}}
-        \prg_replicate:nn {10}
-        {
-          \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
-        }
-        \tl_put_left:NV \l__cal_tmpa_tl \g__spath_moveto_tl
-      }
-    }
-    {
-      \bool_set_false:N \l__cal_taperable_bool
-    }
-    
-    \bool_if:NT \l__cal_taperable_bool
-    {
-      \__cal_taper_aux:
-    }
-    
-  }
-
-  \bool_if:NT \l__cal_taper_end_bool
-  {
-
-    \dim_set:Nn \l__cal_tmpa_dim {\tl_item:Nn \l__cal_tmpa_tl {-2}}
-    \dim_set:Nn \l__cal_tmpb_dim {\tl_item:Nn \l__cal_tmpa_tl {-1}}
-    \tl_set:Nx \l__cal_tmpb_tl {\tl_item:Nn \l__cal_tmpa_tl {-3}}
-
-    \tl_case:NnF \l__cal_tmpb_tl
-    {
-      \g__spath_lineto_tl
-      {
-
-        \bool_set_true:N \l__cal_taperable_bool
-        \dim_set:Nn \l__cal_tmpg_dim {\tl_item:Nn \l__cal_tmpa_tl {-5}}
-        \dim_set:Nn \l__cal_tmph_dim {\tl_item:Nn \l__cal_tmpa_tl {-4}}
-        \dim_set:Nn \l__cal_tmpc_dim {(2\l__cal_tmpa_dim + \l__cal_tmpg_dim)/3}
-        \dim_set:Nn \l__cal_tmpd_dim {(2\l__cal_tmpb_dim + \l__cal_tmph_dim)/3}
-        \dim_set:Nn \l__cal_tmpe_dim {(\l__cal_tmpa_dim + 2\l__cal_tmpg_dim)/3}
-        \dim_set:Nn \l__cal_tmpf_dim {(\l__cal_tmpb_dim + 2\l__cal_tmph_dim)/3}
-        \tl_reverse:N \l__cal_tmpa_tl
-        \prg_replicate:nn {3}
-        {
-          \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
-        }
-        \tl_reverse:N \l__cal_tmpa_tl
-      }
-      \g__spath_curveto_tl
-      {
-        \bool_set_true:N \l__cal_taperable_bool
-        \dim_set:Nn \l__cal_tmpc_dim {\tl_item:Nn \l__cal_tmpa_tl {-5}}
-        \dim_set:Nn \l__cal_tmpd_dim {\tl_item:Nn \l__cal_tmpa_tl {-4}}
-        \dim_set:Nn \l__cal_tmpe_dim {\tl_item:Nn \l__cal_tmpa_tl {-8}}
-        \dim_set:Nn \l__cal_tmpf_dim {\tl_item:Nn \l__cal_tmpa_tl {-7}}
-        \dim_set:Nn \l__cal_tmpg_dim {\tl_item:Nn \l__cal_tmpa_tl {-11}}
-        \dim_set:Nn \l__cal_tmph_dim {\tl_item:Nn \l__cal_tmpa_tl {-10}}
-        \tl_reverse:N \l__cal_tmpa_tl
-        \prg_replicate:nn {9}
-        {
-          \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
-        }
-        \tl_reverse:N \l__cal_tmpa_tl
-      }
-    }
-    {
-      \bool_set_false:N \l__cal_taperable_bool
-    }
-    
-    \bool_if:NT \l__cal_taperable_bool
-    {
-      \__cal_taper_aux:
-    }
-    
-  }
-
-  \pgfsyssoftpath@setcurrentpath\l__cal_tmpa_tl
-  \pgfsetstrokecolor{\pgfkeysvalueof{/tikz/pen~colour}}
-  \pgfusepath{stroke}
-
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\__cal_taper_aux:}
-% Auxiliary macro to avoid unnecessary code duplication.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \__cal_taper_aux:
-{
-  \tl_clear:N \l__cal_tmpb_tl
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_moveto_tl
-
-  \fp_set:Nn \l__cal_tmpa_fp
-  {
-    \l__cal_tmpd_dim - \l__cal_tmpb_dim
-  }
-  \fp_set:Nn \l__cal_tmpb_fp
-  {
-    \l__cal_tmpa_dim - \l__cal_tmpc_dim
-  }
-  \fp_set:Nn \l__cal_tmpe_fp
-  {
-    (\l__cal_tmpa_fp^2 + \l__cal_tmpb_fp^2)^.5
-  }
-  
-  \fp_set:Nn \l__cal_tmpa_fp {.5*\l__cal_taper_width_dim *     \l__cal_tmpa_fp / \l__cal_tmpe_fp}
-  \fp_set:Nn \l__cal_tmpb_fp {.5*\l__cal_taper_width_dim *     \l__cal_tmpb_fp / \l__cal_tmpe_fp}
-
-  \fp_set:Nn \l__cal_tmpc_fp
-  {
-    \l__cal_tmph_dim - \l__cal_tmpf_dim
-  }
-  \fp_set:Nn \l__cal_tmpd_fp
-  {
-    \l__cal_tmpe_dim - \l__cal_tmpg_dim
-  }
-  \fp_set:Nn \l__cal_tmpe_fp
-  {
-    (\l__cal_tmpc_fp^2 + \l__cal_tmpd_fp^2)^.5
-  }
-
-  \fp_set:Nn \l__cal_tmpc_fp {.5*\l__cal_line_width_dim * \l__cal_tmpc_fp / \l__cal_tmpe_fp}
-  \fp_set:Nn \l__cal_tmpd_fp {.5*\l__cal_line_width_dim * \l__cal_tmpd_fp / \l__cal_tmpe_fp}
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp +             \l__cal_tmpb_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpc_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpd_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpe_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmpf_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
-  
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim - \fp_to_dim:n{ 1.32 * \l__cal_tmpd_fp}}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32* \l__cal_tmpc_fp}}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim - \fp_to_dim:n {1.32 * \l__cal_tmpd_fp}}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32 * \l__cal_tmpc_fp}}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpe_dim}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmpf_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpc_dim}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpd_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim + \fp_to_dim:n{ 1.32 * \l__cal_tmpb_fp}}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32* \l__cal_tmpa_fp}}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim + \fp_to_dim:n {1.32 * \l__cal_tmpb_fp}}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32 * \l__cal_tmpa_fp}}}
-  }
-
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
-
-  \tl_put_right:Nx \l__cal_tmpb_tl
-  {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp +             \l__cal_tmpb_dim}}
-  }
-
-  \pgfsyssoftpath@setcurrentpath\l__cal_tmpb_tl
-  \pgfsetfillcolor{\pgfkeysvalueof{/tikz/pen~colour}}
-  \pgfusepath{fill}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% Defines a copperplate pen.
-%    \begin{macrocode}
-\tl_set:Nn \l__cal_tmpa_tl {\pgfsyssoftpath@movetotoken{0pt}{0pt}}
-\MakeSPathList{calligraphy pen copperplate}{\l__cal_tmpa_tl}
-\SPathListPrepare{calligraphy pen copperplate}
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-\ExplSyntaxOff
-%    \end{macrocode}
-%
-% \subsection{Decorations}
-%
-% If a decoration library is loaded we define some decorations that use the calligraphy library, specifically the copperplate pen with its tapering.
-%
-% First, a brace decoration.
-%    \begin{macrocode}
-\expandafter\ifx\csname pgfdeclaredecoration\endcsname\relax
-\else
-\pgfdeclaredecoration{calligraphic brace}{brace}
-{
-  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
-  {
-    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
-    \pgfpathmoveto{\pgfpointorigin}
-    \pgfpathcurveto
-    {\pgfqpoint{.15\pgfdecorationsegmentamplitude}{.3\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-    {
-      \pgftransformxshift{+\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance}
-      \pgfpathlineto{\pgfqpoint{-\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{-.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{-.15\pgfdecorationsegmentamplitude}{.7\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{0\pgfdecorationsegmentamplitude}{1\pgfdecorationsegmentamplitude}}
-      \pgfpathmoveto{\pgfqpoint{0\pgfdecorationsegmentamplitude}{1\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{.15\pgfdecorationsegmentamplitude}{.7\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-    }
-    {
-      \pgftransformxshift{+\pgfdecoratedremainingdistance}
-      \pgfpathlineto{\pgfqpoint{-\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{-.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{-.15\pgfdecorationsegmentamplitude}{.3\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{0pt}{0pt}}
-    }
-    \tikzset{
-      taper width=.5\pgflinewidth,
-      taper
-    }%
-    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
-  }
-  \state{final}{}
-}
-%    \end{macrocode}
-%
-% The second is a straightened parenthesis (so that when very large it doesn't bow out too far).
-%    \begin{macrocode}
-\pgfdeclaredecoration{calligraphic straight parenthesis}{brace}
-{
-  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
-  {
-    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
-    \pgfpathmoveto{\pgfpointorigin}
-    \pgfpathcurveto
-    {\pgfqpoint{.76604\pgfdecorationsegmentamplitude}{.64279\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{2.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{3.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-    {
-      \pgftransformxshift{+\pgfdecoratedremainingdistance}
-      \pgfpathlineto{\pgfqpoint{-3.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{-2.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{-.76604\pgfdecorationsegmentamplitude}{.64279\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{0pt}{0pt}}
-    }
-    \tikzset{
-      taper width=.5\pgflinewidth,
-      taper
-    }%
-    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
-  }
-  \state{final}{}%
-}
-%    \end{macrocode}
-%
-% The third is a curved parenthesis.
-%    \begin{macrocode}
-\pgfdeclaredecoration{calligraphic curved parenthesis}{brace}
-{
-  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
-  {
-    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
-    \pgfpathmoveto{\pgfpointorigin}
-    \pgf@xa=\pgfdecoratedremainingdistance\relax
-    \advance\pgf@xa by -1.5890\pgfdecorationsegmentamplitude\relax
-    \edef\cgrphy@xa{\the\pgf@xa}
-    \pgfpathcurveto
-    {\pgfqpoint{1.5890\pgfdecorationsegmentamplitude}{1.3333\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{\cgrphy@xa}{1.3333\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{\pgfdecoratedremainingdistance}{0pt}}
-    \tikzset{
-      taper width=.5\pgflinewidth,
-      taper
-    }%
-    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
-  }
-  \state{final}{}%
-}
-%    \end{macrocode}
-% End the conditional for if pgfdecoration module is loaded
-%    \begin{macrocode}
-\fi
-%    \end{macrocode}
-% \iffalse
-%</calligraphy>
-% \fi
-% 
-%
-% \iffalse
-%<*knots>
-% \fi
-%%
-% \section{Drawing Knots}
-%
-%
-% \subsection{Initialisation}
-%
-% We load the \Verb+spath3+ library and the \Verb+intersections+ TikZ library.
-% Then we get going.
-%    \begin{macrocode}
-\RequirePackage{spath3}
-\usetikzlibrary{intersections}
-
-\ExplSyntaxOn
-
-\tl_new:N \l__knot_tmpa_tl
-\tl_new:N \l__knot_tmpb_tl
-\tl_new:N \l__knot_tmpc_tl
-\tl_new:N \l__knot_tmpd_tl
-\tl_new:N \l__knot_tmpe_tl
-\tl_new:N \l__knot_tmpf_tl
-\tl_new:N \l__knot_tmpg_tl
-\tl_new:N \l__knot_redraws_tl
-\tl_new:N \l__knot_clip_width_tl
-\tl_new:N \l__knot_name_tl
-\tl_new:N \l__knot_node_tl
-\tl_new:N \l__knot_aux_tl
-\tl_new:N \l__knot_auxa_tl
-
-\int_new:N \l__knot_tmpa_int
-\int_new:N \l__knot_strands_int
-\int_new:N \l__knot_intersections_int
-\int_new:N \l__knot_filaments_int
-\int_new:N \l__knot_component_start_int
-
-\dim_new:N \l__knot_tmpa_dim
-\dim_new:N \l__knot_tmpb_dim
-\dim_new:N \l__knot_tmpc_dim
-\dim_new:N \l__knot_tolerance_dim
-\dim_new:N \l__knot_clip_bg_radius_dim
-\dim_new:N \l__knot_clip_draw_radius_dim
-
-\bool_new:N \l__knot_draft_bool
-\bool_new:N \l__knot_ignore_ends_bool
-\bool_new:N \l__knot_self_intersections_bool
-\bool_new:N \l__knot_splits_bool
-\bool_new:N \l__knot_super_draft_bool
-
-\bool_new:N \l__knot_prepend_prev_bool
-\bool_new:N \l__knot_append_next_bool
-\bool_new:N \l__knot_skip_bool
-\bool_new:N \l__knot_save_bool
-
-\seq_new:N \l__knot_nodes_seq
-
-\bool_set_true:N \l__knot_ignore_ends_bool
-%    \end{macrocode}
-%
-% Configuration is via TikZ keys and styles.
-%    \begin{macrocode}
-\tikzset{
-  knot/.code={
-    \tl_if_eq:nnTF {#1} {none}
-    {
-      \tikz@addmode{\tikz@mode@doublefalse}
-    }
-    {
-      \tikz@addmode{\tikz@mode@doubletrue}
-      \tl_if_eq:nnTF {\pgfkeysnovalue} {#1}
-      {
-        \tikz@addoption{\pgfsetinnerstrokecolor{.}}
-      }
-      {
-        \pgfsetinnerstrokecolor{#1}
-      }
-      \tikz@addoption{
-        \pgfsetstrokecolor{knotbg}
-      }
-      \tl_set:Nn \tikz@double@setup{
-        \pgfsetinnerlinewidth{\pgflinewidth}
-        \pgfsetlinewidth{\dim_eval:n {\tl_use:N \l__knot_gap_tl \pgflinewidth}}
-      }
-    }
-  },
-  knot~ gap/.store~ in=\l__knot_gap_tl,
-  knot~ gap=3,
-  knot~ diagram/.is~family,
-  knot~ diagram/.unknown/.code={
-    \tl_set_eq:NN \l__knot_tmpa_tl \pgfkeyscurrentname
-    \pgfkeysalso{
-      /tikz/\l__knot_tmpa_tl=#1
-    }
-  },
-  background~ colour/.code={%
-    \colorlet{knotbg}{#1}%
-  },
-  background~ color/.code={%
-    \colorlet{knotbg}{#1}%
-  },
-  background~ colour=white,
-  knot~ diagram,
-  name/.store~ in=\l__knot_name_tl,
-  name={knot},
-  save~ intersections/.is~ choice,
-  save~ intersections/.default=true,
-  save~ intersections/true/.code={
-    \bool_set_true:N \l__knot_save_bool
-  },
-  save~ intersections/false/.code={
-    \bool_set_false:N \l__knot_save_bool
-  },
-  every~ strand/.style={draw},
-  ignore~ endpoint~ intersections/.code={
-    \tl_if_eq:nnTF {#1} {true}
-    {
-      \bool_set_true:N \l__knot_ignore_ends_bool
-    }
-    {
-      \bool_set_false:N \l__knot_ignore_ends_bool
-    }
-  },
-  ignore~ endpoint~ intersections/.default=true,
-  consider~ self~ intersections/.is~choice,
-  consider~ self~ intersections/true/.code={
-    \bool_set_true:N \l__knot_self_intersections_bool
-    \bool_set_true:N \l__knot_splits_bool
-  },
-  consider~ self~ intersections/false/.code={
-    \bool_set_false:N \l__knot_self_intersections_bool
-    \bool_set_false:N \l__knot_splits_bool
-  },
-  consider~ self~ intersections/no~ splits/.code={
-    \bool_set_true:N \l__knot_self_intersections_bool
-    \bool_set_false:N \l__knot_splits_bool
-  },
-  consider~ self~ intersections/.default={true},
-  clip~ radius/.code={
-    \dim_set:Nn \l__knot_clip_bg_radius_dim {#1}
-    \dim_set:Nn \l__knot_clip_draw_radius_dim {#1+2pt}
-  },
-  clip~ draw~ radius/.code={
-    \dim_set:Nn \l__knot_clip_draw_radius_dim {#1}
-  },
-  clip~ background~ radius/.code={
-    \dim_set:Nn \l__knot_clip_bg_radius_dim {#1}
-  },
-  clip~ radius=10pt,
-  end~ tolerance/.code={
-    \dim_set:Nn \l__knot_tolerance_dim {#1}
-  },
-  end~ tolerance=14pt,
-  clip/.style={
-    clip
-  },
-  background~ clip/.style={
-    clip
-  },
-  clip~ width/.code={
-    \tl_set:Nn \l__knot_clip_width_tl {#1}
-  },
-  clip~ width=3,
-  flip~ crossing/.code={%
-    \tl_clear_new:c {l__knot_crossing_#1}
-    \tl_set:cn {l__knot_crossing_#1} {x}
-  },
-  ignore~ crossing/.code={%
-    \tl_clear_new:c {l__knot_ignore_crossing_#1}
-    \tl_set:cn {l__knot_ignore_crossing_#1} {x}
-  },
-  draft~ mode/.is~ choice,
-  draft~ mode/off/.code={%
-    \bool_set_false:N \l__knot_draft_bool
-    \bool_set_false:N \l__knot_super_draft_bool
-  },
-  draft~ mode/crossings/.code={%
-    \bool_set_true:N \l__knot_draft_bool
-    \bool_set_false:N \l__knot_super_draft_bool
-  },
-  draft~ mode/strands/.code={%
-    \bool_set_true:N \l__knot_draft_bool
-    \bool_set_true:N \l__knot_super_draft_bool
-  },
-  draft/.is~ family,
-  draft,
-  crossing~ label/.style={
-    overlay,
-    fill=white,
-    fill~ opacity=.5,
-    text~ opacity=1,
-    text=blue,
-    pin~ edge={blue,<-}
-  },
-  strand~ label/.style={
-    overlay,
-    circle,
-    draw=purple,
-    fill=white,
-    fill~ opacity=.5,
-    text~ opacity=1,
-    text=purple,
-    inner~ sep=0pt
-  },
-}
-%    \end{macrocode}
-%
-% Wrapper around \Verb+\tikzset+ for applying keys from a token list, checking for if the given token list exists.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \knot_apply_style:N #1
-{
-  \tl_if_exist:NT #1 {
-    \exp_args:NV \tikzset #1
-  }
-}
-\cs_generate_variant:Nn \knot_apply_style:N {c}
-%    \end{macrocode}
-%
-%\begin{macro}{\flipcrossings}
-% The user can specify a comma separated list of crossings to flip.
-%    \begin{macrocode}
-\NewDocumentCommand \flipcrossings {m}
-{
-  \tikzset{knot~ diagram/flip~ crossing/.list={#1}}%
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\strand}
-% This is how the user specifies a strand of the knot.
-%    \begin{macrocode}
-\NewDocumentCommand \strand { O{} }
-{
-  \int_incr:N \l__knot_strands_int
-  \tl_clear_new:c {l__knot_options_strand \int_use:N \l__knot_strands_int}
-  \tl_set:cn {l__knot_options_strand \int_use:N \l__knot_strands_int} {#1}
-  \path[#1,save~ spath=knot strand \int_use:N  \l__knot_strands_int]
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{knot}
-% This is the wrapper environment that calls the knot generation code.
-%    \begin{macrocode}
-\NewDocumentEnvironment{knot} { O{} }
-{
-  \knot_initialise:n {#1}
-}
-{
-  \knot_render:
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_initialise:n}
-% Set up some stuff before loading in the strands.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_initialise:n #1
-{
-  \tikzset{knot~ diagram/.cd,every~ knot~ diagram/.try,#1}
-  \int_zero:N \l__knot_strands_int
-  \tl_clear:N \l__knot_redraws_tl
-  \seq_gclear:N \l__knot_nodes_seq
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_render:}
-% This is the code that starts the work of rendering the knot.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_render:
-{
-%    \end{macrocode}
-% Start a scope and reset the transformation (since all transformations have already been taken into account when defining the strands).
-%    \begin{macrocode}
-  \pgfscope
-  \pgftransformreset
-%    \end{macrocode}
-% Loop through the strands drawing each one for the first time.
-%    \begin{macrocode}
-  \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_draw_strand:n
-%    \end{macrocode}
-% In super draft mode we don't do anything else.
-%    \begin{macrocode} 
-  \bool_if:NF \l__knot_super_draft_bool
-  {
-%    \end{macrocode}
-% In draft mode we draw labels at the ends of the strands; this also handles splitting curves to avoid self-intersections of Bezier curves if that's requested.
-%    \begin{macrocode}
-    \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_draw_labels:n
-%    \end{macrocode}
-% If we're considering self intersections we need to split the strands into filaments.
-%    \begin{macrocode}
-    \bool_if:NTF \l__knot_self_intersections_bool
-    {
-      \knot_split_strands:
-      \int_set_eq:NN \l__knot_tmpa_int \l__knot_filaments_int
-      \tl_set:Nn \l__knot_prefix_tl {filament}
-    }
-    {
-      \int_set_eq:NN \l__knot_tmpa_int \l__knot_strands_int
-      \tl_set:Nn \l__knot_prefix_tl {strand}
-    }
-%    \end{macrocode}
-% Initialise the intersection count.
-%    \begin{macrocode}
-    \int_gzero:N \l__knot_intersections_int
-%    \end{macrocode}
-% If in draft mode we label the intersections, otherwise we just stick a coordinate at each one.
-%    \begin{macrocode}
-    \bool_if:NTF \l__knot_draft_bool
-    {
-      \tl_set:Nn \l__knot_node_tl {
-        \exp_not:N \node[coordinate,
-          pin={[node~ contents={\int_use:N \l__knot_intersections_int},knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \l__knot_intersections_int \c_space_tl label/.try]
-            }]
-      }
-    }
-    {
-      \tl_set:Nn \l__knot_node_tl {\exp_not:N \node[coordinate]}
-    }
-%    \end{macrocode}
-% This double loop steps through the pieces (strands or filaments) and computes the intersections and does stuff with those.
-%    \begin{macrocode}
-    \int_step_variable:nnnNn {1} {1} {\l__knot_tmpa_int - 1} \l__knot_tmpa_tl
-    {
-      \int_step_variable:nnnNn {\tl_use:N \l__knot_tmpa_tl + 1} {1}     {\l__knot_tmpa_int} \l__knot_tmpb_tl
-      {
-        \knot_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
-      }
-    }
-%    \end{macrocode}
-% If any redraws were requested, do them here.
-%    \begin{macrocode}
-    \tl_use:N \l__knot_redraws_tl
-%    \end{macrocode}
-% Draw the crossing nodes
-%    \begin{macrocode}
-    \seq_use:Nn \l__knot_nodes_seq {}
-  }
-%    \end{macrocode}
-% Close the scope
-%    \begin{macrocode}
-  \endpgfscope
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_draw_strand:n}
-% This renders a strand using the options originally specified.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_draw_strand:n #1
-{
-  \pgfscope
-  \group_begin:
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_strand #1}
-  \tl_put_right:Nn \l_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
-  \spath_bake_round:n {knot strand #1}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot strand #1}
-  \group_end:
-  \endpgfscope
-}
-\cs_generate_variant:Nn \tl_put_right:Nn {Nv}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_draw_labels:n}
-% Draw a label at each end of each strand, if in draft mode.
-% Also, if requested, split potentially self intersecting Bezier curves.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_draw_labels:n #1
-{
-  \bool_if:NT \l__knot_draft_bool
-  {
-    \spath_get:nnN {knot strand #1} {final point} \l__knot_tmpb_tl
-    \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}}
-    \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}}
-    \node[knot~ diagram/draft/strand~label] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
-    \spath_get:nnN {knot strand #1} {initial point} \l__knot_tmpb_tl
-    \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}}
-    \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}}
-    \node[knot~ diagram/draft/strand~label] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
-  }
-  \bool_if:nT {
-    \l__knot_self_intersections_bool
-    &&
-    \l__knot_splits_bool
-  }
-  {
-    \tl_clear:N \l__knot_tmpa_tl
-    \spath_map_segment_function:nN {knot strand #1} \knot_split_self_intersects:NN
-    \spath_put:nnV {knot strand #1} {path} \l__knot_tmpa_tl
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_split_self_intersects:NN}
-% This is the macro that does the split.
-% Figuring out whether a Bezier cubic self intersects is apparently a difficult problem so we don't bother.
-% We compute a point such that if there is an intersection then it lies on either side of the point.
-% I don't recall where the formula came from!
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_split_self_intersects:NN #1#2
-{
-  \tl_case:NnF #1
-  {
-    \g__spath_curvetoa_tl
-    {
-      \fp_set:Nn \l_tmpa_fp
-      {
-        (\tl_item:Nn #2 {3} - 3 * \tl_item:Nn #2 {6} + 3 * \tl_item:Nn #2 {9} - \tl_item:Nn #2 {12})
-        *
-        (3 * \tl_item:Nn #2 {8} - 3 * \tl_item:Nn #2 {11})
-        -
-        (\tl_item:Nn #2 {2} - 3 * \tl_item:Nn #2 {5} + 3 * \tl_item:Nn #2 {8} - \tl_item:Nn #2 {11})
-        *
-        (3 * \tl_item:Nn #2 {9} - 3 * \tl_item:Nn #2 {12})
-      }
-      \fp_set:Nn \l_tmpb_fp
-      {
-        (\tl_item:Nn #2 {2} - 3 * \tl_item:Nn #2 {5} + 3 * \tl_item:Nn #2 {8} - \tl_item:Nn #2 {11})
-        *
-        (3 * \tl_item:Nn #2 {6} - 6 * \tl_item:Nn #2 {9} + 3 * \tl_item:Nn #2 {12})
-        -
-        (\tl_item:Nn #2 {3} - 3 * \tl_item:Nn #2 {6} + 3 * \tl_item:Nn #2 {9} - \tl_item:Nn #2 {12})
-        *
-        (3 * \tl_item:Nn #2 {5} - 6 * \tl_item:Nn #2 {8} + 3 * \tl_item:Nn #2 {11})
-      }
-      \fp_compare:nTF
-      {
-        \l_tmpb_fp != 0
-      }
-      {
-        \fp_set:Nn \l_tmpa_fp {.5 * \l_tmpa_fp / \l_tmpb_fp}
-        \fp_compare:nTF
-        {
-          0 < \l_tmpa_fp && \l_tmpa_fp < 1
-        }
-        {
-          \spath_split_curve:VVNN \l_tmpa_fp #2 \l_tmpa_tl \l_tmpb_tl
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpb_tl
-        }
-        {
-          \tl_set_eq:NN \l_tmpa_tl #2
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
-        }
-      }
-      {
-        \tl_set_eq:NN \l_tmpa_tl #2
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
-      }
-    }
-    \g__spath_lineto_tl
-    {
-      \tl_set_eq:NN \l_tmpa_tl #2
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
-    }
-  }
-  {
-    \tl_put_right:NV \l__knot_tmpa_tl #2
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_intersections:nn}
-% This computes the intersections of two pieces and steps through them.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_intersections:nn #1#2
-{
-  \group_begin:
-  \tl_set_eq:NN \l__knot_tmpa_tl \l__knot_prefix_tl
-  \tl_put_right:Nn \l__knot_tmpa_tl {#1}
-  \tl_set_eq:NN \l__knot_tmpb_tl \l__knot_prefix_tl
-  \tl_put_right:Nn \l__knot_tmpb_tl {#2}
-  \spath_get:nnN {knot \tl_use:N \l__knot_tmpa_tl} {path} \l__knot_tmpc_tl
-  \spath_get:nnN {knot \tl_use:N \l__knot_tmpb_tl} {path} \l__knot_tmpd_tl
-
-  \bool_if:nTF {
-    \l__knot_save_bool
-    &&
-    \tl_if_exist_p:c {knot~ intersections~ \tl_use:N \l__knot_name_tl - \tl_use:N \l__knot_tmpa_tl -  \tl_use:N \l__knot_tmpb_tl}
-  }
-  {
-    \tl_use:c {knot~ intersections~ \tl_use:N \l__knot_name_tl - \tl_use:N \l__knot_tmpa_tl -  \tl_use:N \l__knot_tmpb_tl}
-  }
-  {
-\pgfintersectionofpaths{\pgfsetpath\l__knot_tmpc_tl}{\pgfsetpath\l__knot_tmpd_tl}
-
-  }
-  \int_compare:nT {\pgfintersectionsolutions > 0}
-  {
-    \int_step_function:nnnN {1} {1} {\pgfintersectionsolutions} \knot_do_intersection:n
-  }
-  \knot_save_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
-  \group_end:
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_save_intersections:nn}
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_save_intersections:nn #1#2
-{
-  \bool_if:NT \l__knot_save_bool
-  {
-    \tl_clear:N \l__knot_aux_tl
-    \tl_put_right:Nn \l__knot_aux_tl
-    {
-      \def\pgfintersectionsolutions
-    }
-    \tl_put_right:Nx \l__knot_aux_tl
-    {
-      {\int_eval:n {\pgfintersectionsolutions}}
-    }
-    \int_compare:nT {\pgfintersectionsolutions > 0}
-    {
-      \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
-      {
-        \pgfpointintersectionsolution{##1}
-        \dim_set:Nn \l__knot_tmpa_dim {\pgf@x}
-        \dim_set:Nn \l__knot_tmpb_dim {\pgf@y}
-        \tl_put_right:Nn \l__knot_aux_tl
-        {
-          \expandafter\def\csname pgfpoint@intersect@solution@##1\endcsname
-        }
-        \tl_put_right:Nx \l__knot_aux_tl
-        {
-          {\exp_not:N \pgf@x=\dim_use:N \l__knot_tmpa_dim\exp_not:N\relax\exp_not:N \pgf@y =\dim_use:N \l__knot_tmpb_dim\relax}
-        }
-      }
-      \tl_set:Nn \l__knot_auxa_tl {\expandafter \gdef \csname knot~ intersections~}
-      \tl_put_right:Nx \l__knot_auxa_tl {\tl_use:N \l__knot_name_tl - #1 - #2}
-      \tl_put_right:Nn \l__knot_auxa_tl {\endcsname}
-      \tl_put_right:Nx \l__knot_auxa_tl {{\tl_to_str:N \l__knot_aux_tl}}
-      \protected@write\@auxout{}{\tl_to_str:N \l__knot_auxa_tl}
-    }
-  }
-}
-\cs_generate_variant:Nn \knot_save_intersections:nn {VV}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_do_intersection:n}
-% This handles a specific intersection.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_do_intersection:n #1
-{
-%    \end{macrocode}
-% Get the intersection coordinates.
-%    \begin{macrocode}
-  \pgfpointintersectionsolution{#1}
-  \dim_set:Nn \l__knot_tmpa_dim {\pgf@x}
-  \dim_set:Nn \l__knot_tmpb_dim {\pgf@y}
-%    \end{macrocode}
-% If we're dealing with filaments, we can get false positives from the end points.
-%    \begin{macrocode}
-  \bool_set_false:N \l__knot_skip_bool
-  \bool_if:NT \l__knot_self_intersections_bool
-  {
-%    \end{macrocode}
-% If one filament preceded the other, test for the intersection being at the relevant end point.
-%    \begin{macrocode}
-    \tl_set:Nn \l_tmpa_tl {knot previous}
-    \tl_put_right:NV \l_tmpa_tl \l__knot_tmpa_tl
-    \tl_set:Nv \l_tmpa_tl \l_tmpa_tl
-    \tl_if_eq:NNT \l_tmpa_tl \l__knot_tmpb_tl
-    {
-      \knot_test_endpoint:VnT \l__knot_tmpb_tl {final point}
-      {
-        \bool_set_true:N \l__knot_skip_bool
-      }
-    }
-
-    \tl_set:Nn \l_tmpa_tl {knot previous}
-    \tl_put_right:NV \l_tmpa_tl \l__knot_tmpb_tl
-    \tl_set:Nv \l_tmpa_tl \l_tmpa_tl
-    \tl_if_eq:NNT \l_tmpa_tl \l__knot_tmpa_tl
-    {
-      \knot_test_endpoint:VnT \l__knot_tmpa_tl {final point}
-      {
-        \bool_set_true:N \l__knot_skip_bool
-      }
-    }
-  }
-%    \end{macrocode}
-% The user can also say that end points of filaments (or strands) should simply be ignored anyway.
-%    \begin{macrocode}
-  \bool_if:NT \l__knot_ignore_ends_bool
-  {
-    \knot_test_endpoint:VnT \l__knot_tmpa_tl {initial point}
-    {
-      \bool_set_true:N \l__knot_skip_bool
-    }
-    \knot_test_endpoint:VnT \l__knot_tmpa_tl {final point}
-    {
-      \bool_set_true:N \l__knot_skip_bool
-    }
-    \knot_test_endpoint:VnT \l__knot_tmpb_tl {initial point}
-    {
-      \bool_set_true:N \l__knot_skip_bool
-    }
-    \knot_test_endpoint:VnT \l__knot_tmpb_tl {final point}
-    {
-      \bool_set_true:N \l__knot_skip_bool
-    }
-  }
-%    \end{macrocode}
-% Assuming that we passed all the above tests, we render the crossing.
-%    \begin{macrocode}
-  \bool_if:NF \l__knot_skip_bool
-  {
-
-    \int_gincr:N \l__knot_intersections_int
-%    \end{macrocode}
-% This is the intersection test.
-% If the intersection finder finds too many, it might be useful to ignore some.
-%    \begin{macrocode}
-    \bool_if:nF
-    {
-      \tl_if_exist_p:c {l__knot_ignore_crossing_ \int_use:N
-        \l__knot_intersections_int}
-      &&
-      ! \tl_if_empty_p:c {l__knot_ignore_crossing_ \int_use:N
-        \l__knot_intersections_int}
-    }
-    {
-%    \end{macrocode}
-% This is the flip test.
-% We only render one of the paths.
-% The ``flip'' swaps which one we render.
-%    \begin{macrocode}
-      \bool_if:nTF
-      {
-        \tl_if_exist_p:c {l__knot_crossing_ \int_use:N
-          \l__knot_intersections_int}
-        &&
-        ! \tl_if_empty_p:c {l__knot_crossing_ \int_use:N
-          \l__knot_intersections_int}
-      }
-      {
-        \tl_set_eq:NN \l__knot_tmpg_tl \l__knot_tmpb_tl
-      }
-      {
-        \tl_set_eq:NN \l__knot_tmpg_tl \l__knot_tmpa_tl
-      }
-%    \end{macrocode}
-% Now we know which one we're rendering, we test to see if we should also render its predecessor or successor to ensure that we render a path through the entire crossing region.
-%    \begin{macrocode} 
-      \bool_if:NT \l__knot_self_intersections_bool
-      {
-        \knot_test_endpoint:VnT \l__knot_tmpg_tl {initial point}
-        {
-          \bool_set_true:N \l__knot_prepend_prev_bool
-        }
-        {
-          \bool_set_false:N \l__knot_prepend_prev_bool
-        }
-        \knot_test_endpoint:VnT \l__knot_tmpg_tl {final point}
-        {
-          \bool_set_true:N \l__knot_append_next_bool
-        }
-        {
-          \bool_set_false:N \l__knot_append_next_bool
-        }
-%    \end{macrocode}
-% If either of those tests succeeded, do the appending or prepending.
-%    \begin{macrocode}
-        \bool_if:nT
-        {
-          \l__knot_prepend_prev_bool || \l__knot_append_next_bool
-        }
-        {
-          \spath_clone:nn {knot \tl_use:N \l__knot_tmpg_tl}
-          {knot \tl_use:N \l__knot_prefix_tl -1}
-
-          \tl_set_eq:cc {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1} {l__knot_options_ \tl_use:N \l__knot_tmpg_tl}
-
-          \bool_if:nT
-          {
-            \l__knot_prepend_prev_bool
-            &&
-            \tl_if_exist_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
-            &&
-            !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
-          }
-          {
-            \spath_prepend_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}
-%    \end{macrocode}
-% If we split potentially self intersecting curves, we test to see if we should prepend yet another segment.
-%    \begin{macrocode}
-            \bool_if:nT
-            {
-              \l__knot_splits_bool
-              &&
-              \tl_if_exist_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
-              &&
-              !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
-            }
-            {
-              \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {initial point}
-              {
-                \spath_get:nnN {knot \tl_use:N \l__knot_prefix_tl -1} {path} \l_tmpa_tl
-                \spath_prepend_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}}
-                \spath_get:nnN {knot \tl_use:N \l__knot_prefix_tl -1} {path} \l_tmpa_tl
-              
-              }
-            }
-          }
-%    \end{macrocode}
-% Now the same for appending.
-%    \begin{macrocode}
-          \bool_if:nT
-          {
-            \l__knot_append_next_bool
-            &&
-            \tl_if_exist_p:c {knot next \tl_use:N \l__knot_tmpg_tl}
-            &&
-            !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
-          }
-          {
-            \spath_append_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}
-            \bool_if:nT
-            {
-              \l__knot_splits_bool
-              &&
-              \tl_if_exist_p:c {knot previous \tl_use:N
-                \l__knot_tmpg_tl}
-              &&
-              !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
-            }
-            {
-              \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {final point}
-              {
-                \spath_append_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}}
-                
-              }
-            }
-          }
-
-          \tl_set:Nn \l__knot_tmpg_tl {\tl_use:N \l__knot_prefix_tl -1}
-        }
-      }
-%    \end{macrocode}
-% Now we render the crossing.
-%    \begin{macrocode}
-      \pgfscope
-      \group_begin:
-      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \l__knot_intersections_int/.try}
-      \knot_draw_crossing:nVV {\tl_use:N \l__knot_tmpg_tl} \l__knot_tmpa_dim \l__knot_tmpb_dim
-      \group_end:
-      \endpgfscope
-%    \end{macrocode}
-% This ends the boolean as to whether to consider the intersection at all      
-%    \begin{macrocode}
-    }
-%    \end{macrocode}
-% And stick a coordinate possibly with a label at the crossing.
-%    \begin{macrocode}
-    \seq_gpush:Nx \l__knot_nodes_seq { \l__knot_node_tl (\l__knot_name_tl \c_space_tl \int_use:N \l__knot_intersections_int) at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim) {};}
-
-  }
-}
-
-\cs_generate_variant:Nn \knot_intersections:nn {VV}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_test_endpoint:N}
-% Test whether the point is near the intersection point.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \knot_test_endpoint:N #1 {p,T,F,TF}
-{
-  \dim_compare:nTF
-  {
-    \dim_abs:n { \l__knot_tmpa_dim - \tl_item:Nn #1 {1}}
-    +
-    \dim_abs:n { \l__knot_tmpb_dim - \tl_item:Nn #1 {2}}
-    <
-    \l__knot_tolerance_dim
-  }
-  {
-    \prg_return_true:
-  }
-  {
-    \prg_return_false:
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_test_endpoint:nn}
-% Wrapper around the above.
-%    \begin{macrocode}
-\prg_new_protected_conditional:Npnn \knot_test_endpoint:nn #1#2 {T,F,TF}
-{
-  \spath_get:nnN {knot #1} {#2} \l__knot_tmpd_tl
-  \knot_test_endpoint:NTF \l__knot_tmpd_tl
-  {
-    \prg_return_true:
-  }
-  {
-    \prg_return_false:
-  }
-}
-
-\cs_generate_variant:Nn \knot_test_endpoint:nnT {VnT,vnT}
-\cs_generate_variant:Nn \knot_test_endpoint:nnF {VnF,vnF}
-\cs_generate_variant:Nn \knot_test_endpoint:nnTF {VnTF,vnTF}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_draw_crossing:nnn}
-% This is the code that actually renders a crossing.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \knot_draw_crossing:nnn #1#2#3
-{
-  \group_begin:
-  \pgfscope
-  \path[knot~ diagram/background~ clip] (#2, #3) circle[radius=\l__knot_clip_bg_radius_dim];
-
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
-  \tl_if_exist:cT {l__knot_options_ #1}
-  {
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_ #1}
-  }
-  \tl_put_right:Nn \l_tmpa_tl {,knotbg,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot #1}
-
-  \endpgfscope
-
-  \pgfscope
-  \path[knot~ diagram/clip] (#2, #3) circle[radius=\l__knot_clip_draw_radius_dim];
-
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
-  \tl_if_exist:cT {l__knot_options_ #1}
-  {
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_ #1}
-  }
-  \tl_put_right:Nn \l_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot #1}
-
-  \endpgfscope
-  \group_end:
-}
-
-\cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV}
-
-\cs_new_nopar:Npn \knot_draw_crossing:nn #1#2
-{
-  \tikz@scan@one@point\pgfutil@firstofone #2 \relax
-  \knot_draw_crossing:nVV {#1} \pgf@x \pgf@y
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_split_strands:}
-% This, and the following macros, are for splitting strands into filaments.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_split_strands:
-{
-  \int_gzero:N \l__knot_filaments_int
-  \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_split_strand:n
-  \int_step_function:nnnN {1} {1} {\l__knot_filaments_int} \knot_compute_nexts:n
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_compute_nexts:n}
-% Each filament needs to know its predecessor and successor.
-% We work out the predecessors as we go along, this fills in the successors.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_compute_nexts:n #1
-{
-  \tl_clear_new:c {knot next \tl_use:c {knot previous filament #1}}
-  \tl_set:cn {knot next \tl_use:c {knot previous filament #1}} {filament #1}
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_split_strand:n}
-% Sets up the split for a single strand.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_split_strand:n #1
-{
-  \int_set_eq:NN \l__knot_component_start_int \l__knot_filaments_int
-  \int_incr:N \l__knot_component_start_int
-  \tl_set_eq:Nc \l__knot_tmpa_tl {l__knot_options_strand #1}
-  \spath_map_segment_function:nN {knot strand #1} \knot_save_filament:NN
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\knot_save_filament:NN}
-% Saves a filament as a new \Verb+spath+ object.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \knot_save_filament:NN #1#2
-{
-  \tl_case:NnF #1
-  {
-    \g__spath_moveto_tl
-    {
-      \int_compare:nT {\l__knot_component_start_int < \l__knot_filaments_int}
-      {
-        \int_set_eq:NN \l__knot_component_start_int \l__knot_filaments_int
-      }
-    }
-    \g__spath_lineto_tl
-    {
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} #2
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
-
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
-      {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
-      }
-    }
-    \g__spath_curvetoa_tl
-    {
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} #2
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
-
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
-      {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
-      }
-    }
-    \g__spath_closepath_tl
-    {
-      \tl_show:N #2
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \tl_clear:N \l_tmpa_tl
-      \tl_put_right:Nx {\tl_item:Nn #2 {1}\tl_item:Nn #2 {2}\tl_item:Nn #2 {3}}
-      \tl_put_right:NV \l_tmpa_tl \g__spath_lineto_tl
-      \tl_put_right:Nx {\tl_item:Nn #2 {5}\tl_item:Nn #2 {6}}
-      \tl_show:N \l_tmpa_tl
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} \l_tmpa_tl
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
-      {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
-      }
-      \tl_set:cx {knot previous filament \int_use:N \l__knot_component_start_int} {filament \int_use:N \l__knot_filaments_int}
-    }
-  }
-  {
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\redraw}
-% The user can redraw segments of the strands at specific locations.
-%    \begin{macrocode}
-\NewDocumentCommand \redraw { m m }
-{
-%  \tikz@scan@one@point\pgfutil@firstofone #2 \relax
-  \tl_put_right:Nn \l__knot_redraws_tl {\knot_draw_crossing:nn}
-  \tl_put_right:Nx \l__knot_redraws_tl {
-    {strand #1} {#2}% {\dim_use:N \pgf@x} {\dim_use:N \pgf@y}
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-%    \begin{macrocode}
-\ExplSyntaxOff
-%    \end{macrocode}
-%
-% \begin{macro}{\pgf@sh@@knotanchor}
-% Add the extra anchors for the knot crossing nodes.
-%    \begin{macrocode}
-\def\pgf@sh@@knotanchor#1#2{%
-  \anchor{#2 north west}{%
-    \csname pgf@anchor@knot #1@north west\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 north east}{%
-    \csname pgf@anchor@knot #1@north east\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 south west}{%
-    \csname pgf@anchor@knot #1@south west\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 south east}{%
-    \csname pgf@anchor@knot #1@south east\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 north}{%
-    \csname pgf@anchor@knot #1@north\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 east}{%
-    \csname pgf@anchor@knot #1@east\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 west}{%
-    \csname pgf@anchor@knot #1@west\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-  \anchor{#2 south}{%
-    \csname pgf@anchor@knot #1@south\endcsname%
-    \pgf@x=#2\pgf@x%
-    \pgf@y=#2\pgf@y%
-  }%
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{knot crossing}
-%    \begin{macrocode}
-\pgfdeclareshape{knot crossing}
-{
-  \inheritsavedanchors[from=circle] % this is nearly a circle
-  \inheritanchorborder[from=circle]
-  \inheritanchor[from=circle]{north}
-  \inheritanchor[from=circle]{north west}
-  \inheritanchor[from=circle]{north east}
-  \inheritanchor[from=circle]{center}
-  \inheritanchor[from=circle]{west}
-  \inheritanchor[from=circle]{east}
-  \inheritanchor[from=circle]{mid}
-  \inheritanchor[from=circle]{mid west}
-  \inheritanchor[from=circle]{mid east}
-  \inheritanchor[from=circle]{base}
-  \inheritanchor[from=circle]{base west}
-  \inheritanchor[from=circle]{base east}
-  \inheritanchor[from=circle]{south}
-  \inheritanchor[from=circle]{south west}
-  \inheritanchor[from=circle]{south east}
-  \inheritanchorborder[from=circle]
-  \pgf@sh@@knotanchor{crossing}{2}
-  \pgf@sh@@knotanchor{crossing}{3}
-  \pgf@sh@@knotanchor{crossing}{4}
-  \pgf@sh@@knotanchor{crossing}{8}
-  \pgf@sh@@knotanchor{crossing}{16}
-  \pgf@sh@@knotanchor{crossing}{32}
-  \backgroundpath{
-    \pgfutil@tempdima=\radius%
-    \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}%  
-    \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}%  
-    \ifdim\pgf@xb<\pgf@yb%
-      \advance\pgfutil@tempdima by-\pgf@yb%
-    \else%
-      \advance\pgfutil@tempdima by-\pgf@xb%
-    \fi%
-  }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{knot over cross}
-%    \begin{macrocode}
-\pgfdeclareshape{knot over cross}
-{
-  \inheritsavedanchors[from=rectangle] % this is nearly a circle
-  \inheritanchorborder[from=rectangle]
-  \inheritanchor[from=rectangle]{north}
-  \inheritanchor[from=rectangle]{north west}
-  \inheritanchor[from=rectangle]{north east}
-  \inheritanchor[from=rectangle]{center}
-  \inheritanchor[from=rectangle]{west}
-  \inheritanchor[from=rectangle]{east}
-  \inheritanchor[from=rectangle]{mid}
-  \inheritanchor[from=rectangle]{mid west}
-  \inheritanchor[from=rectangle]{mid east}
-  \inheritanchor[from=rectangle]{base}
-  \inheritanchor[from=rectangle]{base west}
-  \inheritanchor[from=rectangle]{base east}
-  \inheritanchor[from=rectangle]{south}
-  \inheritanchor[from=rectangle]{south west}
-  \inheritanchor[from=rectangle]{south east}
-  \inheritanchorborder[from=rectangle]
-  \backgroundpath{
-    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
-    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
-  }
-  \foregroundpath{
-% store lower right in xa/ya and upper right in xb/yb
-    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
-    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
- }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{knot under cross}
-%    \begin{macrocode}
-\pgfdeclareshape{knot under cross}
-{
-  \inheritsavedanchors[from=rectangle] % this is nearly a circle
-  \inheritanchorborder[from=rectangle]
-  \inheritanchor[from=rectangle]{north}
-  \inheritanchor[from=rectangle]{north west}
-  \inheritanchor[from=rectangle]{north east}
-  \inheritanchor[from=rectangle]{center}
-  \inheritanchor[from=rectangle]{west}
-  \inheritanchor[from=rectangle]{east}
-  \inheritanchor[from=rectangle]{mid}
-  \inheritanchor[from=rectangle]{mid west}
-  \inheritanchor[from=rectangle]{mid east}
-  \inheritanchor[from=rectangle]{base}
-  \inheritanchor[from=rectangle]{base west}
-  \inheritanchor[from=rectangle]{base east}
-  \inheritanchor[from=rectangle]{south}
-  \inheritanchor[from=rectangle]{south west}
-  \inheritanchor[from=rectangle]{south east}
-  \inheritanchorborder[from=rectangle]
-  \backgroundpath{
-    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
-    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
-  }
-  \foregroundpath{
-% store lower right in xa/ya and upper right in xb/yb
-    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
-    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
- }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{knot vert}
-%    \begin{macrocode}
-\pgfdeclareshape{knot vert}
-{
-  \inheritsavedanchors[from=rectangle] % this is nearly a circle
-  \inheritanchorborder[from=rectangle]
-  \inheritanchor[from=rectangle]{north}
-  \inheritanchor[from=rectangle]{north west}
-  \inheritanchor[from=rectangle]{north east}
-  \inheritanchor[from=rectangle]{center}
-  \inheritanchor[from=rectangle]{west}
-  \inheritanchor[from=rectangle]{east}
-  \inheritanchor[from=rectangle]{mid}
-  \inheritanchor[from=rectangle]{mid west}
-  \inheritanchor[from=rectangle]{mid east}
-  \inheritanchor[from=rectangle]{base}
-  \inheritanchor[from=rectangle]{base west}
-  \inheritanchor[from=rectangle]{base east}
-  \inheritanchor[from=rectangle]{south}
-  \inheritanchor[from=rectangle]{south west}
-  \inheritanchor[from=rectangle]{south east}
-  \inheritanchorborder[from=rectangle]
-  \backgroundpath{
-% store lower right in xa/ya and upper right in xb/yb
-    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
-    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
-    \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
- }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{knot horiz}
-%    \begin{macrocode}
-\pgfdeclareshape{knot horiz}
-{
-  \inheritsavedanchors[from=rectangle] % this is nearly a circle
-  \inheritanchorborder[from=rectangle]
-  \inheritanchor[from=rectangle]{north}
-  \inheritanchor[from=rectangle]{north west}
-  \inheritanchor[from=rectangle]{north east}
-  \inheritanchor[from=rectangle]{center}
-  \inheritanchor[from=rectangle]{west}
-  \inheritanchor[from=rectangle]{east}
-  \inheritanchor[from=rectangle]{mid}
-  \inheritanchor[from=rectangle]{mid west}
-  \inheritanchor[from=rectangle]{mid east}
-  \inheritanchor[from=rectangle]{base}
-  \inheritanchor[from=rectangle]{base west}
-  \inheritanchor[from=rectangle]{base east}
-  \inheritanchor[from=rectangle]{south}
-  \inheritanchor[from=rectangle]{south west}
-  \inheritanchor[from=rectangle]{south east}
-  \inheritanchorborder[from=rectangle]
-  \foregroundpath{
-% store lower right in xa/ya and upper right in xb/yb
-    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
-    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
-    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
-    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
- }
-}
-%    \end{macrocode}
-% \end{macro}
-%
-% \iffalse
-%</knots>
-% \fi
-%\Finale
-\endinput
diff --git a/Master/texmf-dist/source/latex/spath3/spath3_code.dtx b/Master/texmf-dist/source/latex/spath3/spath3_code.dtx
new file mode 100644
index 00000000000..c5c584c4f81
--- /dev/null
+++ b/Master/texmf-dist/source/latex/spath3/spath3_code.dtx
@@ -0,0 +1,6719 @@
+% \iffalse meta-comment
+%<*internal>
+\iffalse
+%</internal>
+%<*readme>
+----------------------------------------------------------------
+spath3 --- LaTeX3 functions for manipulating PGF soft paths
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+This package defines some functions used to manipulate PGFs soft paths.
+As applications of its use, included are a package for drawing calligraphic paths and a package for drawing knot diagrams.
+%</readme>
+%<*internal>
+\fi
+\def\nameofplainTeX{plain}
+\ifx\fmtname\nameofplainTeX\else
+  \expandafter\begingroup
+\fi
+%</internal>
+%<*install>
+\input l3docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\preamble
+----------------------------------------------------------------
+spath3 --- Functions for manipulating PGF soft paths
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+\endpreamble
+\postamble
+
+Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License (LPPL), either
+version 1.3c of this license or (at your option) any later
+version.  The latest version of this license is in the file:
+
+http://www.latex-project.org/lppl.txt
+
+This work is "maintained" (as per LPPL maintenance status) by
+Andrew Stacey.
+
+This work consists of the files  spath3.dtx
+                                 calligraphy_doc.tex
+                                 knots_doc.tex
+                                 spath3.tex
+and the derived files            spath3.ins,
+                                 spath3_code.pdf,
+                                 spath3.sty,
+                                 tikzlibrarycalligraphy.code.tex
+                                 tikzlibraryknots.code.tex
+                                 tikzlibraryspath3.code.tex
+                                 calligraphy.pdf
+                                 knots.pdf
+                                 spath3.pdf
+                                 README
+
+\endpostamble
+\usedir{tex/latex/spath3}
+\generate{
+  \file{spath3.sty}{\from{\jobname.dtx}{spath3}}
+}
+\generate{
+  \file{tikzlibrarycalligraphy.code.tex}{\from{\jobname.dtx}{calligraphy}}
+}
+\generate{
+  \file{tikzlibraryknots.code.tex}{\from{\jobname.dtx}{knots}}
+}
+\generate{
+  \file{tikzlibraryspath3.code.tex}{\from{\jobname.dtx}{tikzspath3}}
+}
+%</install>
+%<install>\endbatchfile
+%<*internal>
+\usedir{source/latex/spath3}
+\generate{
+  \file{\jobname.ins}{\from{\jobname.dtx}{install}}
+}
+\nopreamble\nopostamble
+\usedir{doc/latex/demopkg}
+\generate{
+  \file{README.txt}{\from{\jobname.dtx}{readme}}
+}
+\ifx\fmtname\nameofplainTeX
+  \expandafter\endbatchfile
+\else
+  \expandafter\endgroup
+\fi
+%</internal>
+%<*driver>
+\documentclass[full]{l3doc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+%\usepackage{morefloats}
+\usepackage{tikz}
+\usepackage{trace}
+\usepackage{spath3}
+%\traceoff
+%\usepackage[numbered]{hypdoc}
+\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} 
+ 
+\usepackage{listings}
+\lstloadlanguages{[LaTeX]TeX}
+\lstset{
+  breakatwhitespace=true,
+  breaklines=true,
+  language=[LaTeX]TeX,
+  basicstyle=\small\ttfamily,
+  keepspaces=true,
+  columns=fullflexible
+}
+ 
+\usepackage{fancyvrb}
+
+\newenvironment{example}
+  {\VerbatimEnvironment
+   \begin{VerbatimOut}[gobble=2]{example.out}}
+  {\end{VerbatimOut}
+   \begin{center}
+%   \setlength{\parindent}{0pt}
+   \fbox{\begin{minipage}{.9\linewidth}
+     \lstinputlisting[]{example.out}
+   \end{minipage}}
+   \fbox{\begin{minipage}{.9\linewidth}
+     \centering
+     \input{example.out}
+   \end{minipage}}
+\end{center}
+}
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{6848}
+%
+% \CharacterTable
+%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%   Digits        \0\1\2\3\4\5\6\7\8\9
+%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%   Dollar        \$     Percent       \%     Ampersand     \&
+%   Acute accent  \'     Left paren    \(     Right paren   \)
+%   Asterisk      \*     Plus          \+     Comma         \,
+%   Minus         \-     Point         \.     Solidus       \/
+%   Colon         \:     Semicolon     \;     Less than     \<
+%   Equals        \=     Greater than  \>     Question mark \?
+%   Commercial at \@     Left bracket  \[     Backslash     \\
+%   Right bracket \]     Circumflex    \^     Underscore    \_
+%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%   Right brace   \}     Tilde         \~}
+%
+%
+% \changes{1.0}{2011/05/03}{Converted to DTX file}
+% \changes{1.1}{2016/02/19}{Fixes due to changes in LaTeX3}
+% \changes{1.2}{2019/02/12}{More fixes due to changes in LaTeX3}
+% \changes{1.4}{2020/12/18}{A fair amount of code reimplementation and reorganisation, together with defining TikZ keys to make functions available for use.}
+% \changes{2.0}{2021/01/19}{Refactored the code to remove the OO approach and make it functional, introduced the spath3 TikZ library to provide a user interface.}
+%
+% \DoNotIndex{\newcommand,\newenvironment}
+%
+% \providecommand*{\url}{\texttt}
+% \GetFileInfo{spath3.sty}
+% \title{The \textsf{spath3} package: code}
+% \author{Andrew Stacey \\ \url{loopspace@mathforge.org}}
+% \date{\fileversion~from \filedate}
+%
+%
+% \maketitle
+%
+% 
+% \section{Introduction}
+%
+% The \Verb+spath3+ package is intended as a library for manipulating PGF's \emph{soft paths}.
+% In between defining a path and using it, PGF stores a path as a \emph{soft path} where all the defining structure has been resolved into the basic operations but these have not yet been written to the output file.
+% They can therefore still be manipulated by \TeX, and as they have a very rigid form (and limited vocabulary), they are relatively easy to modify.
+% This package provides some methods for working with these paths.
+% It was originally not really intended for use by end users but as a foundation on which other packages can be built.
+% However, over the years I've found myself using it at ever higher levels and so a set of interfaces has been designed using TikZ keys.
+%
+% It also provides the engine that drives a few other packages, such as the  \Verb+calligraphy+, \Verb+knot+, and \Verb+penrose+ packages.
+% The first two of these are subpackages of this one.
+% The \Verb+calligraphy+ package simulates a calligraphic pen stroking a path.
+% The \Verb+knots+ package can be used to draw knot (and similar) diagrams.
+%
+% For usage, see the documentation of the following packages (\Verb+texdoc <package>+):
+%
+% \begin{itemize}
+% \item \Verb+calligraphy+
+% \item \Verb+knots+
+% \item \Verb+penrose+
+% \item \Verb+spath3+ (\emph{this} document is the code, there's another which focusses on usage)
+% \end{itemize}
+%
+% \section{Technical Details}
+%
+% The format of a soft path is a sequence of triples of the form \Verb+\macro {dimension}{dimension}+.
+% The macro is one of a short list, the dimensions are coordinates in points.
+% There are certain further restrictions, particularly that every path must begin with a \Verb+move to+, and B\'ezier curves consist of three triples.
+%
+% In the original implementation, I wrapped this token list in a \Verb+prop+ to store useful information along with the path.
+% Over time, this additional structure has proved a little unwieldy and I've pared it back to working primarily with the original soft path as a token list.
+%
+% A frequent use of this package is to break a path into pieces and do something with each of those pieces.
+% To that end, there are various words that I use to describe the levels of the structure of a path.
+%
+% At the top level is the path itself.
+% At the bottom level are the triples of the form \Verb+\macro{dim}{dim}+, as described above.
+% In between these are the \emph{segments} and \emph{components}.
+%
+% A \emph{segment} is a minimal drawing piece.
+% Thus it might be a straight line or a B\'ezier curve.
+% When a path is broken into segments then each segment is a complete path so it isn't simply a selection of triples from the original path.
+%
+% A \emph{component} is a minimal connected section of the path.
+% So every component starts with a move command and continues until the next move command.
+% For ease of implementation (and to enable a copperplate pen in the calligraphy package!), an isolated move is considered as a component.
+% Thus the following path consists of three components:
+%
+% \begin{Verbatim}
+% \path (0,0) -- (1,0) (2,0) (3,0) to[out=0,in=90] (4,0);
+% \end{Verbatim}
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+% \iffalse
+%<*spath3>
+% \fi
+% \subsection{Initialisation}
+%
+%    \begin{macrocode}
+%<@@=spath>
+%    \end{macrocode}
+%
+% Load the \LaTeX3 foundation and register us as a \LaTeX3\ package.
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\RequirePackage{pgf}
+\ProvidesExplPackage {spath3} {2021/01/19} {2.0} {Functions for
+manipulating PGF soft paths}
+\RequirePackage{xparse}
+%    \end{macrocode}
+%
+% Utilities copied from \url{https://github.com/loopspace/LaTeX3-Utilities} for adding something in braces to a token list.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_tl_put_right_braced:Nn
+{
+  \tl_put_right:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \@@_tl_put_right_braced:Nn { NV, cV, cv, Nx, cx }
+
+\cs_new_protected:Nn \@@_tl_gput_right_braced:Nn
+{
+  \tl_gput_right:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \@@_tl_gput_right_braced:Nn { NV, cV, cv, Nx, cx }
+\cs_new_protected:Nn \@@_tl_put_left_braced:Nn
+{
+  \tl_put_left:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \@@_tl_put_left_braced:Nn { NV, cV, cv, Nx, cx }
+
+\cs_new_protected:Nn \@@_tl_gput_left_braced:Nn
+{
+  \tl_gput_left:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \@@_tl_gput_left_braced:Nn { NV, cV, cv, Nx, cx }
+%    \end{macrocode}
+%
+% We need a slew of temporary variables.
+%    \begin{macrocode}
+\tl_new:N \l_@@_tmpa_tl
+\tl_new:N \l_@@_tmpb_tl
+\tl_new:N \l_@@_tmpc_tl
+\tl_new:N \l_@@_tmpd_tl
+\tl_new:N \l_@@_tmpe_tl
+
+\seq_new:N \l_@@_tmpa_seq
+\seq_new:N \l_@@_tmpb_seq
+
+\tl_new:N \g_@@_output_tl
+\int_new:N \g_@@_output_int
+\seq_new:N \g_@@_output_seq
+
+\dim_new:N \l_@@_tmpa_dim
+\dim_new:N \l_@@_tmpb_dim
+\dim_new:N \l_@@_move_x_dim
+\dim_new:N \l_@@_move_y_dim
+\fp_new:N \l_@@_tmpa_fp
+\fp_new:N \l_@@_tmpb_fp
+\int_new:N \l_@@_tmpa_int
+
+\bool_new:N \g_@@_output_bool
+\bool_new:N \l_@@_closed_bool
+%    \end{macrocode}
+%
+% We need to be able to compare against the macros that can occur in  a soft path so these token lists contain them.
+% These are global constants so that they can be used in other packages.
+%    \begin{macrocode}
+\tl_const:Nn \c_spath_moveto_tl {\pgfsyssoftpath@movetotoken}
+\tl_const:Nn \c_spath_lineto_tl {\pgfsyssoftpath@linetotoken}
+\tl_const:Nn \c_spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
+\tl_const:Nn \c_spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
+\tl_const:Nn \c_spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
+\tl_const:Nn \c_spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
+%    \end{macrocode}
+%
+%
+% We will want to be able to use anonymous spaths internally, so we create a global counter that we can use to refer to them.
+%    \begin{macrocode}
+\int_new:N \g_@@_anon_int
+\int_gzero:N \g_@@_anon_int
+%    \end{macrocode}
+%
+% Groups and iterations don't mix well and I haven't got a good scheme for protecting local calculations when iterating, so we do our best with iteration-specific variables.
+%    \begin{macrocode}
+\tl_new:N \l_@@_itera_tl
+\tl_new:N \l_@@_iterb_tl
+\tl_new:N \l_@@_iterc_tl
+\tl_new:N \l_@@_iterd_tl
+\tl_new:N \l_@@_iterp_tl
+\dim_new:N \l_@@_itera_dim
+\dim_new:N \l_@@_iterb_dim
+\seq_new:N \l_@@_iter_seq
+%    \end{macrocode}
+%
+% And some error messages
+%    \begin{macrocode}
+\msg_new:nnn { spath3 } { unknown path construction } { The~ path~ construction~ element~ #1~ is~ not~ currently~ supported.}
+%    \end{macrocode}
+%
+%
+% \subsection{Functional Implementation}
+%
+% In the functional approach, we start with a token list containing a soft path and do something to it (either calculate some information or manipulate it in some fashion).
+% We then store that information, or the manipulated path, in an appropriate macro.
+% The macro to store it in is the first argument.
+% These functions occur in two versions, the one with the \texttt{g} makes the assignment global.
+%
+% \begin{macro}{
+% \spath_segments_to_seq:Nn,
+% \spath_segments_gto_seq:Nn
+%}
+% Splits a soft path into \emph{segments}, storing the result in a sequence.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_segments_to_seq:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_itera_tl {#1}
+  \tl_clear:N \l_@@_iterb_tl
+  \seq_clear:N \l_@@_iter_seq
+  \dim_zero:N \l_@@_itera_dim
+  \dim_zero:N \l_@@_iterb_dim
+
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_itera_tl
+  }
+  {
+    \tl_set:Nx \l_@@_iterc_tl {\tl_head:N \l_@@_itera_tl}
+    \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+    \tl_case:NnF \l_@@_iterc_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_set_eq:NN \l_@@_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_itera_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_iterb_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+        \tl_set:Nx \l_@@_iterd_tl {\tl_head:N \l_@@_itera_tl}
+        \tl_if_eq:NNF \l_@@_iterd_tl \c_spath_moveto_tl
+        {
+          \tl_clear:N \l_@@_iterb_tl
+        }
+
+      }
+
+      \c_spath_lineto_tl
+      {
+        \tl_set_eq:NN \l_@@_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l_@@_iterb_tl
+        {
+          {\dim_use:N \l_@@_itera_dim}
+          {\dim_use:N \l_@@_iterb_dim}
+        }
+        \tl_put_right:NV \l_@@_iterb_tl \c_spath_lineto_tl
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_itera_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_iterb_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+      }
+
+      \c_spath_curvetoa_tl
+      {
+        \tl_set_eq:NN \l_@@_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l_@@_iterb_tl
+        {
+          {\dim_use:N \l_@@_itera_dim}
+          {\dim_use:N \l_@@_iterb_dim}
+        }
+        \tl_put_right:NV \l_@@_iterb_tl \c_spath_curvetoa_tl
+
+        \prg_replicate:nn {2} {
+          \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+          \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+          \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N               \l_@@_itera_tl}}
+          \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+          \tl_put_right:Nx \l_@@_iterb_tl {\tl_head:N             \l_@@_itera_tl}
+          \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+        }
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_itera_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_iterb_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+      }
+
+      \c_spath_closepath_tl
+      {
+        \tl_set_eq:NN \l_@@_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l_@@_iterb_tl
+        {
+          {\dim_use:N \l_@@_itera_dim}
+          {\dim_use:N \l_@@_iterb_dim}
+        }
+        \tl_put_right:NV \l_@@_iterb_tl \c_spath_lineto_tl
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_itera_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+        \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+        \dim_set:Nn \l_@@_iterb_dim {\tl_head:N \l_@@_itera_tl}
+        \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+      }
+      
+    }    
+    {
+
+      \tl_set_eq:NN \l_@@_iterb_tl \l_@@_iterc_tl
+      \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+      \dim_set:Nn \l_@@_itera_dim {\tl_head:N \l_@@_itera_tl}
+      \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+
+      \tl_put_right:Nx \l_@@_iterb_tl {{\tl_head:N \l_@@_itera_tl}}
+      \dim_set:Nn \l_@@_iterb_dim {\tl_head:N \l_@@_itera_tl}
+      \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+      
+    }
+
+    \tl_if_empty:NF \l_@@_iterb_tl
+    {
+      \seq_put_right:NV \l_@@_iter_seq \l_@@_iterb_tl
+    }
+    \tl_clear:N \l_@@_iterb_tl
+  }
+
+  \seq_gclear:N \g_@@_output_seq
+  \seq_gset_eq:NN \g_@@_output_seq \l_@@_iter_seq
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_segments_to_seq:Nn #1#2
+{
+  \@@_segments_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_set_eq:NN #1 \g_@@_output_seq
+  \seq_gclear:N \g_@@_output_seq
+}
+\cs_generate_variant:Nn \spath_segments_to_seq:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \spath_segments_gto_seq:Nn #1#2
+{
+  \@@_segments_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_gset_eq:NN #1 \g_@@_output_seq
+  \seq_gclear:N \g_@@_output_seq
+}
+\cs_generate_variant:Nn \spath_segments_gto_seq:Nn {NV, cn, cV, Nv, cv}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_components_to_seq:Nn,
+% \spath_components_gto_seq:Nn,
+% \spath_components_to_clist:Nn,
+% \spath_components_gto_clist:Nn,
+% }
+% Splits a soft path into \emph{components}, storing the result in a sequence or a clist.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_components_to_seq:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_itera_tl {#1}
+  \seq_clear:N \l_@@_iter_seq
+  \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+  \tl_put_right:NV \l_@@_itera_tl \c_spath_moveto_tl
+  \tl_set_eq:NN \l_@@_iterb_tl \c_spath_moveto_tl
+  \bool_do_until:nn {
+    \tl_if_empty_p:N \l_@@_itera_tl
+  }
+  {
+    \tl_set:Nx \l_@@_iterc_tl {\tl_head:N \l_@@_itera_tl}
+    \tl_if_eq:NNT \l_@@_iterc_tl \c_spath_moveto_tl
+    {
+      \seq_put_right:NV \l_@@_iter_seq \l_@@_iterb_tl
+      \tl_clear:N \l_@@_iterb_tl
+    }
+    \tl_if_single:NTF \l_@@_iterc_tl
+    {
+      \tl_put_right:NV \l_@@_iterb_tl \l_@@_iterc_tl
+    }
+    {
+      \tl_put_right:Nx \l_@@_iterb_tl {{\l_@@_iterc_tl}}
+    }
+    \tl_set:Nx \l_@@_itera_tl {\tl_tail:N \l_@@_itera_tl}
+  }
+
+  \seq_gclear:N \g_@@_output_seq
+  \seq_gset_eq:NN \g_@@_output_seq \l_@@_iter_seq
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_components_to_seq:Nn #1#2
+{
+  \@@_components_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_set_eq:NN #1 \g_@@_output_seq
+  \seq_gclear:N \g_@@_output_seq
+}
+\cs_generate_variant:Nn \spath_components_to_seq:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_gto_seq:Nn #1#2
+{
+  \@@_components_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_gset_eq:NN #1 \g_@@_output_seq
+  \seq_gclear:N \g_@@_output_seq
+}
+\cs_generate_variant:Nn \spath_components_gto_seq:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_to_clist:Nn #1#2
+{
+  \@@_components_to_seq:n {#2}
+  \clist_clear_new:N #1
+  \clist_set_from_seq:NN #1 \g_@@_output_seq
+  \seq_gclear:N \g_@@_output_seq
+}
+\cs_generate_variant:Nn \spath_components_to_clist:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_gto_clist:Nn #1#2
+{
+  \@@_components_to_seq:n {#2}
+  \clist_clear_new:N #1
+  \clist_gset_from_seq:NN #1 \g_@@_output_seq
+  \seq_gclear:N \g_@@_output_seq
+}
+\cs_generate_variant:Nn \spath_components_gto_clist:Nn {NV, cn, cV, cv, Nv}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\spath_length:n}
+% Counts the number of triples in the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_length:n #1
+{
+  \int_eval:n {\tl_count:n {#1} / 3}
+}
+\cs_generate_variant:Nn \spath_length:n {V}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_reallength:Nn,
+% \spath_greallength:Nn
+% }
+% The real length of a path is the number of triples that actually draw something (that is, the number of lines, curves, and closepaths).
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_reallength:n #1
+{
+  \group_begin:
+  \int_set:Nn \l_@@_tmpa_int {0}
+  \tl_map_inline:nn {#1} {
+    \tl_set:Nn \l_@@_tmpc_tl {##1}
+    \tl_case:NnT \l_@@_tmpc_tl
+    {
+      \c_spath_lineto_tl {}
+      \c_spath_curveto_tl {}
+      \c_spath_closepath_tl {}
+    }
+    {
+      \int_incr:N \l_@@_tmpa_int
+    }
+  }
+  \int_gzero:N \g_@@_output_int
+  \int_gset_eq:NN \g_@@_output_int \l_@@_tmpa_int
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_reallength:Nn #1#2
+{
+  \@@_reallength:n {#2}
+  \int_set_eq:NN #1 \g_@@_output_int
+  \int_gzero:N \g_@@_output_int
+}
+\cs_generate_variant:Nn \spath_reallength:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \spath_greallength:Nn #1#2
+{
+  \@@_reallength:n {#2}
+  \int_gset_eq:NN #1 \g_@@_output_int
+  \int_gzero:N \g_@@_output_int
+}
+\cs_generate_variant:Nn \spath_greallength:Nn {NV, cn, cV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_numberofcomponents:Nn,
+% \spath_gnumberofcomponents:Nn
+% }
+% A component is a continuous segment of the path, separated by moves.
+% Successive moves are not collapsed, and zero length moves count.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_numberofcomponents:n #1
+{
+  \group_begin:
+  \int_set:Nn \l_@@_tmpa_int {0}
+  \tl_map_inline:nn {#1} {
+    \tl_set:Nn \l_@@_tmpa_tl {##1}
+    \tl_case:Nn \l_@@_tmpa_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \int_incr:N \l_@@_tmpa_int
+      }
+    }
+  }
+  \int_gzero:N \g_@@_output_int
+  \int_gset_eq:NN \g_@@_output_int \l_@@_tmpa_int
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_numberofcomponents:Nn #1#2
+{
+  \@@_numberofcomponents:n {#2}
+  \int_set_eq:NN #1 \g_@@_output_int
+  \int_gzero:N \g_@@_output_int
+}
+\cs_generate_variant:Nn \spath_numberofcomponents:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gnumberofcomponents:Nn #1#2
+{
+  \@@_numberofcomponents:n {#2}
+  \int_gset_eq:NN #1 \g_@@_output_int
+  \int_gzero:N \g_@@_output_int
+}
+\cs_generate_variant:Nn \spath_gnumberofcomponents:Nn {NV, cn, cV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_initialpoint:Nn,
+% \spath_ginitialpoint:Nn
+% }
+% The starting point of the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_initialpoint:n #1
+{
+  \group_begin:
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_set:Nx \l_@@_tmpb_tl
+  {
+    { \tl_item:nn {#1} {2} }
+    { \tl_item:nn {#1} {3} }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_initialpoint:Nn #1#2
+{
+  \@@_initialpoint:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_initialpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_ginitialpoint:Nn #1#2
+{
+  \@@_initialpoint:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_ginitialpoint:Nn {NV, cn, cV, Nv}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_finalpoint:Nn,
+% \spath_gfinalpoint:Nn,
+% }
+% The final point of the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_finalpoint:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_reverse:N \l_@@_tmpa_tl
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_set:Nx \l_@@_tmpb_tl
+  {
+    { \tl_item:Nn \l_@@_tmpa_tl {2} }
+    { \tl_item:Nn \l_@@_tmpa_tl {1} }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalpoint:Nn #1#2
+{
+  \@@_finalpoint:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_finalpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_gfinalpoint:Nn #1#2
+{
+  \@@_finalpoint:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gfinalpoint:Nn {NV, cn, cV, Nv}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_reverse:Nn,
+% \spath_greverse:Nn
+% }
+% This computes the reverse of the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_reverse:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_clear:N \l_@@_tmpd_tl
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  
+  \tl_put_left:Nx \l_@@_tmpd_tl
+  {
+    {\dim_use:N \l_@@_tmpa_dim}
+    {\dim_use:N \l_@@_tmpb_dim}
+  }
+  
+  \bool_set_false:N \l_@@_closed_bool
+  
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_set:Nx \l_@@_tmpc_tl {\tl_head:N \l_@@_tmpa_tl}
+
+    \tl_case:NnTF \l_@@_tmpc_tl
+    {
+      \c_spath_moveto_tl {
+        
+        \bool_if:NT \l_@@_closed_bool
+        {
+          \tl_put_right:NV \l_@@_tmpd_tl \c_spath_closepath_tl
+          \tl_set:Nx \l_@@_tmpe_tl {\tl_tail:N \l_@@_tmpd_tl}
+          \tl_put_right:Nx \l_@@_tmpd_tl
+          {
+            { \tl_head:N \l_@@_tmpd_tl }
+            { \tl_head:N \l_@@_tmpe_tl }
+          }
+        }
+        \bool_set_false:N \l_@@_closed_bool
+        \tl_put_left:NV \l_@@_tmpd_tl \c_spath_moveto_tl
+        \tl_put_left:NV \l_@@_tmpb_tl \l_@@_tmpd_tl
+        \tl_clear:N \l_@@_tmpd_tl
+      }
+      \c_spath_lineto_tl {
+        \tl_put_left:NV \l_@@_tmpd_tl \c_spath_lineto_tl
+      }
+      \c_spath_curveto_tl {
+        \tl_put_left:NV \l_@@_tmpd_tl \c_spath_curvetoa_tl
+      }
+      \c_spath_curvetoa_tl {
+        \tl_put_left:NV \l_@@_tmpd_tl \c_spath_curveto_tl
+      }
+      \c_spath_curvetob_tl {
+        \tl_put_left:NV \l_@@_tmpd_tl \c_spath_curvetob_tl
+      }
+    }
+    {
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+      \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl}
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+      \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl}
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+      \tl_put_left:Nx \l_@@_tmpd_tl
+      {
+        {\dim_use:N \l_@@_tmpa_dim}
+        {\dim_use:N \l_@@_tmpb_dim}
+      }
+
+    }
+    {
+      \tl_if_eq:NNTF \l_@@_tmpc_tl \c_spath_closepath_tl
+      {
+        \bool_set_true:N \l_@@_closed_bool
+      }
+      {
+        \msg_warning:nnx { spath3 } { unknown path construction } {\l_@@_tmpc_tl }
+      }
+
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    }
+  }
+
+  \bool_if:NT \l_@@_closed_bool
+  {
+    \tl_put_right:NV \l_@@_tmpd_tl \c_spath_closepath_tl
+    \tl_set:Nx \l_@@_tmpe_tl {\tl_tail:N \l_@@_tmpd_tl}
+    \tl_put_right:Nx \l_@@_tmpd_tl
+    {
+      { \tl_head:N \l_@@_tmpd_tl }
+      { \tl_head:N \l_@@_tmpe_tl }
+    }
+  }
+
+  \bool_set_false:N \l_@@_closed_bool
+  \tl_put_left:NV \l_@@_tmpd_tl \c_spath_moveto_tl
+  \tl_put_left:NV \l_@@_tmpb_tl \l_@@_tmpd_tl
+
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_reverse:Nn #1#2
+{
+  \@@_reverse:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_reverse:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_reverse:N #1
+{
+  \spath_reverse:NV #1#1
+}
+\cs_generate_variant:Nn \spath_reverse:N {c}
+\cs_new_protected_nopar:Npn \spath_greverse:Nn #1#2
+{
+  \@@_reverse:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_greverse:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_greverse:N #1
+{
+  \spath_greverse:NV #1#1
+}
+\cs_generate_variant:Nn \spath_greverse:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_initialaction:Nn,
+% \spath_ginitialaction:Nn,
+% }
+% This is the first thing that the path does (after the initial move).
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_initialaction:n #1
+{
+  \group_begin:
+  \tl_clear:N \l_@@_tmpa_tl
+  \int_compare:nT
+  {
+    \tl_count:n {#1} > 3
+  }
+  {
+    \tl_set:Nx \l_@@_tmpa_tl
+    {
+      \tl_item:Nn {#1} {4}
+    }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_initialaction:Nn #1#2
+{
+  \@@_initialaction:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_initialaction:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_ginitialaction:Nn #1#2
+{
+  \@@_initialaction:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_ginitialaction:Nn {NV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_finalaction:Nn,
+% \spath_gfinalaction:Nn
+% }
+% This is the last thing that the path does.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_finalaction:n #1
+{
+  \group_begin:
+  \tl_clear:N \l_@@_tmpb_tl
+  \int_compare:nT
+  {
+    \tl_count:n {#1} > 3
+  }
+  {
+    \tl_set:Nn \l_@@_tmpa_tl {#1}
+    \tl_reverse:N \l_@@_tmpa_tl
+    \tl_set:Nx \l_@@_tmpb_tl
+    {
+      \tl_item:Nn \l_@@_tmpa_tl {3}
+    }
+    \tl_if_eq:NNT \l_@@_tmpb_tl \c_spath_curvetoa_tl
+    {
+      \tl_set_eq:NN \l_@@_tmpb_tl \c_spath_curveto_tl
+    }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalaction:Nn #1#2
+{
+  \@@_finalaction:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_finalaction:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gfinalaction:Nn #1#2
+{
+  \@@_finalaction:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gfinalaction:Nn {NV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_minbb:Nn,
+% \spath_gminbb:Nn
+% }
+% This computes the minimum (bottom left) of the bounding box of the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_minbb:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    \dim_set:Nn \l_@@_tmpa_dim {\dim_min:nn {\tl_head:N \l_@@_tmpa_tl} {\l_@@_tmpa_dim}}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    \dim_set:Nn \l_@@_tmpb_dim {\dim_min:nn {\tl_head:N \l_@@_tmpa_tl} {\l_@@_tmpb_dim}}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  }
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_use:N \l_@@_tmpa_dim}
+    {\dim_use:N \l_@@_tmpb_dim}
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_minbb:Nn #1#2
+{
+  \@@_minbb:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_minbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gminbb:Nn #1#2
+{
+  \@@_minbb:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gminbb:Nn {NV, cn, cV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_maxbb:Nn,
+% \spath_gmaxbb:Nn,
+% }
+% This computes the maximum (top right) of the bounding box of the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_maxbb:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl}
+  \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    \dim_set:Nn \l_@@_tmpa_dim {\dim_max:nn {\tl_head:N \l_@@_tmpa_tl} {\l_@@_tmpa_dim}}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    \dim_set:Nn \l_@@_tmpb_dim {\dim_max:nn {\tl_head:N \l_@@_tmpa_tl} {\l_@@_tmpb_dim}}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+  }
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_use:N \l_@@_tmpa_dim}
+    {\dim_use:N \l_@@_tmpb_dim}
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_maxbb:Nn #1#2
+{
+  \@@_maxbb:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_maxbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gmaxbb:Nn #1#2
+{
+  \@@_maxbb:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gmaxbb:Nn {NV, cn, cV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_save_to_aux:Nn,
+% \spath_save_to_aux:N
+% }
+% This saves a soft path to the auxfile.
+% The first argument is the macro that will be assigned to the soft path when the aux file is read back in.
+%    \begin{macrocode}
+\int_set:Nn \l_@@_tmpa_int {\char_value_catcode:n {`@}}
+\char_set_catcode_letter:N @
+\cs_new_protected_nopar:Npn \spath_save_to_aux:Nn #1#2 {
+  \tl_if_empty:nF {#2}
+  {
+    \tl_clear:N \l_@@_tmpa_tl
+    \tl_put_right:Nn \l_@@_tmpa_tl {
+      \ExplSyntaxOn
+      \tl_clear:N #1
+      \tl_set:Nn #1 {#2}
+      \ExplSyntaxOff
+    }
+    \protected@write\@auxout{}{
+      \tl_to_str:N \l_@@_tmpa_tl
+    }
+  }
+}
+\char_set_catcode:nn {`@} {\l_@@_tmpa_int}
+\cs_generate_variant:Nn \spath_save_to_aux:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_save_to_aux:N #1
+{
+  \tl_if_exist:NT #1
+  {
+    \spath_save_to_aux:NV #1#1
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Path Manipulation}
+%
+% These functions all manipulate a soft path.
+% They come with a variety of different argument specifications.
+% As a general rule, the first argument is the macro in which to store the modified path, the second is the path to manipulate, and the rest are the information about what to do.
+% There is always a variant in which the path is specified by a macro and restored back in that same macro. 
+%
+%
+% \begin{macro}{
+% \spath_translate:Nnnn,
+% \spath_translate:Nnn,
+% \spath_gtranslate:Nnnn,
+% \spath_gtranslate:Nnn
+% }
+% Translates a path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_translate:nnn #1#2#3
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_clear:N \l_@@_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_put_right:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    
+    \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl + #2}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl + #3}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    \tl_put_right:Nx \l_@@_tmpb_tl
+    {
+      {\dim_use:N \l_@@_tmpa_dim}
+      {\dim_use:N \l_@@_tmpb_dim}
+    }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_translate:Nnnn #1#2#3#4
+{
+  \@@_translate:nnn {#2}{#3}{#4}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_translate:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_translate:Nnn #1#2#3
+{
+  \spath_translate:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_translate:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nnnn #1#2#3#4
+{
+  \@@_translate:nnn {#2}{#3}{#4}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nnn #1#2#3
+{
+  \spath_gtranslate:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nnn {NVV, cnn, cVV}
+%    \end{macrocode}
+%
+% This variant allows for passing the coordinates as a single braced group as it strips off the outer braces of the second argument.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_translate:Nn #1#2
+{
+  \spath_translate:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_translate:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nn #1#2
+{
+  \spath_gtranslate:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nn {NV}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_scale:Nnnn,
+% \spath_scale:Nnn,
+% \spath_gscale:Nnnn,
+% \spath_gscale:Nnn
+% }
+% Scale a path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_scale:nnn #1#2#3
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_clear:N \l_@@_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_put_right:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        
+    \fp_set:Nn \l_@@_tmpa_fp {\tl_head:N \l_@@_tmpa_tl * #2}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    \fp_set:Nn \l_@@_tmpb_fp {\tl_head:N \l_@@_tmpa_tl * #3}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    \tl_put_right:Nx \l_@@_tmpb_tl
+    {
+      {\fp_to_dim:N \l_@@_tmpa_fp}
+      {\fp_to_dim:N \l_@@_tmpb_fp}
+    }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_scale:Nnnn #1#2#3#4
+{
+  \@@_scale:nnn {#2}{#3}{#4}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_scale:Nnnn {NVnn, Nnxx}
+\cs_new_protected_nopar:Npn \spath_scale:Nnn #1#2#3
+{
+  \spath_scale:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_scale:Nnn {cnn, cVV, NVV}
+\cs_new_protected_nopar:Npn \spath_gscale:Nnnn #1#2#3#4
+{
+  \@@_scale:nnn {#2}{#3}{#4}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gscale:Nnnn {NVnn, Nnxx}
+\cs_new_protected_nopar:Npn \spath_gscale:Nnn #1#2#3
+{
+  \spath_gscale:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gscale:Nnn {cnn, cVV, NVV}
+%    \end{macrocode}
+%
+% This variant allows for passing the coordinates as a single braced group as it strips off the outer braces of the second argument.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_scale:Nn #1#2
+{
+  \spath_scale:Nnn #1 #2
+}
+
+\cs_generate_variant:Nn \spath_scale:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gscale:Nn #1#2
+{
+  \spath_gscale:Nnn #1 #2
+}
+
+\cs_generate_variant:Nn \spath_gscale:Nn {NV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_transform:Nnnnnnnn,
+% \spath_transform:Nnnnnnn,
+% \spath_gtransform:Nnnnnnnn,
+% \spath_gtransform:Nnnnnnn,
+% }
+% Applies an affine (matrix and vector) transformation to path.
+% The matrix is specified in rows first.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_transform:nnnnnnn #1#2#3#4#5#6#7
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_clear:N \l_@@_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_put_right:Nx \l_@@_tmpb_tl {\tl_head:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpc_tl {\tl_head:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpd_tl {\tl_head:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    \fp_set:Nn \l_@@_tmpa_fp {\l_@@_tmpc_tl * #2 + \l_@@_tmpd_tl * #4 + #6}
+    \fp_set:Nn \l_@@_tmpb_fp {\l_@@_tmpc_tl * #3 + \l_@@_tmpd_tl * #5 + #7}
+    \tl_put_right:Nx \l_@@_tmpb_tl
+    {
+      {\fp_to_dim:N \l_@@_tmpa_fp}
+      {\fp_to_dim:N \l_@@_tmpb_fp}
+    }
+  }
+
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_transform:Nnnnnnnn #1#2#3#4#5#6#7#8
+{
+  \@@_transform:nnnnnnn {#2}{#3}{#4}{#5}{#6}{#7}{#8}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_transform:Nnnnnnnn {NVnnnnnn, Nnxxxxxx, cnnnnnnn}
+\cs_new_protected_nopar:Npn \spath_transform:Nnnnnnn #1#2#3#4#5#6#7
+{
+  \spath_transform:NVnnnnnn #1#1{#2}{#3}{#4}{#5}{#6}{#7}
+}
+\cs_generate_variant:Nn \spath_transform:Nnnnnnn {cnnnnnn}
+\cs_new_protected_nopar:Npn \spath_transform:Nnn #1#2#3
+{
+  \spath_transform:Nnnnnnnn #1{#2}#3
+}
+\cs_generate_variant:Nn \spath_transform:Nnn {cnn, cVn, NVn, NnV}
+\cs_new_protected_nopar:Npn \spath_transform:Nn #1#2
+{
+  \spath_transform:NVnnnnnn #1#1#2
+}
+\cs_generate_variant:Nn \spath_transform:Nn {cn, cV, NV}
+
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnnnnnnn #1#2#3#4#5#6#7#8
+{
+  \@@_transform:nnnnnnn {#2}{#3}{#4}{#5}{#6}{#7}{#8}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnnnnnnn {NVnnnnnn, Nnxxxxxx, cnnnnnnn}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnnnnnn #1#2#3#4#5#6#7
+{
+  \spath_gtransform:NVnnnnnn #1#1{#2}{#3}{#4}{#5}{#6}{#7}
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnnnnnn {cnnnnnn}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnn #1#2#3
+{
+  \spath_gtransform:Nnnnnnnn #1{#2}#3
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnn {cnn, cVn, NVn, NnV}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nn #1#2
+{
+  \spath_gtransform:NVnnnnnn #1#1#2
+}
+\cs_generate_variant:Nn \spath_gtransform:Nn {cn, cV, NV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_weld:Nnn,
+% \spath_weld:Nn,
+% \spath_gweld:Nnn,
+% \spath_gweld:Nn
+% }
+% This welds one path to another, moving the second so that its initial point coincides with the first's final point.
+% It is called a \emph{weld} because the initial move of the second path is removed.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_weld:nn #1#2
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_set:Nn \l_@@_tmpb_tl {#2}
+
+  \spath_finalpoint:NV \l_@@_tmpc_tl \l_@@_tmpa_tl
+  \spath_initialpoint:NV \l_@@_tmpd_tl \l_@@_tmpb_tl
+
+  \dim_set:Nn \l_@@_tmpa_dim
+  {
+    \tl_item:Nn \l_@@_tmpc_tl {1}
+    -
+    \tl_item:Nn \l_@@_tmpd_tl {1}
+  }
+  \dim_set:Nn \l_@@_tmpb_dim
+  {
+    \tl_item:Nn \l_@@_tmpc_tl {2}
+    -
+    \tl_item:Nn \l_@@_tmpd_tl {2}
+  }
+
+  \spath_translate:NVV \l_@@_tmpb_tl \l_@@_tmpa_dim \l_@@_tmpb_dim
+
+  \prg_replicate:nn {3}
+  {
+    \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+  }
+
+  \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpb_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_weld:Nnn #1#2#3
+{
+  \@@_weld:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_weld:Nnn {NVV,NVn}
+\cs_new_protected_nopar:Npn \spath_weld:Nn #1#2
+{
+  \spath_weld:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_weld:Nn {NV, Nv, cV, cv}
+\cs_new_protected_nopar:Npn \spath_gweld:Nnn #1#2#3
+{
+  \@@_weld:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gweld:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gweld:Nn #1#2
+{
+  \spath_gweld:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gweld:Nn {NV, Nv, cV, cv}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_append_no_move:Nnn,
+% \spath_append_no_move:Nn,
+% \spath_gappend_no_move:Nnn,
+% \spath_gappend_no_move:Nn,
+% }
+% Append the path from the second \Verb+spath+ to the first, removing
+% the adjoining move.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_append_no_move:nn #1#2
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_set:Nn \l_@@_tmpb_tl {#2}
+  \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+  \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+  \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+  
+  \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpb_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_append_no_move:Nnn #1#2#3
+{
+  \@@_append_no_move:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_append_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_append_no_move:Nn #1#2
+{
+  \spath_append_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_append_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_gappend_no_move:Nnn #1#2#3
+{
+  \@@_append_no_move:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gappend_no_move:Nn #1#2
+{
+  \spath_gappend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nn {NV, cv}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_append:Nnn,
+% \spath_append:Nn,
+% \spath_gappend:Nnn,
+% \spath_gappend:Nn,
+% }
+% Prepend the path from the second \Verb+spath+ to the first.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_append:Nnn #1#2#3
+{
+  \tl_set:Nn #1 {#2}
+  \tl_put_right:Nn #1 {#3}
+}
+\cs_generate_variant:Nn \spath_append:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_append:Nn #1#2
+{
+  \spath_append:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_append:Nn {NV, Nv}
+\cs_new_protected_nopar:Npn \spath_gappend:Nnn #1#2#3
+{
+  \tl_gset:Nn #1 {#2}
+  \tl_gput_right:Nn #1 {#3}
+}
+\cs_generate_variant:Nn \spath_gappend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gappend:Nn #1#2
+{
+  \spath_gappend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gappend:Nn {NV, Nv}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_prepend_no_move:Nnn,
+% \spath_prepend_no_move:Nn,
+% \spath_gprepend_no_move:Nnn,
+% \spath_gprepend_no_move:Nn,
+% }
+% Prepend the path from the second \Verb+spath+ to the first, removing
+% the adjoining move.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_prepend_no_move:Nnn #1#2#3
+{
+  \spath_append_no_move:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_prepend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_prepend_no_move:Nn #1#2
+{
+  \spath_prepend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_prepend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_gprepend_no_move:Nnn #1#2#3
+{
+  \spath_gappend_no_move:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gprepend_no_move:Nn #1#2
+{
+  \spath_gprepend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend_no_move:Nn {NV, cv}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_prepend:Nnn,
+% \spath_prepend:Nn,
+% \spath_gprepend:Nnn,
+% \spath_gprepend:Nn
+% }
+% Prepend the path from the second \Verb+spath+ to the first.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_prepend:Nnn #1#2#3
+{
+  \spath_append:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_prepend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_prepend:Nn #1#2
+{
+  \spath_prepend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_prepend:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gprepend:Nnn #1#2#3
+{
+  \spath_gappend:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gprepend:Nn #1#2
+{
+  \spath_gprepend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend:Nn {NV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_bake_round:Nn,
+% \spath_bake_round:N,
+% \spath_gbake_round:Nn,
+% \spath_gbake_round:N
+% }
+%
+% The corner rounding routine is applied quite late in the process of building a soft path so this ensures that it is done.
+% 
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_bake_round:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \pgf@@@@processround \l_@@_tmpa_tl\l_@@_tmpb_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_bake_round:Nn #1#2
+{
+  \@@_bake_round:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_bake_round:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_bake_round:N #1
+{
+  \spath_bake_round:NV #1#1
+}
+\cs_generate_variant:Nn \spath_bake_round:N {c}
+\cs_new_protected_nopar:Npn \spath_gbake_round:Nn #1#2
+{
+  \@@_bake_round:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gbake_round:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gbake_round:N #1
+{
+  \spath_gbake_round:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gbake_round:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_close:Nn,
+% \spath_close:N,
+% \spath_gclose:Nn,
+% \spath_gclose:N
+% }
+% Appends a close path to the end of the path.
+% For now, the point is the initial or final point (respectively).
+% To be future proof, it ought to be the point of the adjacent move to.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_close:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \spath_initialpoint:NV \l_@@_tmpb_tl \l_@@_tmpa_tl
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_closepath_tl
+  \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpb_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_close:Nn #1#2
+{
+  \@@_close:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_close:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_close:N #1
+{
+  \spath_close:NV #1#1
+}
+\cs_generate_variant:Nn \spath_close:N {c}
+\cs_new_protected_nopar:Npn \spath_gclose:Nn #1#2
+{
+  \@@_close:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gclose:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gclose:N #1
+{
+  \spath_gclose:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gclose:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_open:Nn,
+% \spath_open:N,
+% \spath_gopen:Nn,
+% \spath_gopen:N
+% }
+% Removes all close paths from the path, replacing them by \Verb+lineto+ if they move any distance.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_open:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_clear:N \l_@@_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_tmpa_tl
+  }
+  {
+    \tl_set:Nx \l_@@_tmpc_tl {\tl_head:N \l_@@_tmpa_tl}
+    \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+    \tl_case:NnF \l_@@_tmpc_tl
+    {
+      \c_spath_closepath_tl {
+
+        \bool_if:nF
+        {
+          \dim_compare_p:n
+          {
+            \l_@@_move_x_dim == \l_@@_tmpa_dim
+          }
+          &&
+          \dim_compare_p:n
+          {
+            \l_@@_move_y_dim == \l_@@_tmpb_dim
+          }
+        }
+        {
+          \tl_put_right:NV \l_@@_tmpb_tl \c_spath_lineto_tl
+        
+          \tl_put_right:Nx \l_@@_tmpb_tl {
+            { \dim_use:N \l_@@_move_x_dim }
+            { \dim_use:N \l_@@_move_y_dim }
+          }
+        }
+        
+        \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl}
+        \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl}
+        \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+      }
+
+      \c_spath_moveto_tl {
+        \tl_put_right:NV \l_@@_tmpb_tl \l_@@_tmpc_tl
+        
+        \dim_set:Nn \l_@@_move_x_dim {\tl_head:N \l_@@_tmpa_tl}
+        \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        \dim_set:Nn \l_@@_move_y_dim {\tl_head:N \l_@@_tmpa_tl}
+        \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+        \tl_put_right:Nx \l_@@_tmpb_tl {
+          { \dim_use:N \l_@@_move_x_dim }
+          { \dim_use:N \l_@@_move_y_dim }
+        }
+
+        \dim_set_eq:NN \l_@@_tmpa_dim \l_@@_move_x_dim
+        \dim_set_eq:NN \l_@@_tmpb_dim \l_@@_move_y_dim
+      }
+    }
+    {
+      \tl_put_right:NV \l_@@_tmpb_tl \l_@@_tmpc_tl
+      
+      \dim_set:Nn \l_@@_tmpa_dim {\tl_head:N \l_@@_tmpa_tl}
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+      \dim_set:Nn \l_@@_tmpb_dim {\tl_head:N \l_@@_tmpa_tl}
+      \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+
+      \tl_put_right:Nx \l_@@_tmpb_tl {
+        { \dim_use:N \l_@@_tmpa_dim }
+        { \dim_use:N \l_@@_tmpb_dim }
+      }
+    }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_open:Nn #1#2
+{
+  \@@_open:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_open:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_open:N #1
+{
+  \spath_open:NV #1#1
+}
+\cs_new_protected_nopar:Npn \spath_gopen:Nn #1#2
+{
+  \@@_open:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gopen:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gopen:N #1
+{
+  \spath_gopen:NV #1#1
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_remove_empty_components:Nn,
+% \spath_remove_empty_components:N,
+% \spath_gremove_empty_components:Nn,
+% \spath_gremove_empty_components:N
+% }
+% Remove any component that is simply a moveto.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_remove_empty_components:n #1
+{
+  \group_begin:
+  \spath_components_to_seq:Nn \l_@@_tmpa_seq {#1}
+  \tl_clear:N \l_@@_tmpa_tl
+  \seq_map_inline:Nn \l_@@_tmpa_seq
+  {
+    \int_compare:nF
+    {
+      \tl_count:n {##1} == 3
+    }
+    {
+      \tl_put_right:Nn \l_@@_tmpa_tl {##1}
+    }
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_remove_empty_components:Nn #1#2
+{
+  \@@_remove_empty_components:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_remove_empty_components:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_remove_empty_components:N #1
+{
+  \spath_remove_empty_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_remove_empty_components:N {c}
+\cs_new_protected_nopar:Npn \spath_gremove_empty_components:Nn #1#2
+{
+  \@@_remove_empty_components:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gremove_empty_components:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gremove_empty_components:N #1
+{
+  \spath_gremove_empty_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gremove_empty_components:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\spath_if_eq:nn}
+% Test if two soft paths are equal, we allow a little tolerance on the calculations.
+%    \begin{macrocode}
+\prg_new_protected_conditional:Npnn \spath_if_eq:nn #1#2 { T, F, TF }
+{
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_set:Nn \l_@@_tmpb_tl {#2}
+  \bool_gset_true:N \g_@@_tmpa_bool
+  \int_compare:nNnTF {\tl_count:N \l_@@_tmpa_tl} = {\tl_count:N \l_@@_tmpb_tl}
+  {
+    \int_step_inline:nnnn {1} {3} {\tl_count:N \l_@@_tmpa_tl}
+    {
+      \tl_set:Nx \l_@@_tmpc_tl {\tl_item:Nn \l_@@_tmpa_tl {##1}}
+      \tl_set:Nx \l_@@_tmpd_tl {\tl_item:Nn \l_@@_tmpb_tl {##1}}
+      \tl_if_eq:NNF \l_@@_tmpc_tl \l_@@_tmpd_tl
+      {
+        \bool_gset_false:N \g_@@_tmpa_bool
+      }
+      \dim_set:Nn \l_@@_tmpa_dim {\tl_item:Nn \l_@@_tmpa_tl {##1+1}}
+      \dim_set:Nn \l_@@_tmpb_dim {\tl_item:Nn \l_@@_tmpb_tl {##1+1}}
+      \dim_compare:nF { \dim_abs:n { \l_@@_tmpa_dim - \l_@@_tmpb_dim} < 0.001pt }
+      {
+        \bool_gset_false:N \g_@@_tmpa_bool
+      }
+      \dim_set:Nn \l_@@_tmpa_dim {\tl_item:Nn \l_@@_tmpa_tl {##1+2}}
+      \dim_set:Nn \l_@@_tmpb_dim {\tl_item:Nn \l_@@_tmpb_tl {##1+2}}
+      \dim_compare:nF { \dim_abs:n { \l_@@_tmpa_dim - \l_@@_tmpb_dim} < 0.001pt }
+      {
+        \bool_gset_false:N \g_@@_tmpa_bool
+      }
+    }
+  }
+  {
+    \bool_gset_false:N \g_@@_tmpa_bool
+  }
+  \group_end:
+  \bool_if:NTF \g_@@_tmpa_bool
+  {
+    \prg_return_true:
+  }
+  {
+    \prg_return_false:
+  }
+}
+\prg_generate_conditional_variant:Nnn \spath_if_eq:nn {VV, Vn, nV, vv} {TF, T, F}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Splitting Commands}
+%
+% \begin{macro}{
+% \spath_split_curve:NNnn,
+% \spath_gsplit_curve:NNnn
+% }
+% Splits a Bezier cubic into pieces, storing the pieces in the first two arguments.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_split_curve:nn #1#2
+{
+  \group_begin:
+  \tl_set_eq:NN \l_@@_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl {
+    {\tl_item:nn {#1} {2}}
+    {\tl_item:nn {#1} {3}}
+  }
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_curvetoa_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_curvetob_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {2} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {5} + (#2)^2 * \tl_item:nn {#1} {8}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {3} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {6} + (#2)^2 * \tl_item:nn {#1} {9}
+    }}
+  }
+
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_curveto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+      {
+      (1 - #2)^3 * \tl_item:nn {#1} {2} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {5} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {8} + (#2)^3 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^3 * \tl_item:nn {#1} {3} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {6} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {9} + (#2)^3 * \tl_item:nn {#1} {12}
+    }}
+  }
+
+  \tl_gclear:N \g_@@_output_tl
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_tmpa_tl
+
+  \tl_clear:N \l_@@_tmpa_tl
+  \tl_set_eq:NN \l_@@_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+      {
+      (1 - #2)^3 * \tl_item:nn {#1} {2} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {5} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {8} + (#2)^3 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^3 * \tl_item:nn {#1} {3} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {6} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {9} + (#2)^3 * \tl_item:nn {#1} {12}
+    }}
+  }
+
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_curvetoa_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {5} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {8} + (#2)^2 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {6} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {9} + (#2)^2 * \tl_item:nn {#1} {12}
+    }}
+  }
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_curvetob_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {8} + (#2) * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {9} + (#2) * \tl_item:nn {#1} {12}
+    }}
+  }
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_curveto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl {
+    {\tl_item:nn {#1} {11}}
+    {\tl_item:nn {#1} {12}}
+  }
+
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_curve:NNnn #1#2#3#4
+{
+  \@@_split_curve:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_split_curve:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_curve:NNnn #1#2#3#4
+{
+  \@@_split_curve:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_curve:NNnn {NNnV, NNVn, NNVV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_split_line:NNnn,
+% \spath_gsplit_line:NNnn
+% }
+% Splits a line segment.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_split_line:nn #1#2
+{
+  \group_begin:
+  \tl_set_eq:NN \l_@@_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl {
+    {\tl_item:nn {#1} {2}}
+    {\tl_item:nn {#1} {3}}
+  }
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_lineto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+  \tl_gclear:N \g_@@_output_tl
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_tmpa_tl
+
+  \tl_clear:N \l_@@_tmpa_tl
+  \tl_set_eq:NN \l_@@_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+  \tl_put_right:NV \l_@@_tmpa_tl \c_spath_lineto_tl
+  \tl_put_right:Nx \l_@@_tmpa_tl {
+    {\tl_item:nn {#1} {5}}
+    {\tl_item:nn {#1} {6}}
+  }
+
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_line:NNnn #1#2#3#4
+{
+  \@@_split_line:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_split_line:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_line:NNnn #1#2#3#4
+{
+  \@@_split_line:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_line:NNnn {NNnV, NNVn, NNVV}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\int_new:N \l_@@_split_int
+\int_new:N \l_@@_splitat_int
+\fp_new:N \l_@@_split_fp
+\bool_new:N \l_@@_split_bool
+\tl_new:N \l_@@_split_path_tl
+\tl_new:N \l_@@_split_patha_tl
+\tl_new:N \l_@@_split_pathb_tl
+\tl_new:N \l_@@_split_intoa_tl
+\tl_new:N \l_@@_split_intob_tl
+\dim_new:N \l_@@_splitx_dim
+\dim_new:N \l_@@_splity_dim
+%    \end{macrocode}
+%
+% \begin{macro}{
+% \spath_split_at:NNnn,
+% \spath_split_at:Nnn,
+% \spath_split_at:Nn,
+% \spath_gsplit_at:NNnn
+% \spath_gsplit_at:Nnn,
+% \spath_gsplit_at:Nn
+% }
+% Split a path according to the parameter generated by the intersection routine.
+% The versions with two \texttt{N} arguments stores the two parts in two macros, the version with a single \texttt{N} joins them back into a single path (as separate components).
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_split_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l_@@_splitat_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l_@@_split_fp {#2 - floor(#2)}
+
+  % Is split point near one end or other of a component?
+  \fp_compare:nT
+  {
+    \l_@@_split_fp < 0.01
+  }
+  {
+    % Near the start, so we'll place it at the start
+    \fp_set:Nn \l_@@_split_fp {0}
+  }
+  \fp_compare:nT
+  {
+    \l_@@_split_fp > 0.99
+  }
+  {
+    % Near the end, so we'll place it at the end
+    \fp_set:Nn \l_@@_split_fp {0}
+    \int_incr:N \l_@@_splitat_int
+  }
+  
+  \int_zero:N \l_@@_split_int
+  \bool_set_true:N \l_@@_split_bool
+
+  \tl_set:Nn \l_@@_split_path_tl {#1}
+  \tl_clear:N \l_@@_split_patha_tl
+
+  \dim_zero:N \l_@@_splitx_dim
+  \dim_zero:N \l_@@_splity_dim
+
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l_@@_split_path_tl
+    ||
+    \int_compare_p:n { \l_@@_splitat_int == \l_@@_split_int  }
+  }
+  {
+    \tl_set:Nx \l_@@_tmpc_tl {\tl_head:N \l_@@_split_path_tl}
+    \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+    \tl_case:Nn \l_@@_tmpc_tl
+    {
+      \c_spath_lineto_tl
+      {
+        \int_incr:N \l_@@_split_int
+      }
+      \c_spath_curvetoa_tl
+      {
+        \int_incr:N \l_@@_split_int
+      }
+    }
+    \int_compare:nT { \l_@@_split_int < \l_@@_splitat_int  }
+    {
+      \tl_put_right:NV \l_@@_split_patha_tl \l_@@_tmpc_tl
+      
+      \tl_put_right:Nx \l_@@_split_patha_tl
+      {{ \tl_head:N \l_@@_split_path_tl }}
+      \dim_set:Nn \l_@@_splitx_dim {\tl_head:N \l_@@_split_path_tl}
+      \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+      
+      \tl_put_right:Nx \l_@@_split_patha_tl
+      {{ \tl_head:N \l_@@_split_path_tl }}
+      \dim_set:Nn \l_@@_splity_dim {\tl_head:N \l_@@_split_path_tl}
+      \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+      
+    }
+  }
+
+  \tl_clear:N \l_@@_split_pathb_tl
+  \tl_put_right:NV \l_@@_split_pathb_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l_@@_split_pathb_tl
+  {
+    {\dim_use:N \l_@@_splitx_dim}
+    {\dim_use:N \l_@@_splity_dim}
+  }
+
+  \fp_compare:nTF
+  {
+    \l_@@_split_fp == 0
+  }
+  {
+    \tl_set_eq:NN \l_@@_split_intob_tl \l_@@_split_pathb_tl
+    \tl_if_empty:NF \l_@@_split_path_tl
+    {
+      \tl_put_right:NV \l_@@_split_intob_tl \l_@@_tmpc_tl
+      \tl_put_right:NV \l_@@_split_intob_tl \l_@@_split_path_tl
+    }
+  }
+  {
+
+    \tl_case:Nn \l_@@_tmpc_tl
+    {
+      \c_spath_lineto_tl
+      {
+        \tl_put_right:NV \l_@@_split_pathb_tl \l_@@_tmpc_tl
+        \tl_put_right:Nx \l_@@_split_pathb_tl
+        {{ \tl_head:N \l_@@_split_path_tl }}
+        \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+      
+        \tl_put_right:Nx \l_@@_split_pathb_tl
+        {{ \tl_head:N \l_@@_split_path_tl }}
+        \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+
+        \spath_split_line:NNVV
+        \l_@@_split_intoa_tl
+        \l_@@_split_intob_tl
+        \l_@@_split_pathb_tl
+        \l_@@_split_fp
+
+        \prg_replicate:nn {3} {
+          \tl_set:Nx \l_@@_split_intoa_tl {\tl_tail:N \l_@@_split_intoa_tl}
+        }
+
+        \tl_put_right:NV \l_@@_split_patha_tl \l_@@_split_intoa_tl
+        \tl_put_right:NV \l_@@_split_intob_tl \l_@@_split_path_tl
+      }
+      \c_spath_curvetoa_tl
+      {
+        \tl_put_right:NV \l_@@_split_pathb_tl \l_@@_tmpc_tl
+        \tl_put_right:Nx \l_@@_split_pathb_tl
+        {{ \tl_head:N \l_@@_split_path_tl }}
+        \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+      
+        \tl_put_right:Nx \l_@@_split_pathb_tl
+        {{ \tl_head:N \l_@@_split_path_tl }}
+        \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+      
+        \prg_replicate:nn {2} {
+        
+          \tl_put_right:Nx \l_@@_split_pathb_tl
+          { \tl_head:N \l_@@_split_path_tl }
+          \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+        
+          \tl_put_right:Nx \l_@@_split_pathb_tl
+          {{ \tl_head:N \l_@@_split_path_tl }}
+          \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+      
+          \tl_put_right:Nx \l_@@_split_pathb_tl
+          {{ \tl_head:N \l_@@_split_path_tl }}
+          \tl_set:Nx \l_@@_split_path_tl {\tl_tail:N \l_@@_split_path_tl }
+        }
+
+        \spath_split_curve:NNVV
+        \l_@@_split_intoa_tl
+        \l_@@_split_intob_tl
+        \l_@@_split_pathb_tl \l_@@_split_fp
+
+        \prg_replicate:nn {3} {
+          \tl_set:Nx \l_@@_split_intoa_tl {\tl_tail:N \l_@@_split_intoa_tl}
+        }
+
+        \tl_put_right:NV \l_@@_split_patha_tl \l_@@_split_intoa_tl
+        \tl_put_right:NV \l_@@_split_intob_tl \l_@@_split_path_tl
+      }
+    }
+  }
+
+  \tl_gclear:N \g_@@_output_tl
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_split_patha_tl
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_split_intob_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_at:NNnn #1#2#3#4
+{
+  \@@_split_at:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at:NNnn {NNVn, NNVV, NNnV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:NNnn #1#2#3#4
+{
+  \@@_split_at:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at:NNnn {NNVn, NNVV, NNnV}
+%    \end{macrocode}
+%
+% 
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_split_at:Nnn #1#2#3
+{
+  \@@_split_at:nn {#2}{#3}
+  \tl_set:Nx #1 {\tl_item:Nn \g_@@_output_tl {1} \tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_split_at:Nn #1#2
+{
+  \spath_split_at:NVn #1#1{#2}
+}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:Nnn #1#2#3
+{
+  \@@_split_at:nn {#2}{#3}
+  \tl_gset:Nx #1 {\tl_item:Nn \g_@@_output_tl {1} \tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:Nn #1#2
+{
+  \spath_gsplit_at:NVn #1#1{#2}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Shortening Paths}
+%
+% This code relates to shortening paths.
+% For curved paths, the routine uses the derivative at the end to figure out how far back to shorten.
+% This means that the actual length that it shortens by is approximate, but it is guaranteed to be along its length.
+%
+% As in the previous section, there are various versions.
+% In particular, there are versions where the path can be specified by a macro and is saved back into that macro.
+%
+%    \begin{macrocode}
+\tl_new:N \l_@@_shorten_fa_tl
+\tl_new:N \l_@@_shorten_path_tl
+\tl_new:N \l_@@_shorten_last_tl
+\tl_new:N \l_@@_shorten_lasta_tl
+\tl_new:N \l_@@_shorten_lastb_tl
+\int_new:N \l_@@_shorten_int
+\fp_new:N \l_@@_shorten_x_fp
+\fp_new:N \l_@@_shorten_y_fp
+\fp_new:N \l_@@_shorten_len_fp
+%    \end{macrocode}
+%
+% \begin{macro}{
+% \spath_shorten_at_end:Nnn
+% }
+% This macro shortens a path from the end by a dimension.
+%
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_shorten_at_end:nn #1#2
+{
+  \int_compare:nTF
+  {
+    \tl_count:n {#1} > 3
+  }
+  {
+    \group_begin:
+    \tl_set:Nn \l_@@_shorten_path_tl {#1}
+    \tl_reverse:N \l_@@_shorten_path_tl
+
+    \tl_set:Nx \l_@@_shorten_fa_tl {\tl_item:Nn \l_@@_shorten_path_tl {3}}
+
+    \tl_clear:N \l_@@_shorten_last_tl
+    \tl_if_eq:NNTF \l_@@_shorten_fa_tl \c_spath_curveto_tl
+    {
+      \int_set:Nn \l_@@_shorten_int {3}
+    }
+    {
+      \int_set:Nn \l_@@_shorten_int {1}
+    }
+
+    \prg_replicate:nn { \l_@@_shorten_int }
+    {
+      \tl_put_right:Nx \l_@@_shorten_last_tl
+      {
+        {\tl_head:N \l_@@_shorten_path_tl}
+      }
+      \tl_set:Nx \l_@@_shorten_path_tl {\tl_tail:N \l_@@_shorten_path_tl}
+      \tl_put_right:Nx \l_@@_shorten_last_tl
+      {
+        {\tl_head:N \l_@@_shorten_path_tl}
+      }
+      \tl_set:Nx \l_@@_shorten_path_tl {\tl_tail:N \l_@@_shorten_path_tl}
+      \tl_put_right:Nx \l_@@_shorten_last_tl
+      {
+        \tl_head:N \l_@@_shorten_path_tl
+      }
+      \tl_set:Nx \l_@@_shorten_path_tl {\tl_tail:N \l_@@_shorten_path_tl}
+    }
+
+    \tl_put_right:Nx \l_@@_shorten_last_tl
+    {
+      {\tl_item:Nn \l_@@_shorten_path_tl {1}}
+      {\tl_item:Nn \l_@@_shorten_path_tl {2}}
+    }
+    \tl_put_right:NV \l_@@_shorten_last_tl \c_spath_moveto_tl
+    
+    \tl_reverse:N \l_@@_shorten_path_tl
+
+    \fp_set:Nn \l_@@_shorten_x_fp
+    {
+      \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {4}}
+      -
+      \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {1}}
+    }
+  
+    \fp_set:Nn \l_@@_shorten_y_fp
+    {
+      \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {5}}
+      -
+      \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {2}}
+    }
+
+    \fp_set:Nn \l_@@_shorten_len_fp
+    {
+      sqrt( \l_@@_shorten_x_fp * \l_@@_shorten_x_fp +  \l_@@_shorten_y_fp *  \l_@@_shorten_y_fp )
+    }
+
+    \fp_compare:nTF
+    {
+      \l_@@_shorten_len_fp > #2
+    }
+    {
+  
+      \fp_set:Nn \l_@@_shorten_len_fp
+      {
+        (\l_@@_shorten_len_fp - #2)/ \l_@@_shorten_len_fp
+      }
+
+      \tl_reverse:N \l_@@_shorten_last_tl
+
+      \tl_if_eq:NNTF \l_@@_shorten_fa_tl \c_spath_curveto_tl
+      {
+        \fp_set:Nn \l_@@_shorten_len_fp
+        {
+          1 - (1 -\l_@@_shorten_len_fp)/3
+        }
+        \spath_split_curve:NNVV
+        \l_@@_shorten_lasta_tl
+        \l_@@_shorten_lastb_tl
+        \l_@@_shorten_last_tl
+        \l_@@_shorten_len_fp
+      }
+      {
+        \spath_split_line:NNVV
+        \l_@@_shorten_lasta_tl
+        \l_@@_shorten_lastb_tl
+        \l_@@_shorten_last_tl
+        \l_@@_shorten_len_fp
+      }
+
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l_@@_shorten_lasta_tl {\tl_tail:N \l_@@_shorten_lasta_tl}
+      }
+
+      \tl_put_right:NV \l_@@_shorten_path_tl \l_@@_shorten_lasta_tl
+
+    }
+    {
+
+      \int_compare:nT
+      {
+        \tl_count:N \l_@@_shorten_path_tl > 3
+      }
+      {
+        \dim_set:Nn \l_@@_tmpa_dim {\fp_to_dim:n {#2 - \l_@@_shorten_len_fp } }
+        \spath_shorten_at_end:NV \l_@@_shorten_path_tl \l_@@_tmpa_dim
+      }
+    }
+
+    \tl_gset_eq:NN \g_@@_output_tl \l_@@_shorten_path_tl
+    \group_end:
+  }
+  {
+    \tl_gset:Nn \g_@@_output_tl {#1}
+  }
+}
+\cs_new_protected_nopar:Npn \spath_shorten_at_end:Nnn #1#2#3
+{
+  \@@_shorten_at_end:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_shorten_at_end:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_shorten_at_end:Nn #1#2
+{
+  \spath_shorten_at_end:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_shorten_at_end:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_end:Nnn #1#2#3
+{
+  \@@_shorten_at_end:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gshorten_at_end:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_end:Nn #1#2
+{
+  \spath_gshorten_at_end:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gshorten_at_end:Nn {cn, cV, NV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_shorten_at_start:Nnn,
+% \spath_shorten_at_start:Nn,
+% \spath_gshorten_at_start:Nnn,
+% \spath_gshorten_at_start:Nn
+% }
+% 
+% This macro shortens a path from the start by a dimension.
+%
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_shorten_at_start:nn #1#2
+{
+  \int_compare:nTF
+  {
+    \tl_count:n {#1} > 3
+  }
+  {
+  \group_begin:
+  \tl_set:Nn \l_@@_shorten_path_tl {#1}
+
+  \tl_set:Nx \l_@@_shorten_fa_tl {\tl_item:Nn \l_@@_shorten_path_tl {4}}
+
+    \tl_clear:N \l_@@_shorten_last_tl
+
+  \tl_if_eq:NNTF \l_@@_shorten_fa_tl \c_spath_curvetoa_tl
+  {
+    \int_set:Nn \l_@@_shorten_int {3}
+  }
+  {
+    \int_set:Nn \l_@@_shorten_int {1}
+  }
+
+  \tl_set_eq:NN \l_@@_shorten_last_tl \c_spath_moveto_tl
+  \tl_set:Nx \l_@@_shorten_path_tl {\tl_tail:N \l_@@_shorten_path_tl }
+
+  \prg_replicate:nn { \l_@@_shorten_int }
+  {
+    \@@_tl_put_right_braced:Nx \l_@@_shorten_last_tl {\tl_item:Nn \l_@@_shorten_path_tl {1}}
+    \@@_tl_put_right_braced:Nx \l_@@_shorten_last_tl {\tl_item:Nn \l_@@_shorten_path_tl {2}}
+    \tl_put_right:Nx \l_@@_shorten_last_tl {\tl_item:Nn \l_@@_shorten_path_tl {3}}
+
+    \prg_replicate:nn {3}
+    {
+      \tl_set:Nx \l_@@_shorten_path_tl {\tl_tail:N \l_@@_shorten_path_tl }
+    }
+  }
+  \@@_tl_put_right_braced:Nx \l_@@_shorten_last_tl {\tl_item:Nn \l_@@_shorten_path_tl {1}}
+  \@@_tl_put_right_braced:Nx \l_@@_shorten_last_tl {\tl_item:Nn \l_@@_shorten_path_tl {2}}
+
+  \fp_set:Nn \l_@@_shorten_x_fp
+  {
+    \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {5}}
+    -
+    \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {2}}
+  }
+  
+  \fp_set:Nn \l_@@_shorten_y_fp
+  {
+    \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {6}}
+    -
+    \dim_to_fp:n {\tl_item:Nn \l_@@_shorten_last_tl {3}}
+  }
+
+  \fp_set:Nn \l_@@_shorten_len_fp
+  {
+    sqrt( \l_@@_shorten_x_fp * \l_@@_shorten_x_fp +  \l_@@_shorten_y_fp *  \l_@@_shorten_y_fp )
+  }
+
+  \fp_compare:nTF
+  {
+    \l_@@_shorten_len_fp > #2
+  }
+  {
+  
+    \fp_set:Nn \l_@@_shorten_len_fp
+    {
+      #2/ \l_@@_shorten_len_fp
+    }
+
+    \tl_if_eq:NNTF \l_@@_shorten_fa_tl \c_spath_curvetoa_tl
+    {
+      \fp_set:Nn \l_@@_shorten_len_fp
+      {
+        \l_@@_shorten_len_fp/3
+      }
+      \spath_split_curve:NNVV
+      \l_@@_shorten_lasta_tl
+      \l_@@_shorten_lastb_tl
+      \l_@@_shorten_last_tl
+      \l_@@_shorten_len_fp
+    }
+    {
+      \spath_split_line:NNVV
+      \l_@@_shorten_lasta_tl
+      \l_@@_shorten_lastb_tl
+      \l_@@_shorten_last_tl
+      \l_@@_shorten_len_fp
+    }
+
+    \prg_replicate:nn {2}
+    {
+      \tl_set:Nx \l_@@_shorten_path_tl {\tl_tail:N \l_@@_shorten_path_tl}
+    }
+
+    \tl_put_left:NV \l_@@_shorten_path_tl \l_@@_shorten_lastb_tl
+
+  }
+  {
+
+    \tl_put_left:NV \l_@@_shorten_path_tl \c_spath_moveto_tl
+    
+    \int_compare:nT
+    {
+      \tl_count:N \l_@@_shorten_path_tl > 3
+    }
+    {
+      \dim_set:Nn \l_@@_tmpa_dim {\fp_to_dim:n {#2 - \l_@@_shorten_len_fp } }
+      \spath_shorten_at_start:NV \l_@@_shorten_path_tl \l_@@_tmpa_dim
+    }
+  }
+
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_shorten_path_tl
+  \group_end:
+  }
+  {
+    \tl_gset:Nn \g_@@_output_tl {#1}
+  }
+}
+\cs_new_protected_nopar:Npn \spath_shorten_at_start:Nnn #1#2#3
+{
+  \@@_shorten_at_start:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_shorten_at_start:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_shorten_at_start:Nn #1#2
+{
+  \spath_shorten_at_start:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_shorten_at_start:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_start:Nnn #1#2#3
+{
+  \@@_shorten_at_start:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gshorten_at_start:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_start:Nn #1#2
+{
+  \spath_gshorten_at_start:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gshorten_at_start:Nn {cn, cV, NV}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Points on a Path}
+%
+% \begin{macro}{
+% \spath_point_at:Nnn,
+% \spath_gpoint_at:Nnn,
+% }
+%
+% Get the location of a point on a path, using the same location specification as the intersection library.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_point_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l_@@_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l_@@_tmpa_fp {#2 - floor(#2)}
+
+  \spath_segments_to_seq:Nn \l_@@_tmpa_seq {#1}
+
+  \int_compare:nTF
+  {
+    \l_@@_tmpa_int < 1
+  }
+  {
+    \spath_initialpoint:Nn \l_@@_tmpc_tl {#1}
+  }
+  {
+    \int_compare:nTF
+    {
+      \l_@@_tmpa_int > \seq_count:N \l_@@_tmpa_seq
+    }
+    {
+      \spath_finalpoint:Nn \l_@@_tmpc_tl {#1}
+    }
+    {
+  
+      \tl_set:Nx \l_@@_tmpa_tl {\seq_item:Nn \l_@@_tmpa_seq { \l_@@_tmpa_int} }
+
+      \int_compare:nTF
+      {
+        \tl_count:N \l_@@_tmpa_tl > 3
+      }
+      {
+        \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_tmpa_tl {4}}
+      }
+      {
+        \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_tmpa_tl {1}}
+      }
+
+      \tl_clear:N \l_@@_tmpc_tl
+  
+      \tl_case:Nn \l_@@_tmpb_tl
+      {
+        \c_spath_moveto_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {
+              \tl_item:Nn \l_@@_tmpa_tl {2}
+            }
+            {
+              \tl_item:Nn \l_@@_tmpa_tl {3}
+            }
+          }
+        }
+        
+        \c_spath_lineto_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l_@@_tmpa_fp) * ( \tl_item:Nn \l_@@_tmpa_tl {2} )
+                +
+                \l_@@_tmpa_fp * ( \tl_item:Nn \l_@@_tmpa_tl {5} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                (1 - \l_@@_tmpa_fp) * ( \tl_item:Nn \l_@@_tmpa_tl {3} )
+                +
+                \l_@@_tmpa_fp * ( \tl_item:Nn \l_@@_tmpa_tl {6} )
+              }
+            }
+          }
+        }
+
+        \c_spath_closepath_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l_@@_tmpa_fp) * ( \tl_item:Nn \l_@@_tmpa_tl {2} )
+                +
+                \l_@@_tmpa_fp * ( \tl_item:Nn \l_@@_tmpa_tl {5} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                (1 - \l_@@_tmpa_fp) * ( \tl_item:Nn \l_@@_tmpa_tl {3} )
+                +
+                \l_@@_tmpa_fp * ( \tl_item:Nn \l_@@_tmpa_tl {6} )
+              }
+            }
+          }
+        }
+    
+        \c_spath_curvetoa_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l_@@_tmpa_fp)^3 * \tl_item:Nn \l_@@_tmpa_tl {2} + 3 * (1 - \l_@@_tmpa_fp)^2 * (\l_@@_tmpa_fp) * \tl_item:Nn \l_@@_tmpa_tl {5} + 3 * (1 - \l_@@_tmpa_fp) * (\l_@@_tmpa_fp)^2 * \tl_item:Nn \l_@@_tmpa_tl {8} + (\l_@@_tmpa_fp)^3 * \tl_item:Nn \l_@@_tmpa_tl {11}
+            }}
+            {\fp_to_dim:n
+              {
+                (1 - \l_@@_tmpa_fp)^3 * \tl_item:Nn \l_@@_tmpa_tl {3} + 3 * (1 - \l_@@_tmpa_fp)^2 * (\l_@@_tmpa_fp) * \tl_item:Nn \l_@@_tmpa_tl {6} + 3 * (1 - \l_@@_tmpa_fp) * (\l_@@_tmpa_fp)^2 * \tl_item:Nn \l_@@_tmpa_tl {9} + (\l_@@_tmpa_fp)^3 * \tl_item:Nn \l_@@_tmpa_tl {12}
+            }}
+          }
+        }
+      }
+    }
+  }
+
+  \tl_gclear:N \g_@@_output_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpc_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_point_at:Nnn #1#2#3
+{
+  \@@_point_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_point_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \spath_gpoint_at:Nnn #1#2#3
+{
+  \@@_point_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gpoint_at:Nnn {NVn, NVV, NnV}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_tangent_at:Nnn,
+% \spath_gtangent_at:Nnn,
+% }
+%
+% Get the tangent at a point on a path, using the same location specification as the intersection library.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_tangent_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l_@@_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l_@@_tmpa_fp {#2 - floor(#2)}
+
+  \spath_segments_to_seq:Nn \l_@@_tmpa_seq {#1}
+
+  \int_compare:nTF
+  {
+    \l_@@_tmpa_int < 1
+  }
+  {
+    \spath_initialpoint:Nn \l_@@_tmpc_tl {#1}
+  }
+  {
+    \int_compare:nTF
+    {
+      \l_@@_tmpa_int > \seq_count:N \l_@@_tmpa_seq
+    }
+    {
+      \spath_finalpoint:Nn \l_@@_tmpc_tl {#1}
+    }
+    {
+  
+      \tl_set:Nx \l_@@_tmpa_tl {\seq_item:Nn \l_@@_tmpa_seq { \l_@@_tmpa_int} }
+
+      \int_compare:nTF
+      {
+        \tl_count:N \l_@@_tmpa_tl > 3
+      }
+      {
+        \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_tmpa_tl {4}}
+      }
+      {
+        \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_tmpa_tl {1}}
+      }
+
+      \tl_clear:N \l_@@_tmpc_tl
+  
+      \tl_case:Nn \l_@@_tmpb_tl
+      {
+        \c_spath_moveto_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {
+              \tl_item:Nn \l_@@_tmpa_tl {2}
+            }
+            {
+              \tl_item:Nn \l_@@_tmpa_tl {3}
+            }
+          }
+        }
+        
+        \c_spath_lineto_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l_@@_tmpa_tl {5} )
+                -
+                ( \tl_item:Nn \l_@@_tmpa_tl {2} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l_@@_tmpa_tl {6} )
+                -
+                ( \tl_item:Nn \l_@@_tmpa_tl {3} )
+              }
+            }
+          }
+        }
+
+        \c_spath_closepath_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l_@@_tmpa_tl {5} )
+                -
+                ( \tl_item:Nn \l_@@_tmpa_tl {2} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l_@@_tmpa_tl {6} )
+                -
+                ( \tl_item:Nn \l_@@_tmpa_tl {3} )
+              }
+            }
+          }
+        }
+    
+        \c_spath_curvetoa_tl
+        {
+          \tl_set:Nx \l_@@_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                3*(1 - \l_@@_tmpa_fp)^2 * (\tl_item:Nn \l_@@_tmpa_tl {5} - \tl_item:Nn \l_@@_tmpa_tl {2})
+                + 6 * (1 - \l_@@_tmpa_fp) * (\l_@@_tmpa_fp) *  (\tl_item:Nn \l_@@_tmpa_tl {8} - \tl_item:Nn \l_@@_tmpa_tl {5})
+                + 3*(\l_@@_tmpa_fp)^2 * (\tl_item:Nn \l_@@_tmpa_tl {11} - \tl_item:Nn \l_@@_tmpa_tl {8})
+              }
+            }
+            {\fp_to_dim:n
+              {
+                3*(1 - \l_@@_tmpa_fp)^2 * (\tl_item:Nn \l_@@_tmpa_tl {6} - \tl_item:Nn \l_@@_tmpa_tl {3})
+                + 6 * (1 - \l_@@_tmpa_fp) * (\l_@@_tmpa_fp) *  (\tl_item:Nn \l_@@_tmpa_tl {9} - \tl_item:Nn \l_@@_tmpa_tl {6})
+                + 3*(\l_@@_tmpa_fp)^2 * (\tl_item:Nn \l_@@_tmpa_tl {12} - \tl_item:Nn \l_@@_tmpa_tl {9})
+            }}
+          }
+        }
+      }
+    }
+  }
+
+  \tl_gclear:N \g_@@_output_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpc_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_tangent_at:Nnn #1#2#3
+{
+  \@@_tangent_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_tangent_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \spath_gtangent_at:Nnn #1#2#3
+{
+  \@@_tangent_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gtangent_at:Nnn {NVn, NVV, NnV}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_transformation_at:Nnn,
+% \spath_gtransformation_at:Nnn
+% }
+% Gets a transformation that will align to a point on the path with the x-axis along the path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_transformation_at:nn #1#2
+{
+  \group_begin:
+  \tl_clear:N \l_@@_tmpa_tl
+  \@@_tangent_at:nn {#1}{#2}
+  \tl_set_eq:NN \l_@@_tmpb_tl \g_@@_output_tl
+  \fp_set:Nn \l_@@_tmpa_fp { sqrt( (\tl_item:Nn \l_@@_tmpb_tl {1})^2 +  (\tl_item:Nn \l_@@_tmpb_tl {2})^2 ) }
+  \fp_compare:nTF {\l_@@_tmpa_fp = 0}
+  {
+    \fp_set:Nn \l_@@_tmpa_fp {1}
+    \fp_set:Nn \l_@@_tmpb_fp {0}
+  }
+  {
+    \fp_set:Nn \l_@@_tmpb_fp { (\tl_item:Nn \l_@@_tmpb_tl {2}) / \l_@@_tmpa_fp }
+    \fp_set:Nn \l_@@_tmpa_fp { (\tl_item:Nn \l_@@_tmpb_tl {1}) / \l_@@_tmpa_fp }
+  }
+  \tl_set:Nx \l_@@_tmpa_tl
+  {
+    { \fp_to_decimal:n { \l_@@_tmpa_fp } }
+    { \fp_to_decimal:n { \l_@@_tmpb_fp } }
+    { \fp_to_decimal:n {- \l_@@_tmpb_fp } }
+    { \fp_to_decimal:n { \l_@@_tmpa_fp } }
+  }
+  \@@_point_at:nn {#1}{#2}
+  \tl_put_right:NV \l_@@_tmpa_tl \g_@@_output_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_transformation_at:Nnn #1#2#3
+{
+  \@@_transformation_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_transformation_at:Nnn {NVn, NVV, NnV, NvV}
+\cs_new_protected_nopar:Npn \spath_gtransformation_at:Nnn #1#2#3
+{
+  \@@_transformation_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gtransformation_at:Nnn {NVn, NVV, NnV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Intersection Routines}
+%
+% Note: I'm not consistent with number schemes.
+% The intersection library is 0-based, but the user interface is 1-based (since if we ``count'' in a \Verb+\foreach+ then it starts at 1).
+% This should be more consistent.
+%
+%    \begin{macrocode}
+\tl_new:N \l_@@_split_path_a_tl
+\tl_new:N \l_@@_split_path_b_tl
+\tl_new:N \l_@@_split_path_a_start_tl
+\tl_new:N \l_@@_split_path_b_start_tl
+\tl_new:N \l_@@_split_path_a_end_tl
+\tl_new:N \l_@@_split_path_b_end_tl
+\tl_new:N \l_@@_split_path_a_final_tl
+\tl_new:N \l_@@_split_path_b_final_tl
+
+\tl_new:N \l_@@_split_prev_first_tl
+\tl_new:N \l_@@_split_prev_second_tl
+
+\seq_new:N \l_@@_split_first_seq
+\seq_new:N \l_@@_split_second_seq
+
+\int_new:N \l_@@_split_segment_int
+%    \end{macrocode}
+%
+% \begin{macro}{
+% \spath_intersect:NN,
+% \spath_intersect:nn,
+% }
+% Pass two spaths to pgf's intersection routine.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_intersect:NN #1#2
+{
+  \pgfintersectionofpaths%
+  {%
+    \pgfsetpath #1
+  }{%
+    \pgfsetpath #2
+  }
+}
+\tl_new:N \l_@@_intersecta_tl
+\tl_new:N \l_@@_intersectb_tl
+\cs_new_protected_nopar:Npn \spath_intersect:nn #1#2
+{
+  \tl_set:Nn \l_@@_intersecta_tl {#1}
+  \tl_set:Nn \l_@@_intersectb_tl {#2}
+  \spath_intersect:NN \l_@@_intersecta_tl \l_@@_intersectb_tl
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_split_at_intersections:NNnn,
+% \spath_split_at_intersections:NN,
+% \spath_gsplit_at_intersections:NNnn,
+% \spath_gsplit_at_intersections:NN
+% }
+% Given two paths, split them at points where they intersect and store them in the macros.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_split_at_intersections:nn #1#2
+{
+  \group_begin:
+
+  % Clear some token lists and sequences
+  \tl_clear:N \l_@@_split_path_a_final_tl
+  \tl_clear:N \l_@@_split_path_b_final_tl
+  \seq_clear:N \l_@@_split_first_seq
+  \seq_clear:N \l_@@_split_second_seq
+  
+  \pgfintersectionsortbyfirstpath
+  % Find the intersections of these segments
+  \tl_set:Nn \l_@@_split_path_a_tl {#1}
+  \tl_set:Nn \l_@@_split_path_b_tl {#2}
+  % Remove empty components
+%  \spath_path_remove_empty_components:N \l_@@_split_path_a_tl
+%  \spath_path_remove_empty_components:N \l_@@_split_path_b_tl
+
+  \spath_intersect:NN \l_@@_split_path_a_tl \l_@@_split_path_b_tl
+  
+  % If we get intersections
+  \int_compare:nT {\pgfintersectionsolutions > 0}
+  {
+    % Find the times of the intersections on each path
+    \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+    {
+    \pgfintersectiongetsolutiontimes{##1}{\l_@@_split_first_tl}{\l_@@_split_second_tl}
+      \seq_put_left:NV \l_@@_split_first_seq \l_@@_split_first_tl
+    }
+  }
+
+  \spath_intersect:NN \l_@@_split_path_b_tl \l_@@_split_path_a_tl
+  
+  % If we get intersections
+  \int_compare:nT {\pgfintersectionsolutions > 0}
+  {
+    % Find the times of the intersections on each path
+    \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+    {
+    \pgfintersectiongetsolutiontimes{##1}{\l_@@_split_first_tl}{\l_@@_split_second_tl}
+      \seq_put_left:NV \l_@@_split_second_seq \l_@@_split_first_tl
+    }
+  }
+
+  \tl_set:Nn \l_@@_split_prev_first_tl {-1}
+
+  \seq_map_inline:Nn \l_@@_split_first_seq
+  {
+    \tl_set:Nn \l_@@_split_first_tl {##1}
+    
+    \tl_set_eq:NN \l_@@_tmpa_tl \l_@@_split_first_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l_@@_split_first_tl) }
+      =
+      \fp_to_int:n {floor( \l_@@_split_prev_first_tl) }
+    }
+    {
+      \tl_set:Nx \l_@@_split_first_tl
+      {
+        \fp_eval:n {
+          floor( \l_@@_split_first_tl )
+          +
+          ( \l_@@_split_first_tl - floor( \l_@@_split_first_tl) )
+          /
+          ( \l_@@_split_prev_first_tl - floor( \l_@@_split_prev_first_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l_@@_split_prev_first_tl \l_@@_tmpa_tl
+    
+    \spath_split_at:NNVV \l_@@_split_path_a_start_tl \l_@@_split_path_a_end_tl  \l_@@_split_path_a_tl \l_@@_split_first_tl
+    
+    \tl_put_left:NV \l_@@_split_path_a_final_tl \l_@@_split_path_a_end_tl
+    \tl_set_eq:NN \l_@@_split_path_a_tl \l_@@_split_path_a_start_tl
+    
+  }
+    
+  \tl_set:Nn \l_@@_split_prev_second_tl {-1}
+
+  \seq_map_inline:Nn \l_@@_split_second_seq
+  {
+    \tl_set:Nn \l_@@_split_second_tl {##1}
+    
+    \tl_set_eq:NN \l_@@_tmpa_tl \l_@@_split_second_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l_@@_split_second_tl) }
+      =
+      \fp_to_int:n {floor( \l_@@_split_prev_second_tl) }
+    }
+    {
+      \tl_set:Nx \l_@@_split_second_tl
+      {
+        \fp_eval:n {
+          floor( \l_@@_split_second_tl )
+          +
+          ( \l_@@_split_second_tl - floor( \l_@@_split_second_tl) )
+          /
+          ( \l_@@_split_prev_second_tl - floor( \l_@@_split_prev_second_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l_@@_split_prev_second_tl \l_@@_tmpa_tl
+
+    \spath_split_at:NNVV \l_@@_split_path_b_start_tl \l_@@_split_path_b_end_tl  \l_@@_split_path_b_tl\l_@@_split_second_tl
+      
+    \tl_put_left:NV \l_@@_split_path_b_final_tl \l_@@_split_path_b_end_tl
+    \tl_set_eq:NN \l_@@_split_path_b_tl \l_@@_split_path_b_start_tl
+    
+  }
+
+  \tl_put_left:NV \l_@@_split_path_a_final_tl \l_@@_split_path_a_tl
+  \tl_put_left:NV \l_@@_split_path_b_final_tl \l_@@_split_path_b_tl
+
+  \tl_if_empty:NT \l_@@_split_path_a_final_tl
+  {
+    \tl_set_eq:NN \l_@@_split_path_a_final_tl \l_@@_split_path_a_tl
+  }
+  \tl_if_empty:NT \l_@@_split_path_b_final_tl
+  {
+    \tl_set_eq:NN \l_@@_split_path_b_final_tl \l_@@_split_path_b_tl
+  }
+  
+  \spath_remove_empty_components:N \l_@@_split_path_a_final_tl
+  \spath_remove_empty_components:N \l_@@_split_path_b_final_tl
+  
+  \tl_gclear:N \g_@@_output_tl
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_split_path_a_final_tl
+  \@@_tl_gput_right_braced:NV \g_@@_output_tl \l_@@_split_path_b_final_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_at_intersections:NNnn #1#2#3#4
+{
+  \@@_split_at_intersections:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_new_protected_nopar:Npn \spath_split_at_intersections:NN #1#2
+{
+  \spath_split_at_intersections:NNVV #1#2#1#2
+}
+\cs_generate_variant:Nn \spath_split_at_intersections:NN {cc}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NNnn #1#2#3#4
+{
+  \@@_split_at_intersections:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g_@@_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g_@@_output_tl {2}}
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NN #1#2
+{
+  \spath_gsplit_at_intersections:NNVV #1#2#1#2
+}
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NN {cc}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_split_at_self_intersections:Nn,
+% \spath_split_at_self_intersections:N,
+% \spath_gsplit_at_self_intersections:Nn,
+% \spath_gsplit_at_self_intersections:N,
+% }
+% Given a path, split it at points where it self-intersects and store in the given macro.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_split_at_self_intersections:n #1
+{
+  \group_begin:
+  
+  % Copy the path
+  \tl_set:Nn \l_@@_split_path_b_tl {#1}
+
+  % Open the path
+  \spath_open:N \l_@@_split_path_b_tl
+  % Remove empty components
+  \spath_remove_empty_components:N \l_@@_split_path_b_tl
+  % Make a copy for later
+  \tl_set_eq:NN \l_@@_split_path_b_final_tl \l_@@_split_path_b_tl
+  
+  % Clear some token lists and sequences
+  \tl_clear:N \l_@@_split_path_a_tl
+  \seq_clear:N \l_@@_split_first_seq
+  \int_zero:N \l_@@_split_segment_int
+
+  \pgfintersectionsortbyfirstpath
+
+  \bool_do_until:nn
+  {
+    \int_compare_p:n
+    {
+      \tl_count:N \l_@@_split_path_b_tl < 4
+    }
+  }
+  {
+    \tl_clear:N \l_@@_split_path_a_tl
+    \tl_put_right:Nx \l_@@_split_path_a_tl
+    {
+      \tl_item:Nn \l_@@_split_path_b_tl {1}
+      {\tl_item:Nn \l_@@_split_path_b_tl {2}}
+      {\tl_item:Nn \l_@@_split_path_b_tl {3}}
+    }
+
+    \tl_set:Nx \l_@@_tmpa_tl { \tl_item:Nn \l_@@_split_path_b_tl {4} }
+
+    \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+
+    \int_zero:N \l_@@_tmpa_int
+    
+    \tl_case:Nn \l_@@_tmpa_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_clear:N \l_@@_split_path_a_tl
+        \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+        \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+        \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+      }
+      \c_spath_lineto_tl
+      {
+        \int_set:Nn \l_@@_tmpa_int {1}
+      }
+      \c_spath_curvetoa_tl
+      {
+        \int_set:Nn \l_@@_tmpa_int {3}
+      }
+    }
+
+    \prg_replicate:nn { \l_@@_tmpa_int }
+    {
+      \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+      \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+      
+      \tl_put_right:Nx \l_@@_split_path_a_tl
+      {
+        \tl_item:Nn \l_@@_split_path_b_tl {1}
+        {\tl_item:Nn \l_@@_split_path_b_tl {2}}
+        {\tl_item:Nn \l_@@_split_path_b_tl {3}}
+      }
+
+      \tl_set:Nx \l_@@_split_path_b_tl {\tl_tail:N \l_@@_split_path_b_tl}
+    }
+    
+    \tl_put_left:NV \l_@@_split_path_b_tl \c_spath_moveto_tl
+
+    \tl_if_empty:NF \l_@@_split_path_a_tl
+    {
+      % Intersect the current segment with the rest of the path
+      \spath_intersect:NN \l_@@_split_path_a_tl \l_@@_split_path_b_tl
+
+
+      % If we get intersections
+      \int_compare:nT {\pgfintersectionsolutions > 0}
+      {
+        % Find the times of the intersections on each path
+        \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+        {
+          \pgfintersectiongetsolutiontimes{##1}{\l_@@_split_first_tl}{\l_@@_split_second_tl}
+          \fp_compare:nT
+          {
+            \l_@@_split_first_tl < .99
+          }
+          {
+            \tl_set:Nx \l_@@_tmpa_tl {\fp_to_decimal:n {\l_@@_split_first_tl +  \l_@@_split_segment_int}}
+            \seq_put_right:NV \l_@@_split_first_seq \l_@@_tmpa_tl
+          }
+        }
+      }
+
+      \spath_intersect:NN \l_@@_split_path_b_tl \l_@@_split_path_a_tl
+
+      % If we get intersections
+      \int_compare:nT {\pgfintersectionsolutions > 0}
+      {
+        % Find the times of the intersections on each path
+        \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+        {
+          \pgfintersectiongetsolutiontimes{##1}{\l_@@_split_first_tl}{\l_@@_split_second_tl}
+          \fp_compare:nT
+          {
+            \l_@@_split_first_tl > .01
+          }
+          {
+            \tl_set:Nx \l_@@_tmpa_tl {\fp_to_decimal:n {\l_@@_split_first_tl +  \l_@@_split_segment_int + 1}}
+            \seq_put_right:NV \l_@@_split_first_seq \l_@@_tmpa_tl
+          }
+        }
+      }
+      
+    }
+    % Increment the segment counter
+    \int_incr:N \l_@@_split_segment_int
+  }
+
+  % Sort the sequence by reverse order along the path
+  \seq_sort:Nn \l_@@_split_first_seq
+  {
+    \fp_compare:nNnTF { ##1 } < { ##2 }
+    { \sort_return_swapped: }
+    { \sort_return_same: }
+  }
+
+  % Restore the original copy of the path
+  \tl_set_eq:NN \l_@@_split_path_b_tl \l_@@_split_path_b_final_tl
+
+  % Clear the token lists
+  \tl_clear:N \l_@@_split_path_b_start_tl
+  \tl_clear:N \l_@@_split_path_b_end_tl
+  \tl_clear:N \l_@@_split_path_b_final_tl
+
+  \tl_set:Nn \l_@@_split_prev_first_tl {-1}
+
+  \seq_map_inline:Nn \l_@@_split_first_seq
+  {
+    \tl_set:Nn \l_@@_split_first_tl {##1}
+    \tl_set_eq:NN \l_@@_tmpa_tl \l_@@_split_first_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l_@@_split_first_tl ) }
+      =
+      \fp_to_int:n {floor( \l_@@_split_prev_first_tl) }
+    }
+    {
+      \tl_set:Nx \l_@@_split_first_tl
+      {
+        \fp_eval:n {
+          floor( \l_@@_split_first_tl )
+          +
+          ( \l_@@_split_first_tl - floor( \l_@@_split_first_tl) )
+          /
+          ( \l_@@_split_prev_first_tl - floor( \l_@@_split_prev_first_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l_@@_split_prev_first_tl \l_@@_tmpa_tl
+
+    \spath_split_at:NNVV \l_@@_split_path_b_start_tl \l_@@_split_path_b_end_tl  \l_@@_split_path_b_tl \l_@@_split_first_tl
+      
+    \tl_put_left:NV \l_@@_split_path_b_final_tl \l_@@_split_path_b_end_tl
+    \tl_set_eq:NN \l_@@_split_path_b_tl \l_@@_split_path_b_start_tl
+
+  }
+
+  \tl_put_left:NV \l_@@_split_path_b_final_tl \l_@@_split_path_b_tl
+
+  \tl_if_empty:NT \l_@@_split_path_b_final_tl
+  {
+    \tl_set_eq:NN \l_@@_split_path_b_final_tl \l_@@_split_path_b_tl
+  }
+
+  \spath_remove_empty_components:N \l_@@_split_path_b_final_tl
+  
+  \tl_gclear:N \g_@@_output_tl
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_split_path_b_final_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_at_self_intersections:Nn #1#2
+{
+  \@@_split_at_self_intersections:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_split_at_self_intersections:N #1
+{
+  \spath_split_at_self_intersections:NV #1#1
+}
+\cs_generate_variant:Nn \spath_split_at_self_intersections:N {c}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:Nn #1#2
+{
+  \@@_split_at_self_intersections:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:N #1
+{
+  \spath_gsplit_at_self_intersections:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{
+% \spath_join_component:Nnn,
+% \spath_join_component:Nn,
+% \spath_gjoin_component:Nnn,
+% \spath_gjoin_component:Nn,
+% }
+% Join the specified component of the spath to its predecessor.
+%    \begin{macrocode}
+\tl_new:N \l_@@_tmpj_tl
+\cs_new_protected_nopar:Npn \@@_join_component:nn #1#2
+{
+  \group_begin:
+  \spath_components_to_seq:Nn \l_@@_tmpa_seq {#1}
+  \int_compare:nT
+  {
+    #2 == 1
+  }
+  {
+    \tl_clear:N \l_@@_tmpj_tl
+    \seq_pop_left:NN \l_@@_tmpa_seq \l_@@_tmpj_tl
+    
+    \prg_replicate:nn {3}
+    {
+      \tl_set:Nx \l_@@_tmpj_tl {\tl_tail:N \l_@@_tmpj_tl}
+    }
+
+    \seq_put_right:NV \l_@@_tmpb_seq \l_@@_tmpj_tl
+  }
+  \bool_if:nT
+  {
+    \int_compare_p:n
+    {
+      #2 > 1
+    }
+    &&
+    \int_compare_p:n
+    {
+      #2 <= \seq_count:N \l_@@_tmpa_seq
+    }
+  }
+  {
+
+    \seq_clear:N \l_@@_tmpb_seq
+    \seq_map_indexed_inline:Nn \l_@@_tmpa_seq
+    {
+      \tl_set:Nn \l_@@_tmpj_tl {##2}
+      \int_compare:nT {##1 = #2}
+      {
+        \prg_replicate:nn {3}
+        {
+          \tl_set:Nx \l_@@_tmpj_tl {\tl_tail:N \l_@@_tmpj_tl}
+        }
+      }
+      \seq_put_right:NV \l_@@_tmpb_seq \l_@@_tmpj_tl
+    }
+
+    \seq_set_eq:NN \l_@@_tmpa_seq \l_@@_tmpb_seq
+  }
+
+  \tl_gset:Nx \g_@@_output_tl {\seq_use:Nn \l_@@_tmpa_seq {} }
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_join_component:Nnn #1#2#3
+{
+  \@@_join_component:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_join_component:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_join_component:Nn #1#2
+{
+  \spath_join_component:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_join_component:Nn {cn, NV, cV}
+\cs_new_protected_nopar:Npn \spath_gjoin_component:Nnn #1#2#3
+{
+  \@@_join_component:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_gjoin_component:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gjoin_component:Nn #1#2
+{
+  \spath_gjoin_component:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gjoin_component:Nn {cn, NV, cV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_spot_weld_components:Nn,
+% \spath_spot_weld_components:N,
+% \spath_spot_gweld_components:Nn,
+% \spath_spot_gweld_components:N,
+% }
+% Weld together any components where the last point of one is at the start point of the next (within a tolerance).
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_spot_weld_components:n #1
+{
+  \group_begin:
+  \dim_zero:N \l_@@_move_x_dim
+  \dim_zero:N \l_@@_move_y_dim
+
+  \spath_components_to_seq:Nn \l_@@_tmpa_seq {#1}
+  \seq_clear:N \l_@@_tmpb_seq
+  \dim_set:Nn \l_@@_move_x_dim {\tl_item:nn {#1} {2} + 10 pt}
+  \dim_set:Nn \l_@@_move_y_dim {\tl_item:nn {#1} {3} + 10 pt}
+
+  \int_set:Nn \l_@@_tmpa_int {\seq_count:N \l_@@_tmpa_seq}
+  
+  \seq_map_inline:Nn \l_@@_tmpa_seq
+  {
+    \tl_set:Nn \l_@@_tmpa_tl {##1}
+    \bool_if:nT
+    {
+      \dim_compare_p:n
+      {
+        \dim_abs:n {\l_@@_move_x_dim - \tl_item:Nn \l_@@_tmpa_tl {2} } < 0.01pt
+      }
+      &&
+      \dim_compare_p:n
+      {
+        \dim_abs:n {\l_@@_move_y_dim - \tl_item:Nn \l_@@_tmpa_tl {3} } < 0.01pt
+      }
+    }
+    {
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+      }
+      \int_decr:N \l_@@_tmpa_int
+    }
+    \tl_reverse:N \l_@@_tmpa_tl
+    \dim_set:Nn \l_@@_move_x_dim {\tl_item:Nn \l_@@_tmpa_tl {2}}
+    \dim_set:Nn \l_@@_move_y_dim {\tl_item:Nn \l_@@_tmpa_tl {1}}
+    \tl_reverse:N \l_@@_tmpa_tl
+    \seq_put_right:NV \l_@@_tmpb_seq \l_@@_tmpa_tl
+  }
+
+  \tl_set:Nx \l_@@_tmpa_tl {\seq_use:Nn \l_@@_tmpb_seq {} }
+  \spath_components_to_seq:NV \l_@@_tmpb_seq \l_@@_tmpa_tl
+  
+
+  \spath_initialpoint:Nn \l_@@_tmpa_tl {#1}
+  \spath_finalpoint:Nn \l_@@_tmpb_tl {#1}
+
+  \bool_if:nT
+  {
+    \dim_compare_p:n
+    {
+      \dim_abs:n {\tl_item:Nn \l_@@_tmpa_tl {1} - \tl_item:Nn \l_@@_tmpb_tl {1} } < 0.01pt
+    }
+    &&
+    \dim_compare_p:n
+    {
+      \dim_abs:n {\tl_item:Nn \l_@@_tmpa_tl {2} - \tl_item:Nn \l_@@_tmpb_tl {2} } < 0.01pt
+    }
+  }
+  {
+    \int_compare:nTF
+    {
+      \seq_count:N \l_@@_tmpb_seq > 1
+    }
+    {
+      \seq_pop_left:NN \l_@@_tmpb_seq \l_@@_tmpb_tl
+
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l_@@_tmpb_tl {\tl_tail:N \l_@@_tmpb_tl}
+      }
+      \seq_put_right:NV \l_@@_tmpb_seq \l_@@_tmpb_tl
+    }
+    {
+      \tl_set:NV \l_@@_tmpb_tl \c_spath_closepath_tl
+      \tl_put_right:Nx \l_@@_tmpb_tl
+      {
+        { \tl_item:Nn \l_@@_tmpa_tl {1} }
+        { \tl_item:Nn \l_@@_tmpa_tl {2} }
+      }
+      \seq_put_right:NV \l_@@_tmpb_seq \l_@@_tmpb_tl
+    }
+  }
+
+  \tl_gset:Nx \g_@@_output_tl {\seq_use:Nn \l_@@_tmpb_seq {}}
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_spot_weld_components:Nn #1#2
+{
+  \@@_spot_weld_components:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_spot_weld_components:Nn {NV, cV, cn}
+\cs_new_protected_nopar:Npn \spath_spot_weld_components:N #1
+{
+  \spath_spot_weld_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_spot_weld_components:N {c}
+\cs_new_protected_nopar:Npn \spath_spot_gweld_components:Nn #1#2
+{
+  \@@_spot_weld_components:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_generate_variant:Nn \spath_spot_gweld_components:Nn {NV, cV, cn}
+\cs_new_protected_nopar:Npn \spath_spot_gweld_components:N #1
+{
+  \spath_spot_gweld_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_spot_gweld_components:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Exporting Commands}
+%
+% \begin{macro}{
+% \spath_convert_to_svg:Nn,
+% \spath_gconvert_to_svg:Nn,
+% }
+% Convert the soft path to an SVG document.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_convert_to_svg:n #1
+{
+  \group_begin:
+  \tl_clear:N \l_@@_tmpa_tl
+  \tl_put_right:Nn \l_@@_tmpa_tl
+  {
+    <?xml~ version="1.0"~ standalone="no"?>
+    \iow_newline:
+    <!DOCTYPE~ svg~ PUBLIC~ "-//W3C//DTD SVG 1.1//EN"~
+    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+    \iow_newline:
+    <svg~ xmlns="http://www.w3.org/2000/svg"~ version="1.1"~viewBox="
+  }
+
+  \spath_minbb:Nn \l_@@_tmpb_tl {#1}
+  \spath_maxbb:Nn \l_@@_tmpc_tl {#1}
+  \tl_put_right:Nx \l_@@_tmpa_tl
+  {
+    \dim_to_decimal:n
+    {
+      \tl_item:Nn \l_@@_tmpb_tl {1} - 10pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
+    {
+      \tl_item:Nn \l_@@_tmpb_tl {2} - 10pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
+    {
+      \tl_item:Nn \l_@@_tmpc_tl {1}
+      -
+      \tl_item:Nn \l_@@_tmpb_tl {1}
+      + 20pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
+    {
+      \tl_item:Nn \l_@@_tmpc_tl {2}
+      -
+      \tl_item:Nn \l_@@_tmpb_tl {2}
+      + 20pt
+    }
+  }
+  
+  \tl_put_right:Nn \l_@@_tmpa_tl
+  {
+    ">
+    \iow_newline:
+    <path~ d="
+  }
+  \tl_set:Nn \l_@@_tmpc_tl {use:n}
+  \tl_map_inline:Nn #1
+  {
+    \tl_set:Nn \l_@@_tmpb_tl {##1}
+    \tl_case:NnF \l_@@_tmpb_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_put_right:Nn \l_@@_tmpa_tl {M~}
+        \tl_set:Nn \l_@@_tmpc_tl {use:n}
+      }
+      \c_spath_lineto_tl
+      {
+        \tl_put_right:Nn \l_@@_tmpa_tl {L~}
+        \tl_set:Nn \l_@@_tmpc_tl {use:n}
+      }
+      \c_spath_closepath_tl
+      {
+        \tl_put_right:Nn \l_@@_tmpa_tl {Z~}
+        \tl_set:Nn \l_@@_tmpc_tl {use_none:n}
+      }
+      \c_spath_curvetoa_tl
+      {
+        \tl_put_right:Nn \l_@@_tmpa_tl {C~}
+        \tl_set:Nn \l_@@_tmpc_tl {use:n}
+      }
+      \c_spath_curvetob_tl {
+        \tl_set:Nn \l_@@_tmpc_tl {use:n}
+      }
+      \c_spath_curveto_tl {
+        \tl_set:Nn \l_@@_tmpc_tl {use:n}
+      }
+    }
+    {
+      \tl_put_right:Nx \l_@@_tmpa_tl {\use:c { \l_@@_tmpc_tl } {\dim_to_decimal:n {##1}} ~}
+    }
+  }
+  \tl_put_right:Nn \l_@@_tmpa_tl
+  {
+    "~ fill="none"~ stroke="black"~ />
+    \iow_newline:
+    </svg>
+    \iow_newline:
+  }
+  \tl_gset_eq:NN \g_@@_output_tl \l_@@_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_convert_to_svg:Nn #1#2
+{
+  \@@_convert_to_svg:n {#2}
+  \tl_set_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+\cs_new_protected_nopar:Npn \spath_gconvert_to_svg:Nn #1#2
+{
+  \@@_convert_to_svg:n {#2}
+  \tl_gset_eq:NN #1 \g_@@_output_tl
+  \tl_gclear:N \g_@@_output_tl
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_export_to_svg:nn
+% }
+% Save a soft path to an SVG file.
+%    \begin{macrocode}
+\iow_new:N \g_@@_stream
+\cs_new_protected_nopar:Npn \spath_export_to_svg:nn #1#2
+{
+  \spath_convert_path_to_svg:Nn \l_@@_iterp_tl {#2}
+  \iow_open:Nn \g_@@_stream {#1 .svg}
+  \iow_now:Nx \g_@@_stream
+  {
+    \tl_use:N \l_@@_iterp_tl
+  }
+  \iow_close:N \g_@@_stream
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\spath_show:n}
+% Displays the soft path on the terminal.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_show:n #1
+{
+  \int_step_inline:nnnn {1} {3} {\tl_count:n {#1}}
+  {
+    \iow_term:x {
+      \tl_item:Nn \l_@@_tmpa_tl {##1}
+      {\tl_item:Nn \l_@@_tmpa_tl {##1+1}}
+      {\tl_item:Nn \l_@@_tmpa_tl {##1+2}}
+    }
+  }
+}
+\cs_generate_variant:Nn \spath_show:n {V, v}
+%    \end{macrocode}
+% \end{macro}
+
+% \subsubsection{PGF and TikZ Interface Functions}
+%
+% Spaths come from PGF so we need some functions that get and set spaths from the pgf system.
+%
+% \begin{macro}{
+% \spath_get_current_path:N,
+% \spath_gget_current_path:N
+% }
+% Grab the current soft path from PGF.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_get_current_path:N #1
+{
+  \pgfsyssoftpath@getcurrentpath #1
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_gget_current_path:N #1
+{
+  \pgfsyssoftpath@getcurrentpath #1
+  \tl_gset_eq:NN #1 #1
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\spath_protocol_path:n}
+% This feeds the bounding box of the soft path to PGF to ensure that its current bounding box contains the soft path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
+{
+  \spath_minbb:Nn \l_@@_tmpa_tl {#1}
+  \exp_last_unbraced:NV \pgf@protocolsizes\l_@@_tmpa_tl
+
+  \spath_maxbb:Nn \l_@@_tmpa_tl {#1}
+  \exp_last_unbraced:NV \pgf@protocolsizes\l_@@_tmpa_tl
+}
+\cs_generate_variant:Nn \spath_protocol_path:n {V}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_set_current_path:n,
+% \spath_set_current_path:N
+% }
+% Sets the current path to the specified soft path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
+{
+  \spath_protocol_path:n {#1}
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \pgfsyssoftpath@setcurrentpath\l_@@_tmpa_tl
+}
+\cs_new_protected_nopar:Npn \spath_set_current_path:N #1
+{
+  \spath_protocol_path:V #1
+  \pgfsyssoftpath@setcurrentpath #1
+}
+\cs_generate_variant:Nn \spath_set_current_path:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{
+% \spath_use_path:nn
+% }
+% Uses the given soft path at the PGF level.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
+{
+  \spath_set_current_path:n {#1}
+  \pgfusepath{#2}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\spath_tikz_path:nn}
+% Uses the given soft path at the TikZ level.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
+{
+  \path[#1] \pgfextra{
+    \spath_set_current_path:n {#2}
+    \tl_put_right:Nn \tikz@preactions {\def\tikz@actions@path{#2}}
+  };
+}
+\cs_generate_variant:Nn \spath_tikz_path:nn {Vn, VV, nv, Vv, nV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\spath_set_tikz_coords:n}
+% Sets the \Verb+\tikz@lastx+ and other coordinates from the soft path.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \spath_set_tikz_coords:n #1
+{
+  \spath_finalpoint:Nn \l_@@_tmpa_tl {#1}
+  \tl_set:Nx \l_@@_tmpa_tl
+  {
+    \exp_not:c {tikz@lastx}=\tl_item:Nn \l_@@_tmpa_tl {1}
+    \exp_not:c {tikz@lasty}=\tl_item:Nn \l_@@_tmpa_tl {2}
+    \exp_not:c {tikz@lastxsaved}=\tl_item:Nn \l_@@_tmpa_tl {1}
+    \exp_not:c {tikz@lastysaved}=\tl_item:Nn \l_@@_tmpa_tl {2}
+  }
+  \tl_use:N \l_@@_tmpa_tl
+}
+\cs_generate_variant:Nn \spath_set_tikz_coords:n {V, v}
+%    \end{macrocode}
+% \end{macro}
+%
+% \iffalse
+%</spath3>
+% \fi
+%
+% \section{The TikZ interface}
+%
+% \iffalse
+%<*tikzspath3>
+% \fi
+%
+% This provides an interface to the soft path manipulation routines via a series of TikZ keys.
+% They all live in the \texttt{spath} family.
+%
+%
+%     \begin{macrocode}
+\RequirePackage{spath3}
+\RequirePackage{expl3}
+\ExplSyntaxOn
+
+\tl_new:N \l_@@_current_tl
+\tl_new:N \l_@@_reverse_tl
+\tl_new:N \l_@@_prefix_tl
+\tl_new:N \l_@@_suffix_tl
+\tl_new:N \g_@@_smuggle_tl
+\seq_new:N \g_@@_tmpa_seq
+\seq_new:N \g_@@_tmpb_seq
+\bool_new:N \l_@@_draft_bool
+%    \end{macrocode}
+%
+% When saving a soft path, by default we use a naming convention that is compatible with the intersections library so that paths saved here and paths saved by the \texttt{name path} facility of the intersections library are mutually exchangeable.
+%
+%    \begin{macrocode}
+\tl_set:Nn \l_@@_prefix_tl {tikz@intersect@path@name@}
+\tl_set:Nn \l_@@_suffix_tl {}
+%    \end{macrocode}
+%
+% When a soft path is grabbed from TikZ we're usually deep in a group so I've adapted the code from the intersections library to dig the definition out of the group without making everything global.
+% 
+%    \begin{macrocode}
+\tl_new:N \g_@@_tikzfinish_tl
+\cs_new_protected_nopar:Npn \spath_at_end_of_path:
+{
+  \tl_use:N \g_@@_tikzfinish_tl
+  \tl_gclear:N \g_@@_tikzfinish_tl
+}
+\tl_put_right:Nn \tikz@finish {\spath_at_end_of_path:}
+
+\cs_new_protected_nopar:Npn \spath_save_path:Nn #1#2
+{
+  \tl_gput_right:Nn \g_@@_tikzfinish_tl
+  {
+    \tl_clear_new:N #1
+    \tl_set:Nn #1 {#2}
+  }
+}
+\cs_generate_variant:Nn \spath_save_path:Nn {cn, NV, cV}
+
+\cs_new_protected_nopar:Npn \spath_gsave_path:Nn #1#2
+{
+  \tl_gput_right:Nn \g_@@_tikzfinish_tl
+  {
+    \tl_gclear_new:N #1
+    \tl_gset:Nn #1 {#2}
+  }
+}
+\cs_generate_variant:Nn \spath_gsave_path:Nn {cn, NV, cV}
+%    \end{macrocode}
+%
+% Now we define all of our keys.
+%
+%    \begin{macrocode}
+\tikzset{
+%    \end{macrocode}
+% 
+% We're in the \texttt{spath} key family.
+%
+%    \begin{macrocode}
+  spath/.is~family,
+  spath/.cd,
+%    \end{macrocode}
+% 
+% We provide for saving soft paths with a specific prefix and suffix in the name.
+% The default is to make it compatible with the intersections library.
+%
+%    \begin{macrocode}
+  set~ prefix/.store~ in=\l_@@_prefix_tl,
+  prefix/.is~choice,
+  prefix/default/.style={
+    /tikz/spath/set~ prefix=tikz@intersect@path@name@
+  },
+  set~ suffix/.store~ in=\l_@@_suffix_tl,
+  suffix/.is~choice,
+  suffix/default/.style={
+    /tikz/spath/set~ suffix={}
+  },
+  set~ name/.style={
+    /tikz/spath/prefix=#1,
+    /tikz/spath/suffix=#1
+  },
+%    \end{macrocode}
+%
+% Keys for saving and cloning a soft path.
+%
+%    \begin{macrocode}
+  save/.code={
+    \tikz@addmode{
+      \spath_get_current_path:N \l_@@_tmpa_tl
+      \spath_bake_round:NV \l_@@_tmpa_tl \l_@@_tmpa_tl
+      \spath_save_path:cV {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl} \l_@@_tmpa_tl
+    }
+  },
+  clone/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+    {
+      \tl_clear_new:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \tl_set_eq:cc
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+  clone~ global/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+    {
+      \tl_gclear_new:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \tl_gset_eq:cc
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+  save~ global/.code={
+    \tikz@addmode{
+      \spath_get_current_path:N \l_@@_tmpa_tl
+      \spath_bake_round:NV \l_@@_tmpa_tl \l_@@_tmpa_tl
+      \spath_gsave_path:cV
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \l_@@_tmpa_tl
+    }
+  },
+%    \end{macrocode}
+%
+% Saves a soft path to the aux file.
+%
+%    \begin{macrocode}
+  save~ to~ aux/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_save_to_aux:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Restores a soft path to the current path.
+%
+%    \begin{macrocode}
+  restore/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_set_current_path:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \spath_set_tikz_coords:v
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Diagnostic, show the current path in the terminal and log.
+%
+%    \begin{macrocode}
+  show~current~path/.code={
+    \tikz@addmode{
+      \pgfsyssoftpath@getcurrentpath\l_@@_tmpa_tl
+      \iow_term:n {---~ current~ soft~ path~ ---}
+      \spath_show:V \l_@@_tmpa_tl
+    }
+  },
+%    \end{macrocode}
+%
+% Diagnostic, show the named soft path in the terminal and log.
+%
+%    \begin{macrocode}
+  show/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \iow_term:n {---~ soft~ path~ #1~ ---}
+      \spath_show:v {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Appends the named path to the current path with a weld.
+%
+%    \begin{macrocode}
+  append/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_get_current_path:N \l_@@_current_tl
+      \spath_weld:Nv
+      \l_@@_current_tl
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \spath_set_current_path:N \l_@@_current_tl
+      \spath_set_tikz_coords:V \l_@@_current_tl
+    }
+  },
+%    \end{macrocode}
+%
+% Joins the second named path to the first.
+%
+%    \begin{macrocode}
+  join~ with/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+      {
+        \spath_append:cv
+        {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+        {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+      }
+    }
+  },
+%    \end{macrocode}
+%
+% Does a ``spot weld'' on a soft path, which means that any components that start where the previous component ends are welded together.
+%
+%    \begin{macrocode}
+  spot~ weld/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_spot_weld_components:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Reverses the named path.
+%
+%    \begin{macrocode}
+  reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_reverse:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Appends the reversal of the path to the current path.
+%
+%    \begin{macrocode}
+  append~ reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_reverse:Nv
+      \l_@@_reverse_tl
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \spath_get_current_path:N \l_@@_current_tl
+      \spath_weld:NV \l_@@_current_tl \l_@@_reverse_tl
+      \spath_set_current_path:N \l_@@_current_tl
+      \spath_set_tikz_coords:V \l_@@_current_tl
+    }
+  },    
+%    \end{macrocode}
+%
+% Inserts the named path into the current path as-is, meaning without transforming or welding it.
+%
+%    \begin{macrocode}
+  insert/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_get_current_path:N \l_@@_current_tl
+      \spath_append:Nv
+      \l_@@_current_tl
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \spath_set_current_path:N \l_@@_current_tl
+      \spath_set_tikz_coords:V \l_@@_current_tl
+    }
+  },
+%    \end{macrocode}
+%
+% Inserts the reverse of the named path.
+% 
+%    \begin{macrocode}
+  insert~ reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_reverse:Nv
+      \l_@@_reverse_tl
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \spath_get_current_path:N \l_@@_current_tl
+      \spath_append:NV \l_@@_current_tl \l_@@_reverse_tl
+      \spath_set_current_path:N \l_@@_current_tl
+      \spath_set_tikz_coords:V \l_@@_current_tl
+    }
+  },
+%    \end{macrocode}
+%
+% These keys shorten the path.
+%
+%    \begin{macrocode}
+  shorten~ at~ end/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_shorten_at_end:cn
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl} {#2}
+    }
+  },
+  shorten~ at~ start/.code~ 2~ args ={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_shorten_at_start:cn
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl} {#2}
+    }
+  },
+  shorten~ at~ both~ ends/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_shorten_at_end:cn
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl} {#2}
+      \spath_shorten_at_start:cn
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl} {#2}
+    }
+  },
+%    \end{macrocode}
+%
+% This translates the named path.
+%
+%    \begin{macrocode}
+  translate/.code~ n~ args={3}{
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_translate:cnn
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}{#2}{#3}
+    }
+  },
+%    \end{macrocode}
+%
+% Exports the path as an SVG file.
+%
+%    \begin{macrocode}
+  export~ to~ svg/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_export_to_svg:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Transforms the named path using TikZ transformation specifications.
+%
+%    \begin{macrocode}
+  transform/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \group_begin:
+      \pgftransformreset
+      \tikzset{#2}
+      \pgfgettransform \l_@@_tmpa_tl
+      \tl_gset:Nn \g_@@_smuggle_tl
+      {
+        \spath_transform:cnnnnnn
+        {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      }
+      \tl_gput_right:NV \g_@@_smuggle_tl \l_@@_tmpa_tl
+      \group_end:
+      \tl_use:N \g_@@_smuggle_tl
+    }
+  },
+  transform~global/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \group_begin:
+      \pgftransformreset
+      \tikzset{#2}
+      \pgfgettransform \l_@@_tmpa_tl
+      \tl_gset:Nn \g_@@_smuggle_tl
+      {
+        \spath_gtransform:cnnnnnn
+        {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      }
+      \tl_gput_right:NV \g_@@_smuggle_tl \l_@@_tmpa_tl
+      \group_end:
+      \tl_use:N \g_@@_smuggle_tl
+    }
+  },
+%    \end{macrocode}
+%
+% Splits two paths at their mutual intersections.
+%
+%    \begin{macrocode}
+  split~ at~ intersections/.code~ n~ args={2}{
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+      {
+        \spath_split_at_intersections:cc
+        {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+        {\tl_use:N \l_@@_prefix_tl #2 \tl_use:N \l_@@_suffix_tl}
+      }
+    }
+  },
+%    \end{macrocode}
+%
+% Splits a path at its self-intersections.
+%
+%    \begin{macrocode}
+  split~ at~ self~ intersections/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_split_at_self_intersections:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% Extract the components of a path into a comma separated list (suitable for using in a \Verb+\foreach+ loop).
+%
+%    \begin{macrocode}
+  get~ components~ of/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \clist_clear_new:N #2
+      \spath_components_to_seq:Nv
+      \l_@@_tmpa_seq
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \seq_map_inline:Nn \l_@@_tmpa_seq
+      {
+        \tl_new:c
+        {\tl_use:N \l_@@_prefix_tl anonymous_\int_use:N \g_@@_anon_int \tl_use:N \l_@@_suffix_tl}
+        \tl_set:cn
+        {\tl_use:N \l_@@_prefix_tl anonymous_\int_use:N \g_@@_anon_int \tl_use:N \l_@@_suffix_tl} {##1}
+        \clist_put_right:Nx #2 {anonymous_\int_use:N \g_@@_anon_int}
+        \int_gincr:N \g_@@_anon_int
+      }
+    }
+  },
+%    \end{macrocode}
+%
+% Loop through the components of a soft path and render each as a separate TikZ path so that they can be individually styled.
+%
+%    \begin{macrocode}
+  render~ components/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \group_begin:
+      \spath_components_to_seq:Nv
+      \l_@@_tmpa_seq
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \seq_map_indexed_inline:Nn \l_@@_tmpa_seq
+      {
+        \spath_tikz_path:nn
+        {
+          every~ spath~ component/.try,
+          spath ~component~ ##1/.try,
+          spath ~component/.try={##1},
+          every~ #1~ component/.try,
+          #1 ~component~ ##1/.try,
+          #1 ~component/.try={##1},
+        }
+        {
+          ##2
+        }
+      }
+      \group_end:
+    }
+  },
+%    \end{macrocode}
+%
+% This puts gaps between components of a soft path.
+% The list of components is passed through a \Verb+\foreach+ loop so can use the shortcut syntax from those loops.
+%
+%    \begin{macrocode}
+  insert~ gaps~ after~ components/.code~ n~ args={3}{
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \group_begin:
+      \seq_gclear:N \g_@@_tmpa_seq
+      \seq_gclear:N \g_@@_tmpb_seq
+      \foreach \l_@@_tmpa_tl in {#3}
+      {
+        \seq_gput_right:NV \g_@@_tmpa_seq \l_@@_tmpa_tl
+        \seq_gput_right:Nx \g_@@_tmpb_seq {\int_eval:n { \l_@@_tmpa_tl + 1 }}
+      }
+      \spath_components_to_seq:Nv
+      \l_@@_tmpa_seq
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \seq_clear:N \l_@@_tmpb_seq
+      \seq_map_indexed_inline:Nn \l_@@_tmpa_seq
+      {
+        \tl_set:Nn \l_@@_tmpa_tl {##2}
+        \seq_if_in:NnT \g_@@_tmpa_seq {##1}
+        {
+          \spath_shorten_at_end:Nn \l_@@_tmpa_tl {#2/2}
+        }
+        \seq_if_in:NnT \g_@@_tmpb_seq {##1}
+        {
+          \spath_shorten_at_start:Nn \l_@@_tmpa_tl {#2/2}
+        }
+        \seq_put_right:NV \l_@@_tmpb_seq \l_@@_tmpa_tl
+      }
+      \tl_gset:Nx \g_@@_output_tl {\seq_use:Nn \l_@@_tmpb_seq {} }
+      \group_end:
+      \tl_set_eq:cN
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      \g_@@_output_tl
+      \tl_gclear:N \g_@@_output_tl
+    }
+  },
+%    \end{macrocode}
+%
+% Join the specified components together, joining each to its previous one.
+%
+%    \begin{macrocode}
+  join~ components/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \seq_gclear:N \g_@@_tmpa_seq
+      \foreach \l_@@_tmpa_tl in {#2}
+      {
+        \seq_gput_right:NV \g_@@_tmpa_seq \l_@@_tmpa_tl
+      }
+      \seq_gsort:Nn \g_@@_tmpa_seq
+      {
+        \int_compare:nNnTF {##1} > {##2}
+        { \sort_return_same: }
+        { \sort_return_swapped: }
+      }
+      \seq_map_inline:Nn \g_@@_tmpa_seq
+      {
+        \spath_join_component:cn
+        {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}{##1}
+      }
+    }
+  },
+%    \end{macrocode}
+%
+% Remove all components of the path that don't actually draw anything.
+%
+%    \begin{macrocode}
+  remove~ empty~ components/.code={
+    \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    {
+      \spath_remove_empty_components:c
+      {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+    }
+  },
+%    \end{macrocode}
+%
+% This puts a conditional around the \texttt{spot weld} key because when figuring out a knot drawing then we will initially want to render it without the spot weld to keep the number of components constant.
+%
+%    \begin{macrocode}
+  draft~ mode/.is~ choice,
+  draft~ mode/true/.code={
+    \bool_set_true:N \l_@@_draft_bool
+  },
+  draft~ mode/false/.code={
+    \bool_set_false:N \l_@@_draft_bool
+  },
+  maybe~ spot~ weld/.code={
+    \bool_if:NF \l_@@_draft_bool
+    {
+      \tl_if_exist:cT {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      {
+        \spath_spot_weld_components:c
+        {\tl_use:N \l_@@_prefix_tl #1 \tl_use:N \l_@@_suffix_tl}
+      }
+    }
+  },
+%    \end{macrocode}
+%
+% Set the transformation to lie along a path.
+%
+%    \begin{macrocode}
+  transform~ to/.code~ 2~ args={
+    \group_begin:
+    \tl_if_exist:cTF
+    {
+      \tl_use:N \l_@@_prefix_tl
+      #1
+      \tl_use:N \l_@@_suffix_tl
+    }
+    {
+      \spath_reallength:Nv
+      \l_@@_tmpa_int
+      {
+        \tl_use:N \l_@@_prefix_tl
+        #1
+        \tl_use:N \l_@@_suffix_tl
+      }
+      
+      \tl_set:Nx \l_@@_tmpb_tl
+      {\fp_to_decimal:n {(#2) * (\l_@@_tmpa_int)}}
+      \spath_transformation_at:NvV \l_@@_tmpc_tl
+      {
+        \tl_use:N \l_@@_prefix_tl
+        #1
+        \tl_use:N \l_@@_suffix_tl
+      }
+      \l_@@_tmpb_tl
+      \tl_gset_eq:NN \g_@@_smuggle_tl \l_@@_tmpc_tl
+    }
+    {
+      \tl_gset_eq:NN \g_@@_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
+    }
+    \group_end:
+    \exp_last_unbraced:NV \pgfsettransformentries \g_@@_smuggle_tl
+    \tl_gclear:N \g_@@_smuggle_tl
+  },
+%    \end{macrocode}
+%
+% As above, but with a possible extra \(180^\circ\) rotation if needed to ensure that the new \(y\)--axis points vaguely upwards.
+%
+%    \begin{macrocode}
+  upright~ transform~ to/.code~ 2~ args={
+    \group_begin:
+    \tl_if_exist:cTF
+    {
+      \tl_use:N \l_@@_prefix_tl
+      #1
+      \tl_use:N \l_@@_suffix_tl
+    }
+    {
+      \spath_reallength:Nv
+      \l_@@_tmpa_int
+      {
+        \tl_use:N \l_@@_prefix_tl
+        #1
+        \tl_use:N \l_@@_suffix_tl
+      }
+      
+      \tl_set:Nx \l_@@_tmpb_tl
+      {\fp_to_decimal:n {(#2) * (\l_@@_tmpa_int)}}
+      \spath_transformation_at:NvV \l_@@_tmpc_tl
+      {
+        \tl_use:N \l_@@_prefix_tl
+        #1
+        \tl_use:N \l_@@_suffix_tl
+      }
+      \l_@@_tmpb_tl
+      \tl_gset_eq:NN \g_@@_smuggle_tl \l_@@_tmpc_tl
+    }
+    {
+      \tl_gset_eq:NN \g_@@_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
+    }
+    \fp_compare:nT { \tl_item:Nn \g_@@_smuggle_tl {4} < 0}
+    {
+      \tl_gset:Nx \g_@@_smuggle_tl
+      {
+        { \fp_eval:n { - (\tl_item:Nn \g_@@_smuggle_tl {1})} }
+        { \fp_eval:n { - (\tl_item:Nn \g_@@_smuggle_tl {2})} }
+        { \fp_eval:n { - (\tl_item:Nn \g_@@_smuggle_tl {3})} }
+        { \fp_eval:n { - (\tl_item:Nn \g_@@_smuggle_tl {4})} }
+        { \tl_item:Nn \g_@@_smuggle_tl {5} }
+        { \tl_item:Nn \g_@@_smuggle_tl {6} }
+      }
+    }
+    \group_end:
+    \exp_last_unbraced:NV \pgfsettransformentries \g_@@_smuggle_tl
+    \tl_gclear:N \g_@@_smuggle_tl
+  },
+%    \end{macrocode}
+%
+% This is a useful set of styles for drawing a knot diagram.
+%
+%    \begin{macrocode}
+  knot/.style~ n~ args={3}{
+    spath/.cd,
+    split~ at~ self~ intersections=#1,
+    insert~ gaps~ after~ components={#1}{#2}{#3},
+    maybe~ spot~ weld=#1,
+    render~ components=#1
+  },
+}
+%    \end{macrocode}
+%
+% This defines a coordinate system that finds a position on a soft path.
+%
+%    \begin{macrocode}
+\tikzdeclarecoordinatesystem{spath}{%
+  \group_begin:
+  \tl_set:Nn \l_@@_tmpa_tl {#1}
+  \tl_trim_spaces:N \l_@@_tmpa_tl
+
+  \seq_set_split:NnV \l_@@_tmpa_seq {~} \l_@@_tmpa_tl
+  \seq_pop_right:NN \l_@@_tmpa_seq \l_@@_tmpb_tl
+
+  \tl_set:Nx \l_@@_tmpa_tl { \seq_use:Nn \l_@@_tmpa_seq {~} }
+  \tl_if_exist:cTF
+  {
+    \tl_use:N \l_@@_prefix_tl
+    \tl_use:N \l_@@_tmpa_tl
+    \tl_use:N \l_@@_suffix_tl
+  }
+  {
+
+    \tl_set_eq:Nc
+    \l_@@_tmpa_tl
+    {
+      \tl_use:N \l_@@_prefix_tl
+      \tl_use:N \l_@@_tmpa_tl
+      \tl_use:N \l_@@_suffix_tl
+    }
+
+    \tl_if_empty:NTF \l_@@_tmpa_tl
+    {
+      \tl_gset_eq:NN \g_@@_smuggle_tl \pgfpointorigin
+    }
+    {
+      \spath_reallength:NV \l_@@_tmpa_int \l_@@_tmpa_tl
+      \tl_set:Nx \l_@@_tmpb_tl
+      {\fp_to_decimal:n {(\l_@@_tmpb_tl) * (\l_@@_tmpa_int)}}
+      \spath_point_at:NVV \l_@@_tmpc_tl \l_@@_tmpa_tl \l_@@_tmpb_tl
+
+      \tl_clear:N \l_@@_tmpd_tl
+      \tl_put_right:Nn \l_@@_tmpd_tl {\pgf@x=}
+      \tl_put_right:Nx \l_@@_tmpd_tl {\tl_item:Nn \l_@@_tmpc_tl {1}}
+      \tl_put_right:Nn \l_@@_tmpd_tl {\relax}
+      \tl_put_right:Nn \l_@@_tmpd_tl {\pgf@y=}
+      \tl_put_right:Nx \l_@@_tmpd_tl {\tl_item:Nn \l_@@_tmpc_tl {2}}
+      \tl_put_right:Nn \l_@@_tmpd_tl {\relax}
+      \tl_gset_eq:NN \g_@@_smuggle_tl \l_@@_tmpd_tl
+    }
+  }
+  {
+    \tl_gset_eq:NN \g_@@_smuggle_tl \pgfpointorigin
+  }
+    \group_end:
+    \tl_use:N \g_@@_smuggle_tl
+}
+
+\ExplSyntaxOff
+%    \end{macrocode}
+% \iffalse
+%</tikzspath3>
+% \fi
+%
+% \iffalse
+%<*calligraphy>
+% \fi
+%
+% \section{The Calligraphy Package}
+%
+%    \begin{macrocode}
+%<@@=cal>
+%    \end{macrocode}
+%
+% \subsection{Initialisation}
+%    \begin{macrocode}
+\RequirePackage{spath3}
+\ExplSyntaxOn
+
+\tl_new:N \l_@@_tmpa_tl
+\tl_new:N \l_@@_tmpb_tl
+\tl_new:N \l_@@_tmp_path_tl
+\tl_new:N \l_@@_tmp_rpath_tl
+\tl_new:N \l_@@_tmp_rpathb_tl
+\tl_new:N \l_@@_tmp_patha_tl
+
+\seq_new:N \l_@@_tmpa_seq
+
+\int_new:N \l_@@_tmpa_int
+\int_new:N \l_@@_tmpb_int
+\int_new:N \g_@@_path_component_int
+\int_new:N \g_@@_label_int
+
+\fp_new:N \l_@@_tmpa_fp
+\fp_new:N \l_@@_tmpb_fp
+\fp_new:N \l_@@_tmpc_fp
+\fp_new:N \l_@@_tmpd_fp
+\fp_new:N \l_@@_tmpe_fp
+
+\dim_new:N \l_@@_tmpa_dim
+\dim_new:N \l_@@_tmpb_dim
+\dim_new:N \l_@@_tmpc_dim
+\dim_new:N \l_@@_tmpd_dim
+\dim_new:N \l_@@_tmpe_dim
+\dim_new:N \l_@@_tmpf_dim
+\dim_new:N \l_@@_tmpg_dim
+\dim_new:N \l_@@_tmph_dim
+
+\bool_new:N \l_@@_annotate_bool
+\bool_new:N \l_@@_taper_start_bool
+\bool_new:N \l_@@_taper_end_bool
+\bool_new:N \l_@@_taperable_bool
+
+\dim_new:N \l_@@_taper_width_dim
+\dim_new:N \l_@@_line_width_dim
+
+\bool_set_true:N \l_@@_taper_start_bool
+\bool_set_true:N \l_@@_taper_end_bool
+
+\cs_generate_variant:Nn \tl_put_right:Nn {Nv}
+
+\msg_new:nnn { calligraphy } { undefined pen } { The~ pen~ "#1"~ is~ not~ defined. }
+%    \end{macrocode}
+%
+% \subsection{TikZ Keys}
+%
+% The public interface to this package is through TikZ keys and styles.
+%    \begin{macrocode}
+\tikzset{
+  define~pen/.code={
+    \tikzset{pen~name=#1}
+    \pgf@relevantforpicturesizefalse
+    \tikz@addmode{
+      \pgfsyssoftpath@getcurrentpath\l_@@_tmpa_tl
+      \spath_components_to_seq:NV \l_@@_tmpa_seq \l_@@_tmpa_tl
+      \seq_gclear_new:c {g_@@_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      \seq_gset_eq:cN {g_@@_pen_\pgfkeysvalueof{/tikz/pen~name}_seq} \l_@@_tmpa_seq
+      \pgfusepath{discard}%
+    }
+  },
+  define~pen/.default={default},
+  use~pen/.code={
+    \tikzset{pen~name=#1}
+    \int_gzero:N \g_@@_path_component_int
+    \cs_set_eq:NN \pgfpathmoveto \cal_moveto:n
+    \tikz@addmode{
+      \pgfsyssoftpath@getcurrentpath\l_@@_tmpa_tl
+      \spath_components_to_seq:NV \l_@@_tmpa_seq \l_@@_tmpa_tl
+      \tl_if_exist:cTF {g_@@_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      {
+        \cal_path_create:Nc \l_@@_tmpa_seq {g_@@_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      }
+      {
+        \msg_warning:nnx { calligraphy } { undefined pen } { \pgfkeysvalueof{/tikz/pen~name} }
+      }
+    }
+  },
+  use~pen/.default={default},
+  pen~name/.initial={default},
+  copperplate/.style={pen~name=copperplate},
+  pen~colour/.initial={black},
+  weight/.is~choice,
+  weight/heavy/.style={
+    line~width=\pgfkeysvalueof{/tikz/heavy~line~width},
+    taper~width=\pgfkeysvalueof{/tikz/light~line~width},
+  },
+  weight/light/.style={
+    line~width=\pgfkeysvalueof{/tikz/light~line~width},
+    taper~width=0pt,
+  },
+  heavy/.style={
+    weight=heavy
+  },
+  light/.style={
+    weight=light
+  },
+  heavy~line~width/.initial=2pt,
+  light~line~width/.initial=1pt,
+  taper/.is~choice,
+  taper/.default=both,
+  taper/none/.style={
+    taper~start=false,
+    taper~end=false,
+  },
+  taper/both/.style={
+    taper~start=true,
+    taper~end=true,
+  },
+  taper/start/.style={
+    taper~start=true,
+    taper~end=false,
+  },
+  taper/end/.style={
+    taper~start=false,
+    taper~end=true,
+  },
+  taper~start/.code={
+    \tl_if_eq:nnTF {#1} {true}
+    {
+      \bool_set_true:N \l_@@_taper_start_bool
+    }
+    {
+      \bool_set_false:N \l_@@_taper_start_bool
+    }
+  },
+  taper~start/.default={true},
+  taper~end/.code={
+    \tl_if_eq:nnTF {#1} {true}
+    {
+      \bool_set_true:N \l_@@_taper_end_bool
+    }
+    {
+      \bool_set_false:N \l_@@_taper_end_bool
+    }
+  },
+  taper~end/.default={true},
+  taper~width/.code={\dim_set:Nn \l_@@_taper_width_dim {#1}},
+  nib~style/.code~2~args={
+    \tl_clear_new:c {l_@@_nib_style_#1}
+    \tl_set:cn {l_@@_nib_style_#1} {#2}
+  },
+  stroke~style/.code~2~args={
+    \tl_clear_new:c {l_@@_stroke_style_#1}
+    \tl_set:cn {l_@@_stroke_style_#1} {#2}
+  },
+  this~stroke~style/.code={
+    \tl_clear_new:c {l_@@_stroke_inline_style_ \int_use:N \g_@@_path_component_int}
+    \tl_set:cn {l_@@_stroke_inline_style_ \int_use:N \g_@@_path_component_int} {#1}
+  },
+  annotate/.style={
+    annotate~if,
+    annotate~reset,
+    annotation~style/.update~value={#1},
+  },
+  annotate~if/.default={true},
+  annotate~if/.code={
+    \tl_if_eq:nnTF {#1} {true}
+    {
+      \bool_set_true:N \l_@@_annotate_bool
+    }
+    {
+      \bool_set_false:N \l_@@_annotate_bool
+    }
+  },
+  annotate~reset/.code={
+    \int_gzero:N \g_@@_label_int
+  },
+  annotation~style/.initial={draw,->},
+  annotation~shift/.initial={(0,1ex)},
+  every~annotation~node/.initial={anchor=south~west},
+  annotation~node~style/.code~2~args={
+    \tl_clear_new:c {l_@@_annotation_style_ #1 _tl}
+    \tl_set:cn {l_@@_annotation_style_ #1 _tl}{#2}
+  },
+  tl~use:N/.code={
+    \exp_args:NV \pgfkeysalso #1
+  },
+  tl~use:c/.code={
+    \tl_if_exist:cT {#1}
+    {
+      \exp_args:Nv \pgfkeysalso {#1}
+    }
+  },
+  /handlers/.update~style/.code={
+    \tl_if_eq:nnF {#1} {\pgfkeysnovalue}
+    {
+      \pgfkeys{\pgfkeyscurrentpath/.code=\pgfkeysalso{#1}}
+    }
+  },
+  /handlers/.update~value/.code={
+    \tl_if_eq:nnF {#1} {\pgfkeysnovalue}
+    {
+      \pgfkeyssetvalue{\pgfkeyscurrentpath}{#1}
+    }
+  },
+}
+%    \end{macrocode}
+%
+% Some wrappers around the TikZ keys.
+%    \begin{macrocode}
+\NewDocumentCommand \pen { O{} }
+{
+  \path[define~ pen,every~ calligraphy~ pen/.try,#1]
+}
+
+\NewDocumentCommand \definepen { O{} }
+{
+  \tikz \path[define~ pen,every~ calligraphy~ pen/.try,#1]
+}
+
+\NewDocumentCommand \calligraphy { O{} }
+{
+  \path[use~ pen,every~ calligraphy/.try,#1]
+}
+%    \end{macrocode}
+%
+% \subsection{The Path Creation}
+%
+% \begin{macro}[internal]{\cal_path_create:NN}
+% This is the main command for creating the calligraphic paths.
+% First argument is the given path
+% Second argument is the pen path
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \cal_path_create:NN #1#2
+{
+  \int_zero:N \l_@@_tmpa_int
+  \seq_map_inline:Nn #1
+  {
+    \int_compare:nT {\tl_count:n {##1} > 3}
+    {
+      
+      \int_incr:N \l_@@_tmpa_int
+      \int_zero:N \l_@@_tmpb_int
+
+      \tl_set:Nn \l_@@_tmp_path_tl {##1}
+      \spath_open:N \l_@@_tmp_path_tl
+      \spath_reverse:NV \l_@@_tmp_rpath_tl \l_@@_tmp_path_tl 
+
+      \seq_map_inline:Nn #2
+      {
+        \int_incr:N \l_@@_tmpb_int
+        \group_begin:
+        \pgfsys@beginscope
+        \cal_apply_style:c {l_@@_stroke_style_ \int_use:N \l_@@_tmpa_int}
+        \cal_apply_style:c {l_@@_stroke_inline_style_ \int_use:N \l_@@_tmpa_int}
+        \cal_apply_style:c {l_@@_nib_style_ \int_use:N \l_@@_tmpb_int}
+
+        \spath_initialpoint:Nn \l_@@_tmpa_tl {####1}
+        \tl_set_eq:NN \l_@@_tmp_patha_tl \l_@@_tmp_path_tl
+        \spath_translate:NV \l_@@_tmp_patha_tl \l_@@_tmpa_tl
+
+        \int_compare:nTF {\tl_count:n {####1} == 3}
+        {
+          \cal_at_least_three:N \l_@@_tmp_patha_tl
+          \spath_protocol_path:V \l_@@_tmp_patha_tl
+
+          \tikz@options
+          \dim_set:Nn \l_@@_line_width_dim {\pgflinewidth}
+          \cal_maybe_taper:N \l_@@_tmp_patha_tl
+        }
+        {
+          \spath_weld:Nn \l_@@_tmp_patha_tl {####1}
+          \spath_weld:NV \l_@@_tmp_patha_tl \l_@@_tmp_rpath_tl
+          \spath_reverse:Nn \l_@@_tmp_rpathb_tl {####1}
+          \spath_weld:NV \l_@@_tmp_patha_tl \l_@@_tmp_rpathb_tl
+
+          \tl_clear:N \l_@@_tmpa_tl
+          \tl_set:Nn \l_@@_tmpa_tl {fill=\pgfkeysvalueof{/tikz/pen~colour},draw=none}
+          \tl_if_exist:cT  {l_@@_stroke_style_ \int_use:N \l_@@_tmpa_int}
+          {
+            \tl_put_right:Nv \l_@@_tmpa_tl {l_@@_stroke_style_ \int_use:N \l_@@_tmpa_int}
+          }
+          \tl_if_exist:cT  {l_@@_stroke_inline_style_ \int_use:N \l_@@_tmpa_int}
+          {
+            \tl_put_right:Nn \l_@@_tmpa_tl {,}
+            \tl_put_right:Nv \l_@@_tmpa_tl {l_@@_stroke_inline_style_ \int_use:N \l_@@_tmpa_int}
+          }
+          \tl_if_exist:cT  {l_@@_nib_style_ \int_use:N \l_@@_tmpb_int}
+          {
+            \tl_put_right:Nn \l_@@_tmpa_tl {,}
+            \tl_put_right:Nv \l_@@_tmpa_tl {l_@@_nib_style_ \int_use:N \l_@@_tmpb_int}
+          }
+          \spath_tikz_path:VV \l_@@_tmpa_tl \l_@@_tmp_patha_tl
+
+        }
+        \pgfsys@endscope
+        \group_end:
+      }
+
+      \bool_if:NT \l_@@_annotate_bool
+      {
+        \seq_get_right:NN #2 \l_@@_tmpa_tl
+        \spath_finalpoint:NV \l_@@_tmpa_tl \l_@@_tmpa_tl
+        \spath_translate:NV \l_@@_tmp_path_tl \l_@@_tmpa_tl
+        \tikz@scan@one@point\pgfutil@firstofone\pgfkeysvalueof{/tikz/annotation~shift}
+
+        \spath_translate:Nnn \l_@@_tmp_path_tl {\pgf@x} {\pgf@y}
+      
+        \pgfkeysgetvalue{/tikz/annotation~style}{\l_@@_tmpa_tl}
+        \spath_tikz_path:VV \l_@@_tmpa_tl \l_@@_tmp_path_tl
+
+        \spath_finalpoint:NV \l_@@_tmpa_tl \l_@@_tmp_path_tl
+
+        \exp_last_unbraced:NV \pgfqpoint \l_@@_tmpa_tl
+        \begin{scope}[reset~ cm]
+        \node[every~annotation~node/.try,tl~use:c =  {l_@@_annotation_style_ \int_use:N \l_@@_tmpa_int _tl}] at (\pgf@x,\pgf@y) {\int_use:N \l_@@_tmpa_int};
+        \end{scope}
+      }
+    }
+  }
+}
+\cs_generate_variant:Nn \cal_path_create:NN {Nc}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\cal_moveto:n}
+% When creating the path, we need to keep track of the number of components so that we can apply styles accordingly.
+%    \begin{macrocode}
+\cs_new_eq:NN \cal_orig_moveto:n \pgfpathmoveto
+\cs_new_nopar:Npn \cal_moveto:n #1
+{
+  \int_gincr:N \g_@@_path_component_int
+  \cal_orig_moveto:n {#1}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\cal_apply_style:N}
+% Interface for applying \Verb+\tikzset+ to a token list.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \cal_apply_style:N #1
+{
+  \tl_if_exist:NT #1 {
+    \exp_args:NV \tikzset #1
+  }
+}
+\cs_generate_variant:Nn \cal_apply_style:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\cal_at_least_three:Nn}
+% A tapered path has to have at least three components.
+% This figures out if it is necessary and sets up the splitting.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \cal_at_least_three:Nn #1#2
+{
+  \spath_reallength:Nn \l_@@_tmpa_int {#2}
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_set:Nn \l_@@_tmpb_tl {#2}
+  \int_compare:nTF {\l_@@_tmpa_int = 1}
+  {
+    \spath_split_at:Nn \l_@@_tmpb_tl {2/3}
+    \spath_split_at:Nn \l_@@_tmpb_tl {1/2}
+  }
+  {
+    \int_compare:nT {\l_@@_tmpa_int = 2}
+    {
+      \spath_split_at:Nn \l_@@_tmpb_tl {1.5}
+      \spath_split_at:Nn \l_@@_tmpb_tl {.5}
+    }
+  }
+  \tl_set_eq:NN #1 \l_@@_tmpb_tl
+}
+\cs_generate_variant:Nn \cal_at_least_three:Nn {NV}
+\cs_new_protected_nopar:Npn \cal_at_least_three:N #1
+{
+  \cal_at_least_three:NV #1#1
+}
+\cs_generate_variant:Nn \cal_at_least_three:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\cal_maybe_taper:N}
+% Possibly tapers the path, depending on the booleans.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \cal_maybe_taper:N #1
+{
+  \tl_set_eq:NN \l_@@_tmpa_tl #1
+
+  \bool_if:NT \l_@@_taper_start_bool
+  {
+
+    \dim_set:Nn \l_@@_tmpa_dim {\tl_item:Nn \l_@@_tmpa_tl {2}}
+    \dim_set:Nn \l_@@_tmpb_dim {\tl_item:Nn \l_@@_tmpa_tl {3}}
+    \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_tmpa_tl {4}}
+
+    \tl_case:NnF \l_@@_tmpb_tl
+    {
+      \c_spath_lineto_tl
+      {
+
+        \bool_set_true:N \l_@@_taperable_bool
+        \dim_set:Nn \l_@@_tmpg_dim {\tl_item:Nn \l_@@_tmpa_tl {5}}
+        \dim_set:Nn \l_@@_tmph_dim {\tl_item:Nn \l_@@_tmpa_tl {6}}
+        \dim_set:Nn \l_@@_tmpc_dim {(2\l_@@_tmpa_dim + \l_@@_tmpg_dim)/3}
+        \dim_set:Nn \l_@@_tmpd_dim {(2\l_@@_tmpb_dim + \l_@@_tmph_dim)/3}
+        \dim_set:Nn \l_@@_tmpe_dim {(\l_@@_tmpa_dim + 2\l_@@_tmpg_dim)/3}
+        \dim_set:Nn \l_@@_tmpf_dim {(\l_@@_tmpb_dim + 2\l_@@_tmph_dim)/3}
+        \prg_replicate:nn {4}
+        {
+          \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        }
+        \tl_put_left:NV \l_@@_tmpa_tl \c_spath_moveto_tl
+      }
+      \c_spath_curvetoa_tl
+      {
+        \bool_set_true:N \l_@@_taperable_bool
+        \dim_set:Nn \l_@@_tmpc_dim {\tl_item:Nn \l_@@_tmpa_tl {5}}
+        \dim_set:Nn \l_@@_tmpd_dim {\tl_item:Nn \l_@@_tmpa_tl {6}}
+        \dim_set:Nn \l_@@_tmpe_dim {\tl_item:Nn \l_@@_tmpa_tl {8}}
+        \dim_set:Nn \l_@@_tmpf_dim {\tl_item:Nn \l_@@_tmpa_tl {9}}
+        \dim_set:Nn \l_@@_tmpg_dim {\tl_item:Nn \l_@@_tmpa_tl {11}}
+        \dim_set:Nn \l_@@_tmph_dim {\tl_item:Nn \l_@@_tmpa_tl {12}}
+        \prg_replicate:nn {10}
+        {
+          \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        }
+        \tl_put_left:NV \l_@@_tmpa_tl \c_spath_moveto_tl
+      }
+    }
+    {
+      \bool_set_false:N \l_@@_taperable_bool
+    }
+    
+    \bool_if:NT \l_@@_taperable_bool
+    {
+      \@@_taper_aux:
+    }
+    
+  }
+
+  \bool_if:NT \l_@@_taper_end_bool
+  {
+
+    \dim_set:Nn \l_@@_tmpa_dim {\tl_item:Nn \l_@@_tmpa_tl {-2}}
+    \dim_set:Nn \l_@@_tmpb_dim {\tl_item:Nn \l_@@_tmpa_tl {-1}}
+    \tl_set:Nx \l_@@_tmpb_tl {\tl_item:Nn \l_@@_tmpa_tl {-3}}
+
+    \tl_case:NnF \l_@@_tmpb_tl
+    {
+      \c_spath_lineto_tl
+      {
+
+        \bool_set_true:N \l_@@_taperable_bool
+        \dim_set:Nn \l_@@_tmpg_dim {\tl_item:Nn \l_@@_tmpa_tl {-5}}
+        \dim_set:Nn \l_@@_tmph_dim {\tl_item:Nn \l_@@_tmpa_tl {-4}}
+        \dim_set:Nn \l_@@_tmpc_dim {(2\l_@@_tmpa_dim + \l_@@_tmpg_dim)/3}
+        \dim_set:Nn \l_@@_tmpd_dim {(2\l_@@_tmpb_dim + \l_@@_tmph_dim)/3}
+        \dim_set:Nn \l_@@_tmpe_dim {(\l_@@_tmpa_dim + 2\l_@@_tmpg_dim)/3}
+        \dim_set:Nn \l_@@_tmpf_dim {(\l_@@_tmpb_dim + 2\l_@@_tmph_dim)/3}
+        \tl_reverse:N \l_@@_tmpa_tl
+        \prg_replicate:nn {3}
+        {
+          \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        }
+        \tl_reverse:N \l_@@_tmpa_tl
+      }
+      \c_spath_curveto_tl
+      {
+        \bool_set_true:N \l_@@_taperable_bool
+        \dim_set:Nn \l_@@_tmpc_dim {\tl_item:Nn \l_@@_tmpa_tl {-5}}
+        \dim_set:Nn \l_@@_tmpd_dim {\tl_item:Nn \l_@@_tmpa_tl {-4}}
+        \dim_set:Nn \l_@@_tmpe_dim {\tl_item:Nn \l_@@_tmpa_tl {-8}}
+        \dim_set:Nn \l_@@_tmpf_dim {\tl_item:Nn \l_@@_tmpa_tl {-7}}
+        \dim_set:Nn \l_@@_tmpg_dim {\tl_item:Nn \l_@@_tmpa_tl {-11}}
+        \dim_set:Nn \l_@@_tmph_dim {\tl_item:Nn \l_@@_tmpa_tl {-10}}
+        \tl_reverse:N \l_@@_tmpa_tl
+        \prg_replicate:nn {9}
+        {
+          \tl_set:Nx \l_@@_tmpa_tl {\tl_tail:N \l_@@_tmpa_tl}
+        }
+        \tl_reverse:N \l_@@_tmpa_tl
+      }
+    }
+    {
+      \bool_set_false:N \l_@@_taperable_bool
+    }
+    
+    \bool_if:NT \l_@@_taperable_bool
+    {
+      \@@_taper_aux:
+    }
+    
+  }
+
+  \pgfsyssoftpath@setcurrentpath\l_@@_tmpa_tl
+  \pgfsetstrokecolor{\pgfkeysvalueof{/tikz/pen~colour}}
+  \pgfusepath{stroke}
+
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\@@_taper_aux:}
+% Auxiliary macro to avoid unnecessary code duplication.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_taper_aux:
+{
+  \tl_clear:N \l_@@_tmpb_tl
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_moveto_tl
+
+  \fp_set:Nn \l_@@_tmpa_fp
+  {
+    \l_@@_tmpd_dim - \l_@@_tmpb_dim
+  }
+  \fp_set:Nn \l_@@_tmpb_fp
+  {
+    \l_@@_tmpa_dim - \l_@@_tmpc_dim
+  }
+  \fp_set:Nn \l_@@_tmpe_fp
+  {
+    (\l_@@_tmpa_fp^2 + \l_@@_tmpb_fp^2)^.5
+  }
+  
+  \fp_set:Nn \l_@@_tmpa_fp {.5*\l_@@_taper_width_dim *     \l_@@_tmpa_fp / \l_@@_tmpe_fp}
+  \fp_set:Nn \l_@@_tmpb_fp {.5*\l_@@_taper_width_dim *     \l_@@_tmpb_fp / \l_@@_tmpe_fp}
+
+  \fp_set:Nn \l_@@_tmpc_fp
+  {
+    \l_@@_tmph_dim - \l_@@_tmpf_dim
+  }
+  \fp_set:Nn \l_@@_tmpd_fp
+  {
+    \l_@@_tmpe_dim - \l_@@_tmpg_dim
+  }
+  \fp_set:Nn \l_@@_tmpe_fp
+  {
+    (\l_@@_tmpc_fp^2 + \l_@@_tmpd_fp^2)^.5
+  }
+
+  \fp_set:Nn \l_@@_tmpc_fp {.5*\l_@@_line_width_dim * \l_@@_tmpc_fp / \l_@@_tmpe_fp}
+  \fp_set:Nn \l_@@_tmpd_fp {.5*\l_@@_line_width_dim * \l_@@_tmpd_fp / \l_@@_tmpe_fp}
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpa_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpb_fp +             \l_@@_tmpb_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetoa_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpc_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpb_fp + \l_@@_tmpd_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetob_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpc_fp + \l_@@_tmpe_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpd_fp + \l_@@_tmpf_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curveto_tl
+  
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpc_fp + \l_@@_tmpg_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpd_fp + \l_@@_tmph_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetoa_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpc_fp + \l_@@_tmpg_dim - \fp_to_dim:n{ 1.32 * \l_@@_tmpd_fp}}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpd_fp + \l_@@_tmph_dim + \fp_to_dim:n {1.32* \l_@@_tmpc_fp}}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetob_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpc_fp + \l_@@_tmpg_dim - \fp_to_dim:n {1.32 * \l_@@_tmpd_fp}}}
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpd_fp + \l_@@_tmph_dim + \fp_to_dim:n {1.32 * \l_@@_tmpc_fp}}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curveto_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpc_fp + \l_@@_tmpg_dim}}
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpd_fp + \l_@@_tmph_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetoa_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpc_fp + \l_@@_tmpe_dim}}
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpd_fp + \l_@@_tmpf_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetob_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpc_dim}}
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpb_fp + \l_@@_tmpd_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curveto_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpa_dim}}
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpb_fp + \l_@@_tmpb_dim}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetoa_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpa_dim + \fp_to_dim:n{ 1.32 * \l_@@_tmpb_fp}}}
+    {\dim_eval:n { -\fp_to_dim:N \l_@@_tmpb_fp + \l_@@_tmpb_dim - \fp_to_dim:n {1.32* \l_@@_tmpa_fp}}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curvetob_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpa_dim + \fp_to_dim:n {1.32 * \l_@@_tmpb_fp}}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpb_fp + \l_@@_tmpb_dim - \fp_to_dim:n {1.32 * \l_@@_tmpa_fp}}}
+  }
+
+  \tl_put_right:NV \l_@@_tmpb_tl \c_spath_curveto_tl
+
+  \tl_put_right:Nx \l_@@_tmpb_tl
+  {
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpa_fp + \l_@@_tmpa_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l_@@_tmpb_fp +             \l_@@_tmpb_dim}}
+  }
+
+  \pgfsyssoftpath@setcurrentpath\l_@@_tmpb_tl
+  \pgfsetfillcolor{\pgfkeysvalueof{/tikz/pen~colour}}
+  \pgfusepath{fill}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% Defines a copperplate pen.
+%    \begin{macrocode}
+\tl_set:Nn \l_@@_tmpa_tl {\pgfsyssoftpath@movetotoken{0pt}{0pt}}
+\spath_components_to_seq:NV \l_@@_tmpa_seq \l_@@_tmpa_tl
+\seq_gclear_new:N \g_@@_pen_copperplate_seq
+\seq_gset_eq:NN \g_@@_pen_copperplate_seq \l_@@_tmpa_seq
+%    \end{macrocode}
+%
+% \begin{macro}{\CopperplatePath}
+% This is used in the decorations section to convert a path to a copperplate path.
+%    \begin{macrocode}
+\DeclareDocumentCommand \CopperplatePath { m }
+{
+  \spath_components_to_seq:NV \l_@@_tmpa_seq #1
+  \cal_path_create:NN \l_@@_tmpa_seq \g_@@_pen_copperplate_seq
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\ExplSyntaxOff
+%    \end{macrocode}
+%
+% \subsection{Decorations}
+%
+% If a decoration library is loaded we define some decorations that use the calligraphy library, specifically the copperplate pen with its tapering.
+%
+% First, a brace decoration.
+%    \begin{macrocode}
+\expandafter\ifx\csname pgfdeclaredecoration\endcsname\relax
+\else
+\pgfdeclaredecoration{calligraphic brace}{brace}
+{
+  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
+  {
+    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
+    \pgfpathmoveto{\pgfpointorigin}
+    \pgfpathcurveto
+    {\pgfqpoint{.15\pgfdecorationsegmentamplitude}{.3\pgfdecorationsegmentamplitude}}
+    {\pgfqpoint{.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+    {\pgfqpoint{\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+    {
+      \pgftransformxshift{+\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance}
+      \pgfpathlineto{\pgfqpoint{-\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+      \pgfpathcurveto
+      {\pgfqpoint{-.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{-.15\pgfdecorationsegmentamplitude}{.7\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{0\pgfdecorationsegmentamplitude}{1\pgfdecorationsegmentamplitude}}
+      \pgfpathmoveto{\pgfqpoint{0\pgfdecorationsegmentamplitude}{1\pgfdecorationsegmentamplitude}}
+      \pgfpathcurveto
+      {\pgfqpoint{.15\pgfdecorationsegmentamplitude}{.7\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+    }
+    {
+      \pgftransformxshift{+\pgfdecoratedremainingdistance}
+      \pgfpathlineto{\pgfqpoint{-\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+      \pgfpathcurveto
+      {\pgfqpoint{-.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{-.15\pgfdecorationsegmentamplitude}{.3\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{0pt}{0pt}}
+    }
+    \tikzset{
+      taper width=.5\pgflinewidth,
+      taper
+    }%
+    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
+    \CopperplatePath{\cal@tmp@path}
+  }
+  \state{final}{}
+}
+%    \end{macrocode}
+%
+% The second is a straightened parenthesis (so that when very large it doesn't bow out too far).
+%    \begin{macrocode}
+\pgfdeclaredecoration{calligraphic straight parenthesis}{brace}
+{
+  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
+  {
+    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
+    \pgfpathmoveto{\pgfpointorigin}
+    \pgfpathcurveto
+    {\pgfqpoint{.76604\pgfdecorationsegmentamplitude}{.64279\pgfdecorationsegmentamplitude}}
+    {\pgfqpoint{2.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
+    {\pgfqpoint{3.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
+    {
+      \pgftransformxshift{+\pgfdecoratedremainingdistance}
+      \pgfpathlineto{\pgfqpoint{-3.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
+      \pgfpathcurveto
+      {\pgfqpoint{-2.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{-.76604\pgfdecorationsegmentamplitude}{.64279\pgfdecorationsegmentamplitude}}
+      {\pgfqpoint{0pt}{0pt}}
+    }
+    \tikzset{
+      taper width=.5\pgflinewidth,
+      taper
+    }%
+    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
+    \CopperplatePath{\cal@tmp@path}
+  }
+  \state{final}{}%
+}
+%    \end{macrocode}
+%
+% The third is a curved parenthesis.
+%    \begin{macrocode}
+\pgfdeclaredecoration{calligraphic curved parenthesis}{brace}
+{
+  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
+  {
+    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
+    \pgfpathmoveto{\pgfpointorigin}
+    \pgf@xa=\pgfdecoratedremainingdistance\relax
+    \advance\pgf@xa by -1.5890\pgfdecorationsegmentamplitude\relax
+    \edef\cgrphy@xa{\the\pgf@xa}
+    \pgfpathcurveto
+    {\pgfqpoint{1.5890\pgfdecorationsegmentamplitude}{1.3333\pgfdecorationsegmentamplitude}}
+    {\pgfqpoint{\cgrphy@xa}{1.3333\pgfdecorationsegmentamplitude}}
+    {\pgfqpoint{\pgfdecoratedremainingdistance}{0pt}}
+    \tikzset{
+      taper width=.5\pgflinewidth,
+      taper
+    }%
+    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
+    \CopperplatePath{\cal@tmp@path}
+  }
+  \state{final}{}%
+}
+%    \end{macrocode}
+% End the conditional for if pgfdecoration module is loaded
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+% \iffalse
+%</calligraphy>
+% \fi
+% 
+%
+% \iffalse
+%<*knots>
+% \fi
+%%
+% \section{Drawing Knots}
+%
+%    \begin{macrocode}
+%<@@=knot>
+%    \end{macrocode}
+%
+% \subsection{Initialisation}
+%
+% We load the \Verb+spath3+ library and the \Verb+intersections+ TikZ library.
+% Then we get going.
+%    \begin{macrocode}
+\RequirePackage{spath3}
+\usetikzlibrary{intersections,spath3}
+
+\ExplSyntaxOn
+
+\tl_new:N \l_@@_tmpa_tl
+\tl_new:N \l_@@_tmpb_tl
+\tl_new:N \l_@@_tmpc_tl
+\tl_new:N \l_@@_tmpd_tl
+\tl_new:N \l_@@_tmpg_tl
+\tl_new:N \l_@@_redraws_tl
+\tl_new:N \l_@@_clip_width_tl
+\tl_new:N \l_@@_name_tl
+\tl_new:N \l_@@_node_tl
+\tl_new:N \l_@@_aux_tl
+\tl_new:N \l_@@_auxa_tl
+\tl_new:N \l_@@_prefix_tl
+
+\seq_new:N \l_@@_segments_seq
+
+\int_new:N \l_@@_tmpa_int
+\int_new:N \l_@@_strands_int
+\int_new:N \g_@@_intersections_int
+\int_new:N \g_@@_filaments_int
+\int_new:N \l_@@_component_start_int
+
+\fp_new:N \l_@@_tmpa_fp
+\fp_new:N \l_@@_tmpb_fp
+
+\dim_new:N \l_@@_tmpa_dim
+\dim_new:N \l_@@_tmpb_dim
+\dim_new:N \l_@@_tolerance_dim
+\dim_new:N \l_@@_clip_bg_radius_dim
+\dim_new:N \l_@@_clip_draw_radius_dim
+
+\bool_new:N \l_@@_draft_bool
+\bool_new:N \l_@@_ignore_ends_bool
+\bool_new:N \l_@@_self_intersections_bool
+\bool_new:N \l_@@_splits_bool
+\bool_new:N \l_@@_super_draft_bool
+
+\bool_new:N \l_@@_prepend_prev_bool
+\bool_new:N \l_@@_append_next_bool
+\bool_new:N \l_@@_skip_bool
+\bool_new:N \l_@@_save_bool
+
+\seq_new:N \g_@@_nodes_seq
+
+\bool_set_true:N \l_@@_ignore_ends_bool
+%    \end{macrocode}
+%
+% Configuration is via TikZ keys and styles.
+%    \begin{macrocode}
+\tikzset{
+  spath/prefix/knot/.style={
+    spath/set~ prefix=knot strand,
+  },
+  spath/suffix/knot/.style={
+    spath/set~ suffix={},
+  },
+  knot/.code={
+    \tl_if_eq:nnTF {#1} {none}
+    {
+      \tikz@addmode{\tikz@mode@doublefalse}
+    }
+    {
+      \tikz@addmode{\tikz@mode@doubletrue}
+      \tl_if_eq:nnTF {\pgfkeysnovalue} {#1}
+      {
+        \tikz@addoption{\pgfsetinnerstrokecolor{.}}
+      }
+      {
+        \pgfsetinnerstrokecolor{#1}
+      }
+      \tikz@addoption{
+        \pgfsetstrokecolor{knotbg}
+      }
+      \tl_set:Nn \tikz@double@setup{
+        \pgfsetinnerlinewidth{\pgflinewidth}
+        \pgfsetlinewidth{\dim_eval:n {\tl_use:N \l_@@_gap_tl \pgflinewidth}}
+      }
+    }
+  },
+  knot~ gap/.store~ in=\l_@@_gap_tl,
+  knot~ gap=3,
+  knot~ diagram/.is~family,
+  knot~ diagram/.unknown/.code={
+    \tl_set_eq:NN \l_@@_tmpa_tl \pgfkeyscurrentname
+    \pgfkeysalso{
+      /tikz/\l_@@_tmpa_tl=#1
+    }
+  },
+  background~ colour/.code={%
+    \colorlet{knotbg}{#1}%
+  },
+  background~ color/.code={%
+    \colorlet{knotbg}{#1}%
+  },
+  background~ colour=white,
+  knot~ diagram,
+  name/.store~ in=\l_@@_name_tl,
+  name={knot},
+  save~ intersections/.is~ choice,
+  save~ intersections/.default=true,
+  save~ intersections/true/.code={
+    \bool_set_true:N \l_@@_save_bool
+  },
+  save~ intersections/false/.code={
+    \bool_set_false:N \l_@@_save_bool
+  },
+  every~ strand/.style={draw},
+  ignore~ endpoint~ intersections/.code={
+    \tl_if_eq:nnTF {#1} {true}
+    {
+      \bool_set_true:N \l_@@_ignore_ends_bool
+    }
+    {
+      \bool_set_false:N \l_@@_ignore_ends_bool
+    }
+  },
+  ignore~ endpoint~ intersections/.default=true,
+  consider~ self~ intersections/.is~choice,
+  consider~ self~ intersections/true/.code={
+    \bool_set_true:N \l_@@_self_intersections_bool
+    \bool_set_true:N \l_@@_splits_bool
+  },
+  consider~ self~ intersections/false/.code={
+    \bool_set_false:N \l_@@_self_intersections_bool
+    \bool_set_false:N \l_@@_splits_bool
+  },
+  consider~ self~ intersections/no~ splits/.code={
+    \bool_set_true:N \l_@@_self_intersections_bool
+    \bool_set_false:N \l_@@_splits_bool
+  },
+  consider~ self~ intersections/.default={true},
+  clip~ radius/.code={
+    \dim_set:Nn \l_@@_clip_bg_radius_dim {#1}
+    \dim_set:Nn \l_@@_clip_draw_radius_dim {#1+2pt}
+  },
+  clip~ draw~ radius/.code={
+    \dim_set:Nn \l_@@_clip_draw_radius_dim {#1}
+  },
+  clip~ background~ radius/.code={
+    \dim_set:Nn \l_@@_clip_bg_radius_dim {#1}
+  },
+  clip~ radius=10pt,
+  end~ tolerance/.code={
+    \dim_set:Nn \l_@@_tolerance_dim {#1}
+  },
+  end~ tolerance=14pt,
+  clip/.style={
+    clip
+  },
+  background~ clip/.style={
+    clip
+  },
+  clip~ width/.code={
+    \tl_set:Nn \l_@@_clip_width_tl {#1}
+  },
+  clip~ width=3,
+  flip~ crossing/.code={%
+    \tl_clear_new:c {l_@@_crossing_#1}
+    \tl_set:cn {l_@@_crossing_#1} {x}
+  },
+  ignore~ crossing/.code={%
+    \tl_clear_new:c {l_@@_ignore_crossing_#1}
+    \tl_set:cn {l_@@_ignore_crossing_#1} {x}
+  },
+  draft~ mode/.is~ choice,
+  draft~ mode/off/.code={%
+    \bool_set_false:N \l_@@_draft_bool
+    \bool_set_false:N \l_@@_super_draft_bool
+  },
+  draft~ mode/crossings/.code={%
+    \bool_set_true:N \l_@@_draft_bool
+    \bool_set_false:N \l_@@_super_draft_bool
+  },
+  draft~ mode/strands/.code={%
+    \bool_set_true:N \l_@@_draft_bool
+    \bool_set_true:N \l_@@_super_draft_bool
+  },
+  draft/.is~ family,
+  draft,
+  crossing~ label/.style={
+    overlay,
+    fill=white,
+    fill~ opacity=.5,
+    text~ opacity=1,
+    text=blue,
+    pin~ edge={blue,<-}
+  },
+  strand~ label/.style={
+    overlay,
+    circle,
+    draw=purple,
+    fill=white,
+    fill~ opacity=.5,
+    text~ opacity=1,
+    text=purple,
+    inner~ sep=0pt
+  },
+}
+%    \end{macrocode}
+%
+% Wrapper around \Verb+\tikzset+ for applying keys from a token list, checking for if the given token list exists.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \knot_apply_style:N #1
+{
+  \tl_if_exist:NT #1 {
+    \exp_args:NV \tikzset #1
+  }
+}
+\cs_generate_variant:Nn \knot_apply_style:N {c}
+%    \end{macrocode}
+%
+%\begin{macro}[internal]{\flipcrossings}
+% The user can specify a comma separated list of crossings to flip.
+%    \begin{macrocode}
+\NewDocumentCommand \flipcrossings {m}
+{
+  \tikzset{knot~ diagram/flip~ crossing/.list={#1}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\strand}
+% This is how the user specifies a strand of the knot.
+%    \begin{macrocode}
+\NewDocumentCommand \strand { O{} }
+{
+  \int_incr:N \l_@@_strands_int
+  \tl_clear_new:c {l_@@_options_strand \int_use:N \l_@@_strands_int}
+  \tl_set:cn {l_@@_options_strand \int_use:N \l_@@_strands_int} {#1}
+  \path[#1,spath/set~ name=knot,spath/save=\int_use:N \l_@@_strands_int]
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{knot}
+% This is the wrapper environment that calls the knot generation code.
+%    \begin{macrocode}
+\NewDocumentEnvironment{knot} { O{} }
+{
+  \knot_initialise:n {#1}
+}
+{
+  \knot_render:
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_initialise:n}
+% Set up some stuff before loading in the strands.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_initialise:n #1
+{
+  \tikzset{knot~ diagram/.cd,every~ knot~ diagram/.try,#1}
+  \int_zero:N \l_@@_strands_int
+  \tl_clear:N \l_@@_redraws_tl
+  \seq_gclear:N \g_@@_nodes_seq
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_render:}
+% This is the code that starts the work of rendering the knot.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_render:
+{
+%    \end{macrocode}
+% Start a scope and reset the transformation (since all transformations have already been taken into account when defining the strands).
+%    \begin{macrocode}
+  \pgfscope
+  \pgftransformreset
+%    \end{macrocode}
+% Loop through the strands drawing each one for the first time.
+%    \begin{macrocode}
+  \int_step_function:nnnN {1} {1} {\l_@@_strands_int} \knot_draw_strand:n
+%    \end{macrocode}
+% In super draft mode we don't do anything else.
+%    \begin{macrocode} 
+  \bool_if:NF \l_@@_super_draft_bool
+  {
+%    \end{macrocode}
+% In draft mode we draw labels at the ends of the strands; this also handles splitting curves to avoid self-intersections of Bezier curves if that's requested.
+%    \begin{macrocode}
+    \int_step_function:nnnN {1} {1} {\l_@@_strands_int} \knot_draw_labels:n
+%    \end{macrocode}
+% If we're considering self intersections we need to split the strands into filaments.
+%    \begin{macrocode}
+    \bool_if:NTF \l_@@_self_intersections_bool
+    {
+      \knot_split_strands:
+      \int_set_eq:NN \l_@@_tmpa_int \g_@@_filaments_int
+      \tl_set:Nn \l_@@_prefix_tl {filament}
+    }
+    {
+      \int_set_eq:NN \l_@@_tmpa_int \l_@@_strands_int
+      \tl_set:Nn \l_@@_prefix_tl {strand}
+    }
+%    \end{macrocode}
+% Initialise the intersection count.
+%    \begin{macrocode}
+    \int_gzero:N \g_@@_intersections_int
+%    \end{macrocode}
+% If in draft mode we label the intersections, otherwise we just stick a coordinate at each one.
+%    \begin{macrocode}
+    \tl_clear:N \l_@@_node_tl
+    \bool_if:NT \l_@@_draft_bool
+    {
+      \tl_set:Nn \l_@@_node_tl {
+        \exp_not:N \node[coordinate,
+          pin={[node~ contents={\int_use:N \g_@@_intersections_int},knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \g_@@_intersections_int \c_space_tl label/.try]
+            }]
+      }
+    }
+%    \end{macrocode}
+% This double loop steps through the pieces (strands or filaments) and computes the intersections and does stuff with those.
+%    \begin{macrocode}
+    \int_step_variable:nnnNn {1} {1} {\l_@@_tmpa_int - 1} \l_@@_tmpa_tl
+    {
+      \int_step_variable:nnnNn {\tl_use:N \l_@@_tmpa_tl + 1} {1}     {\l_@@_tmpa_int} \l_@@_tmpb_tl
+      {
+        \knot_intersections:VV \l_@@_tmpa_tl \l_@@_tmpb_tl
+      }
+    }
+%    \end{macrocode}
+% If any redraws were requested, do them here.
+%    \begin{macrocode}
+    \tl_use:N \l_@@_redraws_tl
+%    \end{macrocode}
+% Draw the crossing nodes
+%    \begin{macrocode}
+    \seq_use:Nn \g_@@_nodes_seq {}
+  }
+%    \end{macrocode}
+% Close the scope
+%    \begin{macrocode}
+  \endpgfscope
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_draw_strand:n}
+% This renders a strand using the options originally specified.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_draw_strand:n #1
+{
+  \pgfscope
+  \group_begin:
+  \spath_bake_round:c {knot strand #1}
+  \tl_set:Nn \l_@@_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_put_right:Nv \l_@@_tmpa_tl {l_@@_options_strand #1}
+  \tl_put_right:Nn \l_@@_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \spath_tikz_path:Vv \l_@@_tmpa_tl {knot strand #1}
+  \group_end:
+  \endpgfscope
+}
+\cs_generate_variant:Nn \tl_put_right:Nn {Nv}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_draw_labels:n}
+% Draw a label at each end of each strand, if in draft mode.
+% Also, if requested, split potentially self intersecting Bezier curves.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_draw_labels:n #1
+{
+  \bool_if:NT \l_@@_draft_bool
+  {
+    \spath_finalpoint:Nv \l_@@_tmpb_tl {knot strand #1}
+    \dim_set:Nn \l_@@_tmpa_dim {\tl_item:Nn \l_@@_tmpb_tl {1}}
+    \dim_set:Nn \l_@@_tmpb_dim {\tl_item:Nn \l_@@_tmpb_tl {2}}
+    \node[knot~ diagram/draft/strand~label] at (\l_@@_tmpa_dim,\l_@@_tmpb_dim) {#1};
+    \spath_initialpoint:Nv \l_@@_tmpb_tl {knot strand #1}
+    \dim_set:Nn \l_@@_tmpa_dim {\tl_item:Nn \l_@@_tmpb_tl {1}}
+    \dim_set:Nn \l_@@_tmpb_dim {\tl_item:Nn \l_@@_tmpb_tl {2}}
+    \node[knot~ diagram/draft/strand~label] at (\l_@@_tmpa_dim,\l_@@_tmpb_dim) {#1};
+  }
+  \bool_if:nT {
+    \l_@@_self_intersections_bool
+    &&
+    \l_@@_splits_bool
+  }
+  {
+    \tl_clear:N \l_@@_tmpa_tl
+    \spath_segments_to_seq:Nv \l_@@_segments_seq {knot strand #1}
+    \seq_map_function:NN \l_@@_segments_seq \knot_split_self_intersects:N
+    \tl_set_eq:cN {knot strand #1} \l_@@_tmpa_tl
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_split_self_intersects:N}
+% This is the macro that does the split.
+% Figuring out whether a Bezier cubic self intersects is apparently a difficult problem so we don't bother.
+% We compute a point such that if there is an intersection then it lies on either side of the point.
+% I don't recall where the formula came from!
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_split_self_intersects:N #1
+{
+  \tl_set:Nx \l_@@_tmpc_tl {\tl_item:nn {#1} {4}}
+  \tl_case:NnF \l_@@_tmpc_tl
+  {
+    \c_spath_curvetoa_tl
+    {
+      \fp_set:Nn \l_@@_tmpa_fp
+      {
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
+        *
+        (3 * \tl_item:nn {#1} {8} - 3 * \tl_item:nn {#1} {11})
+        -
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
+        *
+        (3 * \tl_item:nn {#1} {9} - 3 * \tl_item:nn {#1} {12})
+      }
+      \fp_set:Nn \l_@@_tmpb_fp
+      {
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
+        *
+        (3 * \tl_item:nn {#1} {6} - 6 * \tl_item:nn {#1} {9} + 3 * \tl_item:nn {#1} {12})
+        -
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
+        *
+        (3 * \tl_item:nn {#1} {5} - 6 * \tl_item:nn {#1} {8} + 3 * \tl_item:nn {#1} {11})
+      }
+      \fp_compare:nTF
+      {
+        \l_@@_tmpb_fp != 0
+      }
+      {
+        \fp_set:Nn \l_@@_tmpa_fp {.5 * \l_@@_tmpa_fp / \l_@@_tmpb_fp}
+        \fp_compare:nTF
+        {
+          0 < \l_@@_tmpa_fp && \l_@@_tmpa_fp < 1
+        }
+        {
+          \spath_split_curve:NNnV \l_@@_tmpc_tl \l_@@_tmpd_tl {#1} \l_@@_tmpa_fp
+          \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+          \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+          \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+          \tl_set:Nx \l_@@_tmpd_tl {\tl_tail:N \l_@@_tmpd_tl}
+          \tl_set:Nx \l_@@_tmpd_tl {\tl_tail:N \l_@@_tmpd_tl}
+          \tl_set:Nx \l_@@_tmpd_tl {\tl_tail:N \l_@@_tmpd_tl}
+          \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpc_tl
+          \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpd_tl
+        }
+        {
+          \tl_set:Nn \l_@@_tmpc_tl {#1}
+          \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+          \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+          \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+          \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpc_tl
+        }
+      }
+      {
+        \tl_set:Nn \l_@@_tmpc_tl {#1}
+        \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+        \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+        \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+        \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpc_tl
+      }
+    }
+    \c_spath_lineto_tl
+    {
+      \tl_set:Nn \l_@@_tmpc_tl {#1}
+      \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+      \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+      \tl_set:Nx \l_@@_tmpc_tl {\tl_tail:N \l_@@_tmpc_tl}
+      \tl_put_right:NV \l_@@_tmpa_tl \l_@@_tmpc_tl
+    }
+  }
+  {
+    \tl_put_right:Nn \l_@@_tmpa_tl {#1}
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_intersections:nn}
+% This computes the intersections of two pieces and steps through them.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_intersections:nn #1#2
+{
+  \group_begin:
+  \tl_set_eq:NN \l_@@_tmpa_tl \l_@@_prefix_tl
+  \tl_put_right:Nn \l_@@_tmpa_tl {#1}
+  \tl_set_eq:NN \l_@@_tmpb_tl \l_@@_prefix_tl
+  \tl_put_right:Nn \l_@@_tmpb_tl {#2}
+  \tl_set_eq:Nc \l_@@_tmpc_tl {knot \tl_use:N \l_@@_tmpa_tl}
+  \tl_set_eq:Nc \l_@@_tmpd_tl {knot \tl_use:N \l_@@_tmpb_tl}
+
+  \bool_if:nTF {
+    \l_@@_save_bool
+    &&
+    \tl_if_exist_p:c {knot~ intersections~ \tl_use:N \l_@@_name_tl - \tl_use:N \l_@@_tmpa_tl -  \tl_use:N \l_@@_tmpb_tl}
+  }
+  {
+    \tl_use:c {knot~ intersections~ \tl_use:N \l_@@_name_tl - \tl_use:N \l_@@_tmpa_tl -  \tl_use:N \l_@@_tmpb_tl}
+  }
+  {
+\pgfintersectionofpaths{\pgfsetpath\l_@@_tmpc_tl}{\pgfsetpath\l_@@_tmpd_tl}
+
+  }
+
+  \int_compare:nT {\pgfintersectionsolutions > 0}
+  {
+    \int_step_function:nnnN {1} {1} {\pgfintersectionsolutions} \knot_do_intersection:n
+  }
+
+  \knot_save_intersections:VV \l_@@_tmpa_tl \l_@@_tmpb_tl
+  \group_end:
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_save_intersections:nn}
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_save_intersections:nn #1#2
+{
+  \bool_if:NT \l_@@_save_bool
+  {
+    \tl_clear:N \l_@@_aux_tl
+    \tl_put_right:Nn \l_@@_aux_tl
+    {
+      \def\pgfintersectionsolutions
+    }
+    \tl_put_right:Nx \l_@@_aux_tl
+    {
+      {\int_eval:n {\pgfintersectionsolutions}}
+    }
+    \int_compare:nT {\pgfintersectionsolutions > 0}
+    {
+      \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+      {
+        \pgfpointintersectionsolution{##1}
+        \dim_set:Nn \l_@@_tmpa_dim {\pgf@x}
+        \dim_set:Nn \l_@@_tmpb_dim {\pgf@y}
+        \tl_put_right:Nn \l_@@_aux_tl
+        {
+          \expandafter\def\csname pgfpoint@intersect@solution@##1\endcsname
+        }
+        \tl_put_right:Nx \l_@@_aux_tl
+        {
+          {\exp_not:N \pgf@x=\dim_use:N \l_@@_tmpa_dim\exp_not:N\relax\exp_not:N \pgf@y =\dim_use:N \l_@@_tmpb_dim\relax}
+        }
+      }
+      \tl_set:Nn \l_@@_auxa_tl {\expandafter \gdef \csname knot~ intersections~}
+      \tl_put_right:Nx \l_@@_auxa_tl {\tl_use:N \l_@@_name_tl - #1 - #2}
+      \tl_put_right:Nn \l_@@_auxa_tl {\endcsname}
+      \tl_put_right:Nx \l_@@_auxa_tl {{\tl_to_str:N \l_@@_aux_tl}}
+      \protected@write\@auxout{}{\tl_to_str:N \l_@@_auxa_tl}
+    }
+  }
+}
+\cs_generate_variant:Nn \knot_save_intersections:nn {VV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_do_intersection:n}
+% This handles a specific intersection.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_do_intersection:n #1
+{
+%    \end{macrocode}
+% Get the intersection coordinates.
+%    \begin{macrocode}
+  \pgfpointintersectionsolution{#1}
+  \dim_set:Nn \l_@@_tmpa_dim {\pgf@x}
+  \dim_set:Nn \l_@@_tmpb_dim {\pgf@y}
+%    \end{macrocode}
+% If we're dealing with filaments, we can get false positives from the end points.
+%    \begin{macrocode}
+  \bool_set_false:N \l_@@_skip_bool
+  \bool_if:NT \l_@@_self_intersections_bool
+  {
+%    \end{macrocode}
+% If one filament preceded the other, test for the intersection being at the relevant end point.
+%    \begin{macrocode}
+    \tl_set:Nn \l_@@_tmpc_tl {knot previous}
+    \tl_put_right:NV \l_@@_tmpc_tl \l_@@_tmpa_tl
+    \tl_set:Nv \l_@@_tmpc_tl \l_@@_tmpc_tl
+    \tl_if_eq:NNT \l_@@_tmpc_tl \l_@@_tmpb_tl
+    {
+      \knot_test_endpoint:VnT \l_@@_tmpb_tl {final point}
+      {
+        \bool_set_true:N \l_@@_skip_bool
+      }
+    }
+
+    \tl_set:Nn \l_@@_tmpc_tl {knot previous}
+    \tl_put_right:NV \l_@@_tmpc_tl \l_@@_tmpb_tl
+    \tl_set:Nv \l_@@_tmpc_tl \l_@@_tmpc_tl
+    \tl_if_eq:NNT \l_@@_tmpc_tl \l_@@_tmpa_tl
+    {
+      \knot_test_endpoint:VnT \l_@@_tmpa_tl {final point}
+      {
+        \bool_set_true:N \l_@@_skip_bool
+      }
+    }
+  }
+%    \end{macrocode}
+% The user can also say that end points of filaments (or strands) should simply be ignored anyway.
+%    \begin{macrocode}
+  \bool_if:NT \l_@@_ignore_ends_bool
+  {
+    \knot_test_endpoint:VnT \l_@@_tmpa_tl {initial point}
+    {
+      \bool_set_true:N \l_@@_skip_bool
+    }
+    \knot_test_endpoint:VnT \l_@@_tmpa_tl {final point}
+    {
+      \bool_set_true:N \l_@@_skip_bool
+    }
+    \knot_test_endpoint:VnT \l_@@_tmpb_tl {initial point}
+    {
+      \bool_set_true:N \l_@@_skip_bool
+    }
+    \knot_test_endpoint:VnT \l_@@_tmpb_tl {final point}
+    {
+      \bool_set_true:N \l_@@_skip_bool
+    }
+  }
+%    \end{macrocode}
+% Assuming that we passed all the above tests, we render the crossing.
+%    \begin{macrocode}
+  \bool_if:NF \l_@@_skip_bool
+  {
+
+    \int_gincr:N \g_@@_intersections_int
+%    \end{macrocode}
+% This is the intersection test.
+% If the intersection finder finds too many, it might be useful to ignore some.
+%    \begin{macrocode}
+    \bool_if:nF
+    {
+      \tl_if_exist_p:c {l_@@_ignore_crossing_ \int_use:N
+        \g_@@_intersections_int}
+      &&
+      ! \tl_if_empty_p:c {l_@@_ignore_crossing_ \int_use:N
+        \g_@@_intersections_int}
+    }
+    {
+%    \end{macrocode}
+% This is the flip test.
+% We only render one of the paths.
+% The ``flip'' swaps which one we render.
+%    \begin{macrocode}
+      \bool_if:nTF
+      {
+        \tl_if_exist_p:c {l_@@_crossing_ \int_use:N
+          \g_@@_intersections_int}
+        &&
+        ! \tl_if_empty_p:c {l_@@_crossing_ \int_use:N
+          \g_@@_intersections_int}
+      }
+      {
+        \tl_set_eq:NN \l_@@_tmpg_tl \l_@@_tmpb_tl
+      }
+      {
+        \tl_set_eq:NN \l_@@_tmpg_tl \l_@@_tmpa_tl
+      }
+%    \end{macrocode}
+% Now we know which one we're rendering, we test to see if we should also render its predecessor or successor to ensure that we render a path through the entire crossing region.
+%    \begin{macrocode} 
+      \bool_if:NT \l_@@_self_intersections_bool
+      {
+        \knot_test_endpoint:VnT \l_@@_tmpg_tl {initial point}
+        {
+          \bool_set_true:N \l_@@_prepend_prev_bool
+        }
+        {
+          \bool_set_false:N \l_@@_prepend_prev_bool
+        }
+        \knot_test_endpoint:VnT \l_@@_tmpg_tl {final point}
+        {
+          \bool_set_true:N \l_@@_append_next_bool
+        }
+        {
+          \bool_set_false:N \l_@@_append_next_bool
+        }
+%    \end{macrocode}
+% If either of those tests succeeded, do the appending or prepending.
+%    \begin{macrocode}
+        \bool_if:nT
+        {
+          \l_@@_prepend_prev_bool || \l_@@_append_next_bool
+        }
+        {
+          \tl_clear_new:c {knot \tl_use:N \l_@@_prefix_tl -1}
+          \tl_set_eq:cc {knot \tl_use:N \l_@@_prefix_tl -1} {knot \tl_use:N \l_@@_tmpg_tl}
+
+          \tl_clear_new:c {l_@@_options_ \tl_use:N \l_@@_prefix_tl -1}
+          \tl_set_eq:cc {l_@@_options_ \tl_use:N \l_@@_prefix_tl -1} {l_@@_options_ \tl_use:N \l_@@_tmpg_tl}
+
+          \bool_if:nT
+          {
+            \l_@@_prepend_prev_bool
+            &&
+            \tl_if_exist_p:c {knot previous \tl_use:N \l_@@_tmpg_tl}
+            &&
+            !\tl_if_empty_p:c {knot previous \tl_use:N \l_@@_tmpg_tl}
+          }
+          {
+            \spath_prepend_no_move:cv {knot \tl_use:N \l_@@_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l_@@_tmpg_tl}}
+%    \end{macrocode}
+% If we split potentially self intersecting curves, we test to see if we should prepend yet another segment.
+%    \begin{macrocode}
+            \bool_if:nT
+            {
+              \l_@@_splits_bool
+              &&
+              \tl_if_exist_p:c {knot previous \tl_use:N \l_@@_tmpg_tl}
+              &&
+              !\tl_if_empty_p:c {knot previous \tl_use:N \l_@@_tmpg_tl}
+            }
+            {
+              \knot_test_endpoint:vnT {knot previous \tl_use:N \l_@@_tmpg_tl} {initial point}
+              {
+                
+                \spath_prepend_no_move:cv {knot \tl_use:N \l_@@_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l_@@_tmpg_tl}}}
+                \tl_set_eq:Nc \l_@@_tmpa_tl {knot \tl_use:N \l_@@_prefix_tl -1}
+              }
+            }
+          }
+%    \end{macrocode}
+% Now the same for appending.
+%    \begin{macrocode}
+          \bool_if:nT
+          {
+            \l_@@_append_next_bool
+            &&
+            \tl_if_exist_p:c {knot next \tl_use:N \l_@@_tmpg_tl}
+            &&
+            !\tl_if_empty_p:c {knot previous \tl_use:N \l_@@_tmpg_tl}
+          }
+          {
+            \spath_append_no_move:cv {knot \tl_use:N \l_@@_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l_@@_tmpg_tl}}
+            \bool_if:nT
+            {
+              \l_@@_splits_bool
+              &&
+              \tl_if_exist_p:c {knot previous \tl_use:N
+                \l_@@_tmpg_tl}
+              &&
+              !\tl_if_empty_p:c {knot previous \tl_use:N \l_@@_tmpg_tl}
+            }
+            {
+              \knot_test_endpoint:vnT {knot previous \tl_use:N \l_@@_tmpg_tl} {final point}
+              {
+                \spath_append_no_move:cv {knot \tl_use:N \l_@@_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l_@@_tmpg_tl}}}
+                
+              }
+            }
+          }
+
+          \tl_set:Nn \l_@@_tmpg_tl {\tl_use:N \l_@@_prefix_tl -1}
+        }
+      }
+%    \end{macrocode}
+% Now we render the crossing.
+%    \begin{macrocode}
+      \pgfscope
+      \group_begin:
+      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \g_@@_intersections_int/.try}
+      \knot_draw_crossing:VVV \l_@@_tmpg_tl \l_@@_tmpa_dim \l_@@_tmpb_dim
+      \coordinate (\l_@@_name_tl \c_space_tl \int_use:N \g_@@_intersections_int) at (\dim_use:N \l_@@_tmpa_dim, \dim_use:N \l_@@_tmpb_dim);
+      \group_end:
+      \endpgfscope
+%    \end{macrocode}
+% This ends the boolean as to whether to consider the intersection at all      
+%    \begin{macrocode}
+    }
+%    \end{macrocode}
+% And possibly stick a coordinate with a label at the crossing.
+%    \begin{macrocode}
+    \tl_if_empty:NF \l_@@_node_tl
+    {
+      \seq_gpush:Nx \g_@@_nodes_seq { \l_@@_node_tl at (\dim_use:N \l_@@_tmpa_dim, \dim_use:N \l_@@_tmpb_dim) {};}
+    }
+  }
+}
+
+\cs_generate_variant:Nn \knot_intersections:nn {VV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_test_endpoint:N}
+% Test whether the point is near the intersection point.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \knot_test_endpoint:N #1 {p,T,F,TF}
+{
+  \dim_compare:nTF
+  {
+    \dim_abs:n { \l_@@_tmpa_dim - \tl_item:Nn #1 {1}}
+    +
+    \dim_abs:n { \l_@@_tmpb_dim - \tl_item:Nn #1 {2}}
+    <
+    \l_@@_tolerance_dim
+  }
+  {
+    \prg_return_true:
+  }
+  {
+    \prg_return_false:
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_test_endpoint:nn}
+% Wrapper around the above.
+%    \begin{macrocode}
+\prg_new_protected_conditional:Npnn \knot_test_endpoint:nn #1#2 {T,F,TF}
+{
+  \use:c {spath_#2:Nv} \l_@@_tmpd_tl {knot #1}
+  \knot_test_endpoint:NTF \l_@@_tmpd_tl
+  {
+    \prg_return_true:
+  }
+  {
+    \prg_return_false:
+  }
+}
+
+\cs_generate_variant:Nn \knot_test_endpoint:nnT {VnT,vnT}
+\cs_generate_variant:Nn \knot_test_endpoint:nnF {VnF,vnF}
+\cs_generate_variant:Nn \knot_test_endpoint:nnTF {VnTF,vnTF}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_draw_crossing:nnn}
+% This is the code that actually renders a crossing.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_draw_crossing:nnn #1#2#3
+{
+  \group_begin:
+  \pgfscope
+  \path[knot~ diagram/background~ clip] (#2, #3) circle[radius=\l_@@_clip_bg_radius_dim];
+
+  \tl_set:Nn \l_@@_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_if_exist:cT {l_@@_options_ #1}
+  {
+  \tl_put_right:Nv \l_@@_tmpa_tl {l_@@_options_ #1}
+  }
+  \tl_put_right:Nn \l_@@_tmpa_tl {,knotbg,line~ width= \tl_use:N \l_@@_clip_width_tl * \pgflinewidth}
+  \spath_tikz_path:Vv \l_@@_tmpa_tl {knot #1}
+
+  \endpgfscope
+
+  \pgfscope
+  \path[knot~ diagram/clip] (#2, #3) circle[radius=\l_@@_clip_draw_radius_dim];
+
+  \tl_set:Nn \l_@@_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_if_exist:cT {l_@@_options_ #1}
+  {
+  \tl_put_right:Nv \l_@@_tmpa_tl {l_@@_options_ #1}
+  }
+  \tl_put_right:Nn \l_@@_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \spath_tikz_path:Vv \l_@@_tmpa_tl {knot #1}
+
+  \endpgfscope
+  \group_end:
+}
+
+\cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV, VVV}
+
+\cs_new_protected_nopar:Npn \knot_draw_crossing:nn #1#2
+{
+  \tikz@scan@one@point\pgfutil@firstofone #2 \relax
+  \knot_draw_crossing:nVV {#1} \pgf@x \pgf@y
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_split_strands:}
+% This, and the following macros, are for splitting strands into filaments.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_split_strands:
+{
+  \int_gzero:N \g_@@_filaments_int
+  \int_step_function:nnnN {1} {1} {\l_@@_strands_int} \knot_split_strand:n
+  \int_step_function:nnnN {1} {1} {\g_@@_filaments_int} \knot_compute_nexts:n
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_compute_nexts:n}
+% Each filament needs to know its predecessor and successor.
+% We work out the predecessors as we go along, this fills in the successors.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_compute_nexts:n #1
+{
+  \tl_clear_new:c {knot next \tl_use:c {knot previous filament #1}}
+  \tl_set:cn {knot next \tl_use:c {knot previous filament #1}} {filament #1}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_split_strand:n}
+% Sets up the split for a single strand.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_split_strand:n #1
+{
+  \int_set_eq:NN \l_@@_component_start_int \g_@@_filaments_int
+  \int_incr:N \l_@@_component_start_int
+  \tl_set_eq:Nc \l_@@_tmpa_tl {l_@@_options_strand #1}
+  \spath_segments_to_seq:Nv \l_@@_segments_seq {knot strand #1}
+  \seq_map_function:NN \l_@@_segments_seq \knot_save_filament:N
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\knot_save_filament:N}
+% Saves a filament as a new \Verb+spath+ object.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \knot_save_filament:N #1
+{
+  \tl_set:Nx \l_@@_tmpb_tl {\tl_item:nn {#1} {4}}
+  \tl_case:NnF \l_@@_tmpb_tl
+  {
+    \c_spath_moveto_tl
+    {
+      \int_compare:nT {\l_@@_component_start_int < \g_@@_filaments_int}
+      {
+        \int_set_eq:NN \l_@@_component_start_int \g_@@_filaments_int
+      }
+    }
+    \c_spath_lineto_tl
+    {
+      \int_gincr:N \g_@@_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g_@@_filaments_int}
+      \tl_set:cn {knot filament \int_use:N \g_@@_filaments_int} {#1}
+      
+      \tl_clear_new:c {l_@@_options_filament \int_use:N \g_@@_filaments_int}
+      \tl_set_eq:cN {l_@@_options_filament \int_use:N \g_@@_filaments_int} \l_@@_tmpa_tl
+
+      \tl_clear_new:c {knot previous filament \int_use:N \g_@@_filaments_int}
+      \int_compare:nF {\l_@@_component_start_int == \g_@@_filaments_int}
+      {
+        \tl_set:cx {knot previous filament \int_use:N \g_@@_filaments_int} {filament \int_eval:n {\g_@@_filaments_int - 1}}
+      }
+    }
+    \c_spath_curvetoa_tl
+    {
+      \int_gincr:N \g_@@_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g_@@_filaments_int}
+      \tl_set:cn {knot filament \int_use:N \g_@@_filaments_int} {#1}
+      \tl_clear_new:c {l_@@_options_filament \int_use:N \g_@@_filaments_int}
+      \tl_set_eq:cN {l_@@_options_filament \int_use:N \g_@@_filaments_int} \l_@@_tmpa_tl
+
+      \tl_clear_new:c {knot previous filament \int_use:N \g_@@_filaments_int}
+      \int_compare:nF {\l_@@_component_start_int == \g_@@_filaments_int}
+      {
+        \tl_set:cx {knot previous filament \int_use:N \g_@@_filaments_int} {filament \int_eval:n {\g_@@_filaments_int - 1}}
+      }
+    }
+    \c_spath_closepath_tl
+    {
+      \int_gincr:N \g_@@_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g_@@_filaments_int}
+      \tl_clear:N \l_@@_tmpa_tl
+      \tl_put_right:Nx {\tl_item:nn {#1} {1}\tl_item:nn {#1} {2}\tl_item:nn {#1} {3}}
+      \tl_put_right:NV \l_@@_tmpa_tl \c_spath_lineto_tl
+      \tl_put_right:Nx {\tl_item:nn {#1} {5}\tl_item:nn {#1} {6}}
+
+      \tl_set:cV {knot filament \int_use:N \g_@@_filaments_int} \l_@@_tmpa_tl
+      \tl_set_eq:cN {l_@@_options_filament \int_use:N \g_@@_filaments_int} \l_@@_tmpa_tl
+      \tl_clear_new:c {knot previous filament \int_use:N \g_@@_filaments_int}
+      \int_compare:nF {\l_@@_component_start_int == \g_@@_filaments_int}
+      {
+        \tl_set:cx {knot previous filament \int_use:N \g_@@_filaments_int} {filament \int_eval:n {\g_@@_filaments_int - 1}}
+      }
+      \tl_set:cx {knot previous filament \int_use:N \l_@@_component_start_int} {filament \int_use:N \g_@@_filaments_int}
+    }
+  }
+  {
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\redraw}
+% The user can redraw segments of the strands at specific locations.
+%    \begin{macrocode}
+\NewDocumentCommand \redraw { m m }
+{
+%  \tikz@scan@one@point\pgfutil@firstofone #2 \relax
+  \tl_put_right:Nn \l_@@_redraws_tl {\knot_draw_crossing:nn}
+  \tl_put_right:Nx \l_@@_redraws_tl {
+    {strand #1} {#2}% {\dim_use:N \pgf@x} {\dim_use:N \pgf@y}
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\ExplSyntaxOff
+%    \end{macrocode}
+%<@@=>
+%
+% \begin{macro}[internal]{\pgf@sh@@knotanchor}
+% Add the extra anchors for the knot crossing nodes.
+%    \begin{macrocode}
+\def\pgf@sh@@knotanchor#1#2{%
+  \anchor{#2 north west}{%
+    \csname pgf@anchor@knot #1@north west\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 north east}{%
+    \csname pgf@anchor@knot #1@north east\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 south west}{%
+    \csname pgf@anchor@knot #1@south west\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 south east}{%
+    \csname pgf@anchor@knot #1@south east\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 north}{%
+    \csname pgf@anchor@knot #1@north\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 east}{%
+    \csname pgf@anchor@knot #1@east\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 west}{%
+    \csname pgf@anchor@knot #1@west\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+  \anchor{#2 south}{%
+    \csname pgf@anchor@knot #1@south\endcsname%
+    \pgf@x=#2\pgf@x%
+    \pgf@y=#2\pgf@y%
+  }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{knot crossing}
+%    \begin{macrocode}
+\pgfdeclareshape{knot crossing}
+{
+  \inheritsavedanchors[from=circle] % this is nearly a circle
+  \inheritanchorborder[from=circle]
+  \inheritanchor[from=circle]{north}
+  \inheritanchor[from=circle]{north west}
+  \inheritanchor[from=circle]{north east}
+  \inheritanchor[from=circle]{center}
+  \inheritanchor[from=circle]{west}
+  \inheritanchor[from=circle]{east}
+  \inheritanchor[from=circle]{mid}
+  \inheritanchor[from=circle]{mid west}
+  \inheritanchor[from=circle]{mid east}
+  \inheritanchor[from=circle]{base}
+  \inheritanchor[from=circle]{base west}
+  \inheritanchor[from=circle]{base east}
+  \inheritanchor[from=circle]{south}
+  \inheritanchor[from=circle]{south west}
+  \inheritanchor[from=circle]{south east}
+  \inheritanchorborder[from=circle]
+  \pgf@sh@@knotanchor{crossing}{2}
+  \pgf@sh@@knotanchor{crossing}{3}
+  \pgf@sh@@knotanchor{crossing}{4}
+  \pgf@sh@@knotanchor{crossing}{8}
+  \pgf@sh@@knotanchor{crossing}{16}
+  \pgf@sh@@knotanchor{crossing}{32}
+  \backgroundpath{
+    \pgfutil@tempdima=\radius%
+    \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}%  
+    \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}%  
+    \ifdim\pgf@xb<\pgf@yb%
+      \advance\pgfutil@tempdima by-\pgf@yb%
+    \else%
+      \advance\pgfutil@tempdima by-\pgf@xb%
+    \fi%
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{knot over cross}
+%    \begin{macrocode}
+\pgfdeclareshape{knot over cross}
+{
+  \inheritsavedanchors[from=rectangle] % this is nearly a circle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{north west}
+  \inheritanchor[from=rectangle]{north east}
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  \inheritanchor[from=rectangle]{mid}
+  \inheritanchor[from=rectangle]{mid west}
+  \inheritanchor[from=rectangle]{mid east}
+  \inheritanchor[from=rectangle]{base}
+  \inheritanchor[from=rectangle]{base west}
+  \inheritanchor[from=rectangle]{base east}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{south west}
+  \inheritanchor[from=rectangle]{south east}
+  \inheritanchorborder[from=rectangle]
+  \backgroundpath{
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
+  }
+  \foregroundpath{
+% store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
+ }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{knot under cross}
+%    \begin{macrocode}
+\pgfdeclareshape{knot under cross}
+{
+  \inheritsavedanchors[from=rectangle] % this is nearly a circle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{north west}
+  \inheritanchor[from=rectangle]{north east}
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  \inheritanchor[from=rectangle]{mid}
+  \inheritanchor[from=rectangle]{mid west}
+  \inheritanchor[from=rectangle]{mid east}
+  \inheritanchor[from=rectangle]{base}
+  \inheritanchor[from=rectangle]{base west}
+  \inheritanchor[from=rectangle]{base east}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{south west}
+  \inheritanchor[from=rectangle]{south east}
+  \inheritanchorborder[from=rectangle]
+  \backgroundpath{
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
+  }
+  \foregroundpath{
+% store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
+ }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{knot vert}
+%    \begin{macrocode}
+\pgfdeclareshape{knot vert}
+{
+  \inheritsavedanchors[from=rectangle] % this is nearly a circle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{north west}
+  \inheritanchor[from=rectangle]{north east}
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  \inheritanchor[from=rectangle]{mid}
+  \inheritanchor[from=rectangle]{mid west}
+  \inheritanchor[from=rectangle]{mid east}
+  \inheritanchor[from=rectangle]{base}
+  \inheritanchor[from=rectangle]{base west}
+  \inheritanchor[from=rectangle]{base east}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{south west}
+  \inheritanchor[from=rectangle]{south east}
+  \inheritanchorborder[from=rectangle]
+  \backgroundpath{
+% store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
+    \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
+ }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{knot horiz}
+%    \begin{macrocode}
+\pgfdeclareshape{knot horiz}
+{
+  \inheritsavedanchors[from=rectangle] % this is nearly a circle
+  \inheritanchorborder[from=rectangle]
+  \inheritanchor[from=rectangle]{north}
+  \inheritanchor[from=rectangle]{north west}
+  \inheritanchor[from=rectangle]{north east}
+  \inheritanchor[from=rectangle]{center}
+  \inheritanchor[from=rectangle]{west}
+  \inheritanchor[from=rectangle]{east}
+  \inheritanchor[from=rectangle]{mid}
+  \inheritanchor[from=rectangle]{mid west}
+  \inheritanchor[from=rectangle]{mid east}
+  \inheritanchor[from=rectangle]{base}
+  \inheritanchor[from=rectangle]{base west}
+  \inheritanchor[from=rectangle]{base east}
+  \inheritanchor[from=rectangle]{south}
+  \inheritanchor[from=rectangle]{south west}
+  \inheritanchor[from=rectangle]{south east}
+  \inheritanchorborder[from=rectangle]
+  \foregroundpath{
+% store lower right in xa/ya and upper right in xb/yb
+    \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y
+    \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}
+    \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}
+    \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}
+ }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \iffalse
+%</knots>
+% \fi
+%\Finale
+\endinput
diff --git a/Master/texmf-dist/source/latex/spath3/spath3.ins b/Master/texmf-dist/source/latex/spath3/spath3_code.ins
index b49c85b6e71..6c191765e5e 100644
--- a/Master/texmf-dist/source/latex/spath3/spath3.ins
+++ b/Master/texmf-dist/source/latex/spath3/spath3_code.ins
@@ -1,24 +1,24 @@
 %%
-%% This is file `spath3.ins',
+%% This is file `spath3_code.ins',
 %% generated with the docstrip utility.
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `install')
+%% spath3_code.dtx  (with options: `install')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
 %% 
-\input docstrip.tex
+\input l3docstrip.tex
 \keepsilent
 \askforoverwritefalse
 \preamble
 ----------------------------------------------------------------
 spath3 --- Functions for manipulating PGF soft paths
-E-mail: stacey@math.ntnu.no
+E-mail: loopspace@mathforge.org
 Released under the LaTeX Project Public License v1.3c or later
 See http://www.latex-project.org/lppl.txt
 ----------------------------------------------------------------
@@ -26,7 +26,7 @@ See http://www.latex-project.org/lppl.txt
 \endpreamble
 \postamble
 
-Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 
 This work may be distributed and/or modified under the
 conditions of the LaTeX Project Public License (LPPL), either
@@ -41,19 +41,22 @@ Andrew Stacey.
 This work consists of the files  spath3.dtx
                                  calligraphy_doc.tex
                                  knots_doc.tex
+                                 spath3.tex
 and the derived files            spath3.ins,
                                  spath3_code.pdf,
                                  spath3.sty,
                                  tikzlibrarycalligraphy.code.tex
                                  tikzlibraryknots.code.tex
+                                 tikzlibraryspath3.code.tex
                                  calligraphy.pdf
                                  knots.pdf
+                                 spath3.pdf
                                  README
 
 \endpostamble
 \usedir{tex/latex/spath3}
 \generate{
-  \file{\jobname.sty}{\from{\jobname.dtx}{spath3}}
+  \file{spath3.sty}{\from{\jobname.dtx}{spath3}}
 }
 \generate{
   \file{tikzlibrarycalligraphy.code.tex}{\from{\jobname.dtx}{calligraphy}}
@@ -61,9 +64,12 @@ and the derived files            spath3.ins,
 \generate{
   \file{tikzlibraryknots.code.tex}{\from{\jobname.dtx}{knots}}
 }
+\generate{
+  \file{tikzlibraryspath3.code.tex}{\from{\jobname.dtx}{tikzspath3}}
+}
 \endbatchfile
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -78,14 +84,17 @@ and the derived files            spath3.ins,
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
-%% End of file `spath3.ins'.
+%% End of file `spath3_code.ins'.
diff --git a/Master/texmf-dist/tex/latex/spath3/spath3.sty b/Master/texmf-dist/tex/latex/spath3/spath3.sty
index 43fd64cf5e2..155441947b0 100644
--- a/Master/texmf-dist/tex/latex/spath3/spath3.sty
+++ b/Master/texmf-dist/tex/latex/spath3/spath3.sty
@@ -4,10 +4,10 @@
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `spath3')
+%% spath3_code.dtx  (with options: `spath3')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
@@ -15,335 +15,610 @@
 \NeedsTeXFormat{LaTeX2e}
 \RequirePackage{expl3}
 \RequirePackage{pgf}
-\ProvidesExplPackage {spath3} {2019/02/12} {1.2} {Functions for
+\ProvidesExplPackage {spath3} {2021/01/19} {2.0} {Functions for
 manipulating PGF soft paths}
 \RequirePackage{xparse}
+\cs_new_protected:Nn \__spath_tl_put_right_braced:Nn
+{
+  \tl_put_right:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_put_right_braced:Nn { NV, cV, cv, Nx, cx }
+
+\cs_new_protected:Nn \__spath_tl_gput_right_braced:Nn
+{
+  \tl_gput_right:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_gput_right_braced:Nn { NV, cV, cv, Nx, cx }
+\cs_new_protected:Nn \__spath_tl_put_left_braced:Nn
+{
+  \tl_put_left:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_put_left_braced:Nn { NV, cV, cv, Nx, cx }
+
+\cs_new_protected:Nn \__spath_tl_gput_left_braced:Nn
+{
+  \tl_gput_left:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_gput_left_braced:Nn { NV, cV, cv, Nx, cx }
 \tl_new:N \l__spath_tmpa_tl
 \tl_new:N \l__spath_tmpb_tl
 \tl_new:N \l__spath_tmpc_tl
 \tl_new:N \l__spath_tmpd_tl
-\tl_new:N \l__spath_smuggle_tl
+\tl_new:N \l__spath_tmpe_tl
+
+\seq_new:N \l__spath_tmpa_seq
+\seq_new:N \l__spath_tmpb_seq
+
+\tl_new:N \g__spath_output_tl
+\int_new:N \g__spath_output_int
+\seq_new:N \g__spath_output_seq
+
 \dim_new:N \l__spath_tmpa_dim
 \dim_new:N \l__spath_tmpb_dim
+\dim_new:N \l__spath_move_x_dim
+\dim_new:N \l__spath_move_y_dim
 \fp_new:N \l__spath_tmpa_fp
 \fp_new:N \l__spath_tmpb_fp
 \int_new:N \l__spath_tmpa_int
-\int_new:N \g__spath_map_int
-\tl_new:N \g__spath_moveto_tl
-\tl_new:N \g__spath_lineto_tl
-\tl_new:N \g__spath_curveto_tl
-\tl_new:N \g__spath_curvetoa_tl
-\tl_new:N \g__spath_curvetob_tl
-\tl_new:N \g__spath_closepath_tl
-\tl_set:Nn \g__spath_moveto_tl {\pgfsyssoftpath@movetotoken}
-\tl_set:Nn \g__spath_lineto_tl {\pgfsyssoftpath@linetotoken}
-\tl_set:Nn \g__spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
-\tl_set:Nn \g__spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
-\tl_set:Nn \g__spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
-\tl_set:Nn \g__spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
-\tl_new:N \g__spath_attributes
-\tl_new:N \g__spath_moveable_attributes
-\tl_new:N \g__spath_path_attributes
-\tl_set:Nn \g__spath_attributes {
-  {path}
-  {reverse path}
-  {length}
-  {real length}
-  {number of components}
-  {initial point}
-  {final point}
-  {initial action}
-  {final action}
-  {min bb}
-  {max bb}
-}
-\tl_set:Nn \g__spath_moveable_attributes {
-  {initial point}
-  {final point}
-  {min bb}
-  {max bb}
-}
-\tl_set:Nn \g__spath_path_attributes {
-  {path}
-  {reverse path}
-}
-\cs_new_nopar:Npn \spath_new:n #1
-{
-  \prop_new:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_clear:n #1
-{
-  \prop_gclear:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_clear_new:n #1
-{
-  \prop_gclear_new:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_show:n #1
-{
-  \prop_show:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_put:nnn #1#2#3
-{
-  \prop_gput:cnn {l__spath_#1} {#2} {#3}
-}
-\cs_new_nopar:Npn \spath_remove:nn #1#2
-{
-  \prop_gremove:cn {l__spath_#1} {#2}
-}
-\cs_new_nopar:Npn \__spath_get:nn #1#2
-{
-  \prop_item:cn {l__spath_#1} {#2}
-}
-\cs_new_nopar:Npn \__spath_get:nnN #1#2#3
+
+\bool_new:N \g__spath_output_bool
+\bool_new:N \l__spath_closed_bool
+\tl_const:Nn \c_spath_moveto_tl {\pgfsyssoftpath@movetotoken}
+\tl_const:Nn \c_spath_lineto_tl {\pgfsyssoftpath@linetotoken}
+\tl_const:Nn \c_spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
+\tl_const:Nn \c_spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
+\tl_const:Nn \c_spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
+\tl_const:Nn \c_spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
+\int_new:N \g__spath_anon_int
+\int_gzero:N \g__spath_anon_int
+\tl_new:N \l__spath_itera_tl
+\tl_new:N \l__spath_iterb_tl
+\tl_new:N \l__spath_iterc_tl
+\tl_new:N \l__spath_iterd_tl
+\tl_new:N \l__spath_iterp_tl
+\dim_new:N \l__spath_itera_dim
+\dim_new:N \l__spath_iterb_dim
+\seq_new:N \l__spath_iter_seq
+\msg_new:nnn { spath3 } { unknown path construction } { The~ path~ construction~ element~ #1~ is~ not~ currently~ supported.}
+\cs_new_protected_nopar:Npn \__spath_segments_to_seq:n #1
 {
-  \prop_get:cnN {l__spath_#1} {#2} #3
+  \group_begin:
+  \tl_set:Nn \l__spath_itera_tl {#1}
+  \tl_clear:N \l__spath_iterb_tl
+  \seq_clear:N \l__spath_iter_seq
+  \dim_zero:N \l__spath_itera_dim
+  \dim_zero:N \l__spath_iterb_dim
+
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_itera_tl
+  }
+  {
+    \tl_set:Nx \l__spath_iterc_tl {\tl_head:N \l__spath_itera_tl}
+    \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+    \tl_case:NnF \l__spath_iterc_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_set:Nx \l__spath_iterd_tl {\tl_head:N \l__spath_itera_tl}
+        \tl_if_eq:NNF \l__spath_iterd_tl \c_spath_moveto_tl
+        {
+          \tl_clear:N \l__spath_iterb_tl
+        }
+
+      }
+
+      \c_spath_lineto_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl
+        {
+          {\dim_use:N \l__spath_itera_dim}
+          {\dim_use:N \l__spath_iterb_dim}
+        }
+        \tl_put_right:NV \l__spath_iterb_tl \c_spath_lineto_tl
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      }
+
+      \c_spath_curvetoa_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl
+        {
+          {\dim_use:N \l__spath_itera_dim}
+          {\dim_use:N \l__spath_iterb_dim}
+        }
+        \tl_put_right:NV \l__spath_iterb_tl \c_spath_curvetoa_tl
+
+        \prg_replicate:nn {2} {
+          \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+          \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+          \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N               \l__spath_itera_tl}}
+          \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+          \tl_put_right:Nx \l__spath_iterb_tl {\tl_head:N             \l__spath_itera_tl}
+          \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+        }
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      }
+
+      \c_spath_closepath_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl
+        {
+          {\dim_use:N \l__spath_itera_dim}
+          {\dim_use:N \l__spath_iterb_dim}
+        }
+        \tl_put_right:NV \l__spath_iterb_tl \c_spath_lineto_tl
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      }
+
+    }
+    {
+
+      \tl_set_eq:NN \l__spath_iterb_tl \l__spath_iterc_tl
+      \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+      \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+      \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+      \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+      \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+    }
+
+    \tl_if_empty:NF \l__spath_iterb_tl
+    {
+      \seq_put_right:NV \l__spath_iter_seq \l__spath_iterb_tl
+    }
+    \tl_clear:N \l__spath_iterb_tl
+  }
+
+  \seq_gclear:N \g__spath_output_seq
+  \seq_gset_eq:NN \g__spath_output_seq \l__spath_iter_seq
+  \group_end:
 }
-\prg_new_conditional:Npnn \spath_if_in:nn #1#2 {p, T, F, TF}
+\cs_new_protected_nopar:Npn \spath_segments_to_seq:Nn #1#2
 {
-  \prop_if_in:cnTF {l__spath_#1} {#2}
-  { \prg_return_true: }
-  { \prg_return_false: }
+  \__spath_segments_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_set_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \__prop_split:NnTF {cnTF}
-\prg_new_protected_conditional:Npnn \__spath_get:nnN #1#2#3 {T, F, TF}
+\cs_generate_variant:Nn \spath_segments_to_seq:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \spath_segments_gto_seq:Nn #1#2
 {
-  \__prop_split:cnTF {l__spath_#1} {#2}
-  {
-    \tl_set:Nn #3 {##2}
-    \prg_return_true:
-  }
-  { \prg_return_false: }
+  \__spath_segments_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_gset_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \spath_put:nnn {nnV, nnx, nno}
-\cs_generate_variant:Nn \__spath_get:nn {Vn}
-\cs_generate_variant:Nn \__spath_get:nnN {VnN}
-\prg_new_conditional:Npnn \spath_if_exist:n #1 {p,T,F,TF}
+\cs_generate_variant:Nn \spath_segments_gto_seq:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \__spath_components_to_seq:n #1
 {
-  \prop_if_exist:cTF {l__spath_#1}
-  {
-    \prg_return_true:
-  }
-  {
-    \prg_return_false:
+  \group_begin:
+  \tl_set:Nn \l__spath_itera_tl {#1}
+  \seq_clear:N \l__spath_iter_seq
+  \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+  \tl_put_right:NV \l__spath_itera_tl \c_spath_moveto_tl
+  \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+  \bool_do_until:nn {
+    \tl_if_empty_p:N \l__spath_itera_tl
   }
-}
-\cs_new_nopar:Npn \spath_clone:nn #1 #2
-{
-  \spath_clear_new:n {#2}
-  \tl_map_inline:Nn \g__spath_attributes
   {
-    \spath_if_in:nnT {#1} {##1}
+    \tl_set:Nx \l__spath_iterc_tl {\tl_head:N \l__spath_itera_tl}
+    \tl_if_eq:NNT \l__spath_iterc_tl \c_spath_moveto_tl
+    {
+      \seq_put_right:NV \l__spath_iter_seq \l__spath_iterb_tl
+      \tl_clear:N \l__spath_iterb_tl
+    }
+    \tl_if_single:NTF \l__spath_iterc_tl
+    {
+      \tl_put_right:NV \l__spath_iterb_tl \l__spath_iterc_tl
+    }
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \spath_put:nnV {#2} {##1} \l__spath_tmpa_tl
+      \tl_put_right:Nx \l__spath_iterb_tl {{\l__spath_iterc_tl}}
     }
+    \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
   }
-}
-\cs_new_protected_nopar:Npn \spath_get_current_path:n #1
-{
-  \pgfsyssoftpath@getcurrentpath\l__spath_tmpa_tl
-  \spath_clear_new:n {#1}
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-}
-\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
-{
-  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
 
-  \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \pgfsyssoftpath@setcurrentpath\l__spath_tmpa_tl
-  \pgfsyssoftpath@flushcurrentpath
-}
-\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
-{
-  \spath_set_current_path:n {#1}
-  \pgfusepath{#2}
+  \seq_gclear:N \g__spath_output_seq
+  \seq_gset_eq:NN \g__spath_output_seq \l__spath_iter_seq
+  \group_end:
 }
-\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
+\cs_new_protected_nopar:Npn \spath_components_to_seq:Nn #1#2
 {
-  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
+  \__spath_components_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_set_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
+\cs_generate_variant:Nn \spath_components_to_seq:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_gto_seq:Nn #1#2
 {
-  \path[#1] \pgfextra{
-    \spath_get:nnN {#2} {path} \l__spath_tmpa_tl
-    \pgfsyssoftpath@setcurrentpath \l__spath_tmpa_tl
-  };
+  \__spath_components_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_gset_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \spath_tikz_path:nn {Vn}
-\cs_new_nopar:Npn \spath_get:nn #1#2
+\cs_generate_variant:Nn \spath_components_gto_seq:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_to_clist:Nn #1#2
 {
-  \spath_if_in:nnF {#1} {#2}
-  {
-    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
-  }
-  \__spath_get:nn {#1} {#2}
+  \__spath_components_to_seq:n {#2}
+  \clist_clear_new:N #1
+  \clist_set_from_seq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_new_nopar:Npn \spath_get:nnN #1#2#3
+\cs_generate_variant:Nn \spath_components_to_clist:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_gto_clist:Nn #1#2
 {
-  \spath_if_in:nnF {#1} {#2}
-  {
-    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
-  }
-  \__spath_get:nnN {#1} {#2} #3
+  \__spath_components_to_seq:n {#2}
+  \clist_clear_new:N #1
+  \clist_gset_from_seq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \spath_get:nnN {VnN}
-\cs_new_nopar:Npn \spath_generate_length:n #1
+\cs_generate_variant:Nn \spath_components_gto_clist:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_length:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \spath_put:nnx {#1} {length} {\int_eval:n {\tl_count:N \l__spath_tmpa_tl /3 }}
+  \int_eval:n {\tl_count:n {#1} / 3}
 }
-\cs_new_nopar:Npn \spath_generate_reallength:n #1
+\cs_generate_variant:Nn \spath_length:n {V}
+\cs_new_protected_nopar:Npn \__spath_reallength:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
   \int_set:Nn \l__spath_tmpa_int {0}
-  \tl_map_inline:Nn \l__spath_tmpa_tl {
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@linetotoken}
+  \tl_map_inline:nn {#1} {
+    \tl_set:Nn \l__spath_tmpc_tl {##1}
+    \tl_case:NnT \l__spath_tmpc_tl
     {
-      \int_incr:N \l__spath_tmpa_int
+      \c_spath_lineto_tl {}
+      \c_spath_curveto_tl {}
+      \c_spath_closepath_tl {}
     }
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@curvetotoken}
     {
       \int_incr:N \l__spath_tmpa_int
     }
   }
-  \spath_put:nnx {#1} {real length} {\int_use:N \l__spath_tmpa_int}
+  \int_gzero:N \g__spath_output_int
+  \int_gset_eq:NN \g__spath_output_int \l__spath_tmpa_int
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_reallength:Nn #1#2
+{
+  \__spath_reallength:n {#2}
+  \int_set_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
+}
+\cs_generate_variant:Nn \spath_reallength:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \spath_greallength:Nn #1#2
+{
+  \__spath_reallength:n {#2}
+  \int_gset_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
 }
-\cs_new_nopar:Npn \spath_generate_numberofcomponents:n #1
+\cs_generate_variant:Nn \spath_greallength:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \__spath_numberofcomponents:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
   \int_set:Nn \l__spath_tmpa_int {0}
-  \tl_map_inline:Nn \l__spath_tmpa_tl {
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@movetotoken}
+  \tl_map_inline:nn {#1} {
+    \tl_set:Nn \l__spath_tmpa_tl {##1}
+    \tl_case:Nn \l__spath_tmpa_tl
     {
-      \int_incr:N \l__spath_tmpa_int
+      \c_spath_moveto_tl
+      {
+        \int_incr:N \l__spath_tmpa_int
+      }
     }
   }
-  \spath_put:nnx {#1} {number of components} {\int_use:N \l__spath_tmpa_int}
+  \int_gzero:N \g__spath_output_int
+  \int_gset_eq:NN \g__spath_output_int \l__spath_tmpa_int
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_generate_initialpoint:n #1
+\cs_new_protected_nopar:Npn \spath_numberofcomponents:Nn #1#2
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  \spath_put:nnV {#1} {initial point} \l__spath_tmpb_tl
+  \__spath_numberofcomponents:n {#2}
+  \int_set_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
+}
+\cs_generate_variant:Nn \spath_numberofcomponents:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gnumberofcomponents:Nn #1#2
+{
+  \__spath_numberofcomponents:n {#2}
+  \int_gset_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
 }
-\cs_new_nopar:Npn \spath_generate_finalpoint:n #1
+\cs_generate_variant:Nn \spath_gnumberofcomponents:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \__spath_initialpoint:n #1
 {
+  \group_begin:
   \tl_clear:N \l__spath_tmpb_tl
-  \spath_if_in:nnTF {#1} {reverse path}
+  \tl_set:Nx \l__spath_tmpb_tl
   {
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+    { \tl_item:nn {#1} {2} }
+    { \tl_item:nn {#1} {3} }
   }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_initialpoint:Nn #1#2
+{
+  \__spath_initialpoint:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_initialpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_ginitialpoint:Nn #1#2
+{
+  \__spath_initialpoint:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_ginitialpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \__spath_finalpoint:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_reverse:N \l__spath_tmpa_tl
+  \tl_clear:N \l__spath_tmpb_tl
+  \tl_set:Nx \l__spath_tmpb_tl
   {
-    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \tl_reverse:N \l__spath_tmpa_tl
-    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+    { \tl_item:Nn \l__spath_tmpa_tl {2} }
+    { \tl_item:Nn \l__spath_tmpa_tl {1} }
   }
-  \spath_put:nnV {#1} {final point} \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalpoint:Nn #1#2
+{
+  \__spath_finalpoint:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_finalpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_gfinalpoint:Nn #1#2
+{
+  \__spath_finalpoint:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_generate_variant:Nn \spath_generate_finalpoint:n {V}
-\cs_new_nopar:Npn \spath_generate_reversepath:n #1
+\cs_generate_variant:Nn \spath_gfinalpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \__spath_reverse:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+
   \tl_clear:N \l__spath_tmpb_tl
+  \tl_clear:N \l__spath_tmpd_tl
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_left:Nx \l__spath_tmpb_tl
+
+  \tl_put_left:Nx \l__spath_tmpd_tl
   {
     {\dim_use:N \l__spath_tmpa_dim}
     {\dim_use:N \l__spath_tmpb_dim}
   }
+
+  \bool_set_false:N \l__spath_closed_bool
+
   \bool_until_do:nn {
     \tl_if_empty_p:N \l__spath_tmpa_tl
   }
   {
     \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nn \l__spath_tmpd_tl {}
-    \tl_case:NnF \l__spath_tmpc_tl
+
+    \tl_case:NnTF \l__spath_tmpc_tl
     {
-      \g__spath_moveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl }
-      \g__spath_lineto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl }
-      \g__spath_curveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl }
-      \g__spath_curvetoa_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl }
-      \g__spath_curvetob_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl }
+      \c_spath_moveto_tl {
+
+        \bool_if:NT \l__spath_closed_bool
+        {
+          \tl_put_right:NV \l__spath_tmpd_tl \c_spath_closepath_tl
+          \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpd_tl}
+          \tl_put_right:Nx \l__spath_tmpd_tl
+          {
+            { \tl_head:N \l__spath_tmpd_tl }
+            { \tl_head:N \l__spath_tmpe_tl }
+          }
+        }
+        \bool_set_false:N \l__spath_closed_bool
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_moveto_tl
+        \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
+        \tl_clear:N \l__spath_tmpd_tl
+      }
+      \c_spath_lineto_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_lineto_tl
+      }
+      \c_spath_curveto_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_curvetoa_tl
+      }
+      \c_spath_curvetoa_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_curveto_tl
+      }
+      \c_spath_curvetob_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_curvetob_tl
+      }
     }
     {
-      \tl_show:N \l__spath_tmpc_tl
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+      \tl_put_left:Nx \l__spath_tmpd_tl
+      {
+        {\dim_use:N \l__spath_tmpa_dim}
+        {\dim_use:N \l__spath_tmpb_dim}
+      }
+
     }
-    \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_left:Nx \l__spath_tmpb_tl
     {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
+      \tl_if_eq:NNTF \l__spath_tmpc_tl \c_spath_closepath_tl
+      {
+        \bool_set_true:N \l__spath_closed_bool
+      }
+      {
+        \msg_warning:nnx { spath3 } { unknown path construction } {\l__spath_tmpc_tl }
+      }
+
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
     }
   }
-  \tl_put_left:NV \l__spath_tmpb_tl \g__spath_moveto_tl
-  \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
+
+  \bool_if:NT \l__spath_closed_bool
+  {
+    \tl_put_right:NV \l__spath_tmpd_tl \c_spath_closepath_tl
+    \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpd_tl}
+    \tl_put_right:Nx \l__spath_tmpd_tl
+    {
+      { \tl_head:N \l__spath_tmpd_tl }
+      { \tl_head:N \l__spath_tmpe_tl }
+    }
+  }
+
+  \bool_set_false:N \l__spath_closed_bool
+  \tl_put_left:NV \l__spath_tmpd_tl \c_spath_moveto_tl
+  \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
+
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_generate_initialaction:n #1
+\cs_new_protected_nopar:Npn \spath_reverse:Nn #1#2
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_if_empty:NF \l__spath_tmpa_tl {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-  }
-  \spath_put:nnV {#1} {initial action} \l__spath_tmpb_tl
+  \__spath_reverse:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_generate_finalaction:n #1
+\cs_generate_variant:Nn \spath_reverse:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_reverse:N #1
 {
-  \tl_clear:N \l__spath_tmpb_tl
-  \spath_if_in:nnTF {#1} {reverse path}
+  \spath_reverse:NV #1#1
+}
+\cs_generate_variant:Nn \spath_reverse:N {c}
+\cs_new_protected_nopar:Npn \spath_greverse:Nn #1#2
+{
+  \__spath_reverse:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_greverse:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_greverse:N #1
+{
+  \spath_greverse:NV #1#1
+}
+\cs_generate_variant:Nn \spath_greverse:N {c}
+\cs_new_protected_nopar:Npn \__spath_initialaction:n #1
+{
+  \group_begin:
+  \tl_clear:N \l__spath_tmpa_tl
+  \int_compare:nT
   {
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_count:n {#1} > 3
   }
   {
-    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \tl_reverse:N \l__spath_tmpa_tl
+    \tl_set:Nx \l__spath_tmpa_tl
+    {
+      \tl_item:Nn {#1} {4}
+    }
   }
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_if_empty:NF \l__spath_tmpa_tl {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_initialaction:Nn #1#2
+{
+  \__spath_initialaction:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_initialaction:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_ginitialaction:Nn #1#2
+{
+  \__spath_initialaction:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_ginitialaction:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_finalaction:n #1
+{
+  \group_begin:
+  \tl_clear:N \l__spath_tmpb_tl
+  \int_compare:nT
+  {
+    \tl_count:n {#1} > 3
   }
-  \tl_if_eq:NNT \l__spath_tmpa_tl \g__spath_curvetoa_tl
   {
-    \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_curveto_tl
+    \tl_set:Nn \l__spath_tmpa_tl {#1}
+    \tl_reverse:N \l__spath_tmpa_tl
+    \tl_set:Nx \l__spath_tmpb_tl
+    {
+      \tl_item:Nn \l__spath_tmpa_tl {3}
+    }
+    \tl_if_eq:NNT \l__spath_tmpb_tl \c_spath_curvetoa_tl
+    {
+      \tl_set_eq:NN \l__spath_tmpb_tl \c_spath_curveto_tl
+    }
   }
-  \spath_put:nnV {#1} {final action} \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalaction:Nn #1#2
+{
+  \__spath_finalaction:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_generate_minbb:n #1
+\cs_generate_variant:Nn \spath_finalaction:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gfinalaction:Nn #1#2
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \__spath_finalaction:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gfinalaction:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_minbb:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
@@ -365,11 +640,27 @@ manipulating PGF soft paths}
     {\dim_use:N \l__spath_tmpa_dim}
     {\dim_use:N \l__spath_tmpb_dim}
   }
-  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_minbb:Nn #1#2
+{
+  \__spath_minbb:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_minbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gminbb:Nn #1#2
+{
+  \__spath_minbb:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_generate_maxbb:n #1
+\cs_generate_variant:Nn \spath_gminbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \__spath_maxbb:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
@@ -391,1101 +682,2440 @@ manipulating PGF soft paths}
     {\dim_use:N \l__spath_tmpa_dim}
     {\dim_use:N \l__spath_tmpb_dim}
   }
-  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
-}
-\tl_new:N \l__spath_rp_tl
-\int_new:N \l__spath_l_int
-\int_new:N \l__spath_rl_int
-\int_new:N \l__spath_nc_int
-\tl_new:N \l__spath_ip_tl
-\tl_new:N \l__spath_fp_tl
-\tl_new:N \l__spath_ia_tl
-\tl_new:N \l__spath_fa_tl
-\dim_new:N \l__spath_minx_dim
-\dim_new:N \l__spath_miny_dim
-\dim_new:N \l__spath_maxx_dim
-\dim_new:N \l__spath_maxy_dim
-
-\cs_new_nopar:Npn \spath_generate_all:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-
-  \tl_clear:N \l__spath_rp_tl
-  \int_set:Nn \l__spath_l_int {1}
-  \int_zero:N \l__spath_rl_int
-  \int_set:Nn \l__spath_nc_int {1}
-  \tl_clear:N \l__spath_ip_tl
-  \tl_clear:N \l__spath_fp_tl
-  \tl_clear:N \l__spath_ia_tl
-  \tl_clear:N \l__spath_fa_tl
-  \dim_zero:N \l__spath_minx_dim
-  \dim_zero:N \l__spath_miny_dim
-  \dim_zero:N \l__spath_maxx_dim
-  \dim_zero:N \l__spath_maxy_dim
-
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-  \tl_clear:N \l__spath_ip_tl
-  \tl_put_right:Nx \l__spath_ip_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_maxbb:Nn #1#2
+{
+  \__spath_maxbb:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_maxbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gmaxbb:Nn #1#2
+{
+  \__spath_maxbb:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gmaxbb:Nn {NV, cn, cV}
+\int_set:Nn \l__spath_tmpa_int {\char_value_catcode:n {`@}}
+\char_set_catcode_letter:N @
+\cs_new_protected_nopar:Npn \spath_save_to_aux:Nn #1#2 {
+  \tl_if_empty:nF {#2}
   {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
+    \tl_clear:N \l__spath_tmpa_tl
+    \tl_put_right:Nn \l__spath_tmpa_tl {
+      \ExplSyntaxOn
+      \tl_clear:N #1
+      \tl_set:Nn #1 {#2}
+      \ExplSyntaxOff
+    }
+    \protected@write\@auxout{}{
+      \tl_to_str:N \l__spath_tmpa_tl
+    }
   }
-
-  \dim_set_eq:NN \l__spath_minx_dim \l__spath_tmpa_dim
-  \dim_set_eq:NN \l__spath_miny_dim \l__spath_tmpb_dim
-  \dim_set_eq:NN \l__spath_maxx_dim \l__spath_tmpa_dim
-  \dim_set_eq:NN \l__spath_maxy_dim \l__spath_tmpb_dim
-
-  \tl_put_left:Nx \l__spath_rp_tl
+}
+\char_set_catcode:nn {`@} {\l__spath_tmpa_int}
+\cs_generate_variant:Nn \spath_save_to_aux:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_save_to_aux:N #1
+{
+  \tl_if_exist:NT #1
   {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
+    \spath_save_to_aux:NV #1#1
   }
-
-  \tl_set:Nx \l__spath_ia_tl {\tl_head:N \l__spath_tmpa_tl}
-
+}
+\cs_new_protected_nopar:Npn \__spath_translate:nnn #1#2#3
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
   \bool_until_do:nn {
     \tl_if_empty_p:N \l__spath_tmpa_tl
   }
   {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nn \l__spath_tmpd_tl {}
-    \tl_set_eq:NN \l__spath_fa_tl \l__spath_tmpc_tl
-    \int_incr:N \l__spath_l_int
-
-    \tl_case:NnF \l__spath_tmpc_tl
-    {
-      \g__spath_moveto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl
-        \int_incr:N \l__spath_nc_int
-      }
-      \g__spath_lineto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl
-        \int_incr:N \l__spath_rl_int
-      }
-      \g__spath_curveto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl
-        \int_incr:N \l__spath_rl_int
-      }
-      \g__spath_curvetoa_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl
-      }
-      \g__spath_curvetob_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl
-      }
-    }
-    {
-      \tl_show:N \l__spath_tmpc_tl
-    }
-    \tl_put_left:NV \l__spath_rp_tl \l__spath_tmpd_tl
+    \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \dim_set:Nn \l__spath_minx_dim {\dim_min:nn { \l__spath_minx_dim} {\l__spath_tmpa_dim}}
-    \dim_set:Nn \l__spath_miny_dim {\dim_min:nn { \l__spath_miny_dim} {\l__spath_tmpb_dim}}
-    \dim_set:Nn \l__spath_maxx_dim {\dim_max:nn { \l__spath_maxx_dim} {\l__spath_tmpa_dim}}
-    \dim_set:Nn \l__spath_maxy_dim {\dim_max:nn { \l__spath_maxy_dim} {\l__spath_tmpb_dim}}
+    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \tl_put_left:Nx \l__spath_rp_tl
+    \tl_put_right:Nx \l__spath_tmpb_tl
     {
       {\dim_use:N \l__spath_tmpa_dim}
       {\dim_use:N \l__spath_tmpb_dim}
     }
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_translate:Nnnn #1#2#3#4
+{
+  \__spath_translate:nnn {#2}{#3}{#4}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_translate:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_translate:Nnn #1#2#3
+{
+  \spath_translate:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_translate:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nnnn #1#2#3#4
+{
+  \__spath_translate:nnn {#2}{#3}{#4}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nnn #1#2#3
+{
+  \spath_gtranslate:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_translate:Nn #1#2
+{
+  \spath_translate:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_translate:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nn #1#2
+{
+  \spath_gtranslate:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_scale:nnn #1#2#3
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
+  }
+  {
+    \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \tl_set:Nx \l__spath_fp_tl
+    \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+    \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+    \tl_put_right:Nx \l__spath_tmpb_tl
     {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
+      {\fp_to_dim:N \l__spath_tmpa_fp}
+      {\fp_to_dim:N \l__spath_tmpb_fp}
     }
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_scale:Nnnn #1#2#3#4
+{
+  \__spath_scale:nnn {#2}{#3}{#4}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_scale:Nnnn {NVnn, Nnxx}
+\cs_new_protected_nopar:Npn \spath_scale:Nnn #1#2#3
+{
+  \spath_scale:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_scale:Nnn {cnn, cVV, NVV}
+\cs_new_protected_nopar:Npn \spath_gscale:Nnnn #1#2#3#4
+{
+  \__spath_scale:nnn {#2}{#3}{#4}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gscale:Nnnn {NVnn, Nnxx}
+\cs_new_protected_nopar:Npn \spath_gscale:Nnn #1#2#3
+{
+  \spath_gscale:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gscale:Nnn {cnn, cVV, NVV}
+\cs_new_protected_nopar:Npn \spath_scale:Nn #1#2
+{
+  \spath_scale:Nnn #1 #2
+}
+
+\cs_generate_variant:Nn \spath_scale:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gscale:Nn #1#2
+{
+  \spath_gscale:Nnn #1 #2
+}
 
+\cs_generate_variant:Nn \spath_gscale:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_transform:nnnnnnn #1#2#3#4#5#6#7
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
   }
+  {
+    \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpd_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-  \tl_put_left:NV \l__spath_rp_tl \g__spath_moveto_tl
+    \fp_set:Nn \l__spath_tmpa_fp {\l__spath_tmpc_tl * #2 + \l__spath_tmpd_tl * #4 + #6}
+    \fp_set:Nn \l__spath_tmpb_fp {\l__spath_tmpc_tl * #3 + \l__spath_tmpd_tl * #5 + #7}
+    \tl_put_right:Nx \l__spath_tmpb_tl
+    {
+      {\fp_to_dim:N \l__spath_tmpa_fp}
+      {\fp_to_dim:N \l__spath_tmpb_fp}
+    }
+  }
 
-  \spath_put:nnV {#1} {reverse path} \l__spath_rp_tl
-  \spath_put:nnV {#1} {length} \l__spath_l_int
-  \spath_put:nnV {#1} {real length} \l__spath_rl_int
-  \spath_put:nnV {#1} {number of components} \l__spath_nc_int
-  \spath_put:nnV {#1} {initial point} \l__spath_ip_tl
-  \spath_put:nnV {#1} {final point} \l__spath_fp_tl
-  \spath_put:nnV {#1} {initial action} \l__spath_ia_tl
-  \spath_put:nnV {#1} {final action} \l__spath_fa_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_transform:Nnnnnnnn #1#2#3#4#5#6#7#8
+{
+  \__spath_transform:nnnnnnn {#2}{#3}{#4}{#5}{#6}{#7}{#8}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_transform:Nnnnnnnn {NVnnnnnn, Nnxxxxxx, cnnnnnnn}
+\cs_new_protected_nopar:Npn \spath_transform:Nnnnnnn #1#2#3#4#5#6#7
+{
+  \spath_transform:NVnnnnnn #1#1{#2}{#3}{#4}{#5}{#6}{#7}
+}
+\cs_generate_variant:Nn \spath_transform:Nnnnnnn {cnnnnnn}
+\cs_new_protected_nopar:Npn \spath_transform:Nnn #1#2#3
+{
+  \spath_transform:Nnnnnnnn #1{#2}#3
+}
+\cs_generate_variant:Nn \spath_transform:Nnn {cnn, cVn, NVn, NnV}
+\cs_new_protected_nopar:Npn \spath_transform:Nn #1#2
+{
+  \spath_transform:NVnnnnnn #1#1#2
+}
+\cs_generate_variant:Nn \spath_transform:Nn {cn, cV, NV}
 
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnnnnnnn #1#2#3#4#5#6#7#8
+{
+  \__spath_transform:nnnnnnn {#2}{#3}{#4}{#5}{#6}{#7}{#8}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnnnnnnn {NVnnnnnn, Nnxxxxxx, cnnnnnnn}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnnnnnn #1#2#3#4#5#6#7
+{
+  \spath_gtransform:NVnnnnnn #1#1{#2}{#3}{#4}{#5}{#6}{#7}
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnnnnnn {cnnnnnn}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnn #1#2#3
+{
+  \spath_gtransform:Nnnnnnnn #1{#2}#3
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnn {cnn, cVn, NVn, NnV}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nn #1#2
+{
+  \spath_gtransform:NVnnnnnn #1#1#2
+}
+\cs_generate_variant:Nn \spath_gtransform:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \__spath_weld:nn #1#2
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nn \l__spath_tmpb_tl {#2}
+
+  \spath_finalpoint:NV \l__spath_tmpc_tl \l__spath_tmpa_tl
+  \spath_initialpoint:NV \l__spath_tmpd_tl \l__spath_tmpb_tl
+
+  \dim_set:Nn \l__spath_tmpa_dim
   {
-    {\dim_use:N \l__spath_minx_dim}
-    {\dim_use:N \l__spath_miny_dim}
+    \tl_item:Nn \l__spath_tmpc_tl {1}
+    -
+    \tl_item:Nn \l__spath_tmpd_tl {1}
+  }
+  \dim_set:Nn \l__spath_tmpb_dim
+  {
+    \tl_item:Nn \l__spath_tmpc_tl {2}
+    -
+    \tl_item:Nn \l__spath_tmpd_tl {2}
   }
-  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
 
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
+  \spath_translate:NVV \l__spath_tmpb_tl \l__spath_tmpa_dim \l__spath_tmpb_dim
+
+  \prg_replicate:nn {3}
   {
-    {\dim_use:N \l__spath_maxx_dim}
-    {\dim_use:N \l__spath_maxy_dim}
+    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
   }
-  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
 
+  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_translate:nnn #1#2#3
+\cs_new_protected_nopar:Npn \spath_weld:Nnn #1#2#3
 {
-  \tl_map_inline:Nn \g__spath_moveable_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
+  \__spath_weld:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_weld:Nnn {NVV,NVn}
+\cs_new_protected_nopar:Npn \spath_weld:Nn #1#2
+{
+  \spath_weld:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_weld:Nn {NV, Nv, cV, cv}
+\cs_new_protected_nopar:Npn \spath_gweld:Nnn #1#2#3
+{
+  \__spath_weld:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gweld:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gweld:Nn #1#2
+{
+  \spath_gweld:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gweld:Nn {NV, Nv, cV, cv}
+\cs_new_protected_nopar:Npn \__spath_append_no_move:nn #1#2
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nn \l__spath_tmpb_tl {#2}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
 
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
+  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_append_no_move:Nnn #1#2#3
+{
+  \__spath_append_no_move:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_append_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_append_no_move:Nn #1#2
+{
+  \spath_append_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_append_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_gappend_no_move:Nnn #1#2#3
+{
+  \__spath_append_no_move:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gappend_no_move:Nn #1#2
+{
+  \spath_gappend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_append:Nnn #1#2#3
+{
+  \tl_set:Nn #1 {#2}
+  \tl_put_right:Nn #1 {#3}
+}
+\cs_generate_variant:Nn \spath_append:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_append:Nn #1#2
+{
+  \spath_append:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_append:Nn {NV, Nv}
+\cs_new_protected_nopar:Npn \spath_gappend:Nnn #1#2#3
+{
+  \tl_gset:Nn #1 {#2}
+  \tl_gput_right:Nn #1 {#3}
+}
+\cs_generate_variant:Nn \spath_gappend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gappend:Nn #1#2
+{
+  \spath_gappend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gappend:Nn {NV, Nv}
+\cs_new_protected_nopar:Npn \spath_prepend_no_move:Nnn #1#2#3
+{
+  \spath_append_no_move:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_prepend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_prepend_no_move:Nn #1#2
+{
+  \spath_prepend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_prepend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_gprepend_no_move:Nnn #1#2#3
+{
+  \spath_gappend_no_move:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gprepend_no_move:Nn #1#2
+{
+  \spath_gprepend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_prepend:Nnn #1#2#3
+{
+  \spath_append:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_prepend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_prepend:Nn #1#2
+{
+  \spath_prepend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_prepend:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gprepend:Nnn #1#2#3
+{
+  \spath_gappend:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gprepend:Nn #1#2
+{
+  \spath_gprepend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_bake_round:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \pgf@@processround \l__spath_tmpa_tl\l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_bake_round:Nn #1#2
+{
+  \__spath_bake_round:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_bake_round:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_bake_round:N #1
+{
+  \spath_bake_round:NV #1#1
+}
+\cs_generate_variant:Nn \spath_bake_round:N {c}
+\cs_new_protected_nopar:Npn \spath_gbake_round:Nn #1#2
+{
+  \__spath_bake_round:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gbake_round:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gbake_round:N #1
+{
+  \spath_gbake_round:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gbake_round:N {c}
+\cs_new_protected_nopar:Npn \__spath_close:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \spath_initialpoint:NV \l__spath_tmpb_tl \l__spath_tmpa_tl
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_closepath_tl
+  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_close:Nn #1#2
+{
+  \__spath_close:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_close:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_close:N #1
+{
+  \spath_close:NV #1#1
+}
+\cs_generate_variant:Nn \spath_close:N {c}
+\cs_new_protected_nopar:Npn \spath_gclose:Nn #1#2
+{
+  \__spath_close:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gclose:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gclose:N #1
+{
+  \spath_gclose:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gclose:N {c}
+\cs_new_protected_nopar:Npn \__spath_open:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
   }
-  \tl_map_inline:Nn \g__spath_path_attributes
   {
-    \spath_if_in:nnT {#1} {##1}
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+    \tl_case:NnF \l__spath_tmpc_tl
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
-      {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \c_spath_closepath_tl {
 
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
+        \bool_if:nF
+        {
+          \dim_compare_p:n
+          {
+            \l__spath_move_x_dim == \l__spath_tmpa_dim
+          }
+          &&
+          \dim_compare_p:n
+          {
+            \l__spath_move_y_dim == \l__spath_tmpb_dim
+          }
+        }
+        {
+          \tl_put_right:NV \l__spath_tmpb_tl \c_spath_lineto_tl
+
+          \tl_put_right:Nx \l__spath_tmpb_tl {
+            { \dim_use:N \l__spath_move_x_dim }
+            { \dim_use:N \l__spath_move_y_dim }
+          }
+        }
+
+        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
         \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      }
 
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
+      \c_spath_moveto_tl {
+        \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+
+        \dim_set:Nn \l__spath_move_x_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+        \dim_set:Nn \l__spath_move_y_dim {\tl_head:N \l__spath_tmpa_tl}
         \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
+        \tl_put_right:Nx \l__spath_tmpb_tl {
+          { \dim_use:N \l__spath_move_x_dim }
+          { \dim_use:N \l__spath_move_y_dim }
         }
+
+        \dim_set_eq:NN \l__spath_tmpa_dim \l__spath_move_x_dim
+        \dim_set_eq:NN \l__spath_tmpb_dim \l__spath_move_y_dim
+      }
+    }
+    {
+      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+      \tl_put_right:Nx \l__spath_tmpb_tl {
+        { \dim_use:N \l__spath_tmpa_dim }
+        { \dim_use:N \l__spath_tmpb_dim }
       }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
     }
   }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
 }
-
-\cs_generate_variant:Nn \spath_translate:nnn {nxx}
-\cs_new_nopar:Npn \spath_translate:nn #1#2
+\cs_new_protected_nopar:Npn \spath_open:Nn #1#2
 {
-  \spath_translate:nnn {#1} #2
+  \__spath_open:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-
-\cs_generate_variant:Nn \spath_translate:nn {nV}
-\cs_new_nopar:Npn \spath_scale:nnn #1#2#3
+\cs_generate_variant:Nn \spath_open:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_open:N #1
+{
+  \spath_open:NV #1#1
+}
+\cs_new_protected_nopar:Npn \spath_gopen:Nn #1#2
+{
+  \__spath_open:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gopen:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gopen:N #1
+{
+  \spath_gopen:NV #1#1
+}
+\cs_new_protected_nopar:Npn \__spath_remove_empty_components:n #1
 {
-  \tl_map_inline:Nn \g__spath_moveable_attributes
+  \group_begin:
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \tl_clear:N \l__spath_tmpa_tl
+  \seq_map_inline:Nn \l__spath_tmpa_seq
   {
-    \spath_if_in:nnT {#1} {##1}
+    \int_compare:nF
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-
-      \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\fp_to_dim:N \l__spath_tmpa_fp}
-        {\fp_to_dim:N \l__spath_tmpb_fp}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
+      \tl_count:n {##1} == 3
+    }
+    {
+      \tl_put_right:Nn \l__spath_tmpa_tl {##1}
     }
   }
-  \tl_map_inline:Nn \g__spath_path_attributes
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_remove_empty_components:Nn #1#2
+{
+  \__spath_remove_empty_components:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_remove_empty_components:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_remove_empty_components:N #1
+{
+  \spath_remove_empty_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_remove_empty_components:N {c}
+\cs_new_protected_nopar:Npn \spath_gremove_empty_components:Nn #1#2
+{
+  \__spath_remove_empty_components:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gremove_empty_components:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gremove_empty_components:N #1
+{
+  \spath_gremove_empty_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gremove_empty_components:N {c}
+\prg_new_protected_conditional:Npnn \spath_if_eq:nn #1#2 { T, F, TF }
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nn \l__spath_tmpb_tl {#2}
+  \bool_gset_true:N \g__spath_tmpa_bool
+  \int_compare:nNnTF {\tl_count:N \l__spath_tmpa_tl} = {\tl_count:N \l__spath_tmpb_tl}
   {
-    \spath_if_in:nnT {#1} {##1}
+    \int_step_inline:nnnn {1} {3} {\tl_count:N \l__spath_tmpa_tl}
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
+      \tl_set:Nx \l__spath_tmpc_tl {\tl_item:Nn \l__spath_tmpa_tl {##1}}
+      \tl_set:Nx \l__spath_tmpd_tl {\tl_item:Nn \l__spath_tmpb_tl {##1}}
+      \tl_if_eq:NNF \l__spath_tmpc_tl \l__spath_tmpd_tl
+      {
+        \bool_gset_false:N \g__spath_tmpa_bool
       }
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_item:Nn \l__spath_tmpa_tl {##1+1}}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_item:Nn \l__spath_tmpb_tl {##1+1}}
+      \dim_compare:nF { \dim_abs:n { \l__spath_tmpa_dim - \l__spath_tmpb_dim} < 0.001pt }
       {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\fp_to_dim:N \l__spath_tmpa_fp}
-          {\fp_to_dim:N \l__spath_tmpb_fp}
-        }
+        \bool_gset_false:N \g__spath_tmpa_bool
+      }
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_item:Nn \l__spath_tmpa_tl {##1+2}}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_item:Nn \l__spath_tmpb_tl {##1+2}}
+      \dim_compare:nF { \dim_abs:n { \l__spath_tmpa_dim - \l__spath_tmpb_dim} < 0.001pt }
+      {
+        \bool_gset_false:N \g__spath_tmpa_bool
       }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
     }
   }
+  {
+    \bool_gset_false:N \g__spath_tmpa_bool
+  }
+  \group_end:
+  \bool_if:NTF \g__spath_tmpa_bool
+  {
+    \prg_return_true:
+  }
+  {
+    \prg_return_false:
+  }
 }
-\cs_generate_variant:Nn \spath_scale:nnn {nxx}
-\cs_new_nopar:Npn \spath_scale:nn #1#2
+\prg_generate_conditional_variant:Nnn \spath_if_eq:nn {VV, Vn, nV, vv} {TF, T, F}
+\cs_new_protected_nopar:Npn \__spath_split_curve:nn #1#2
 {
-  \spath_scale:nnn {#1} #2
-}
+  \group_begin:
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {2}}
+    {\tl_item:nn {#1} {3}}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetoa_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
 
-\cs_generate_variant:Nn \spath_scale:nn {nV}
-\cs_new_nopar:Npn \spath_transform:nnnnnnn #1#2#3#4#5#6#7
-{
-  \tl_map_inline:Nn \g__spath_moveable_attributes
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetob_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
   {
-    \spath_if_in:nnT {#1} {##1}
+    {\fp_to_dim:n
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
-      \fp_set:Nn \l__spath_tmpa_fp {\l__spath_tmpa_tl * #2 + \l__spath_tmpb_tl * #3 + #6}
-      \fp_set:Nn \l__spath_tmpb_fp {\l__spath_tmpa_tl * #4 + \l__spath_tmpb_tl * #5 + #7}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\fp_to_dim:N \l__spath_tmpa_fp}
-        {\fp_to_dim:N \l__spath_tmpb_fp}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
+      (1 - #2)^2 * \tl_item:nn {#1} {2} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {5} + (#2)^2 * \tl_item:nn {#1} {8}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {3} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {6} + (#2)^2 * \tl_item:nn {#1} {9}
+    }}
   }
-  \tl_map_inline:Nn \g__spath_path_attributes
+
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
   {
-    \spath_if_in:nnT {#1} {##1}
+    {\fp_to_dim:n
+      {
+      (1 - #2)^3 * \tl_item:nn {#1} {2} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {5} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {8} + (#2)^3 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
+      (1 - #2)^3 * \tl_item:nn {#1} {3} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {6} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {9} + (#2)^3 * \tl_item:nn {#1} {12}
+    }}
+  }
+
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
+
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
       {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      (1 - #2)^3 * \tl_item:nn {#1} {2} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {5} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {8} + (#2)^3 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^3 * \tl_item:nn {#1} {3} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {6} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {9} + (#2)^3 * \tl_item:nn {#1} {12}
+    }}
+  }
 
-        \fp_set:Nn \l__spath_tmpa_fp {\l_tmpa_tl * #2 + \l_tmpb_tl * #3 + #6}
-        \fp_set:Nn \l__spath_tmpb_fp {\l_tmpa_tl * #4 + \l_tmpb_tl * #5 + #7}
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\fp_to_dim:N \l__spath_tmpa_fp}
-          {\fp_to_dim:N \l__spath_tmpb_fp}
-        }
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetoa_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {5} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {8} + (#2)^2 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {6} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {9} + (#2)^2 * \tl_item:nn {#1} {12}
+    }}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetob_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {8} + (#2) * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {9} + (#2) * \tl_item:nn {#1} {12}
+    }}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {11}}
+    {\tl_item:nn {#1} {12}}
   }
-}
 
-\cs_generate_variant:Nn \spath_transform:nnnnnnn {nxxxxxx}
-\cs_new_nopar:Npn \spath_transform:nn #1#2
-{
-  \spath_transform:nnnnnnn {#1} #2
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
 }
-
-\cs_generate_variant:Nn \spath_transform:nn {nV}
-\cs_new_nopar:Npn \spath_reverse:n #1
+\cs_new_protected_nopar:Npn \spath_split_curve:NNnn #1#2#3#4
 {
-  \spath_if_in:nnF {#1} {reverse path} {
-    \use:c {spath_generate_reverse path:n} {#1}
-  }
-  \spath_swap:nnn {#1} {path} {reverse path}
-  \spath_swap:nnn {#1} {initial point} {final point}
-  \spath_swap:nnn {#1} {initial action} {final action}
+  \__spath_split_curve:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_swap:nnn #1#2#3
+\cs_generate_variant:Nn \spath_split_curve:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_curve:NNnn #1#2#3#4
 {
-  \__spath_get:nnNF {#1} {#2} \l__spath_tmpa_tl {\tl_clear:N \l__spath_tmpa_tl}
-  \__spath_get:nnNF {#1} {#3} \l__spath_tmpb_tl {\tl_clear:N \l__spath_tmpb_tl}
-  \tl_if_empty:NTF \l__spath_tmpb_tl
-  {\spath_remove:nn {#1} {#2}}
-  {\spath_put:nnV {#1} {#2} \l__spath_tmpb_tl}
-  \tl_if_empty:NTF \l__spath_tmpa_tl
-  {\spath_remove:nn {#1} {#3}}
-  {\spath_put:nnV {#1} {#3} \l__spath_tmpa_tl}
+  \__spath_split_curve:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_weld:nn #1#2
+\cs_generate_variant:Nn \spath_gsplit_curve:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \__spath_split_line:nn #1#2
 {
-  \spath_clone:nn {#2} {tmp_path}
-  \spath_get:nnN {#1} {final point} \l__spath_tmpa_tl
-
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-  \spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
-
-  \dim_sub:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_sub:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-  \spath_translate:nxx {tmp_path} {\dim_use:N \l__spath_tmpa_dim} {\dim_use:N \l__spath_tmpb_dim}
+  \group_begin:
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {2}}
+    {\tl_item:nn {#1} {3}}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_lineto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
 
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \__spath_get:nnN {tmp_path} {path} \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_lineto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {5}}
+    {\tl_item:nn {#1} {6}}
+  }
 
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_line:NNnn #1#2#3#4
+{
+  \__spath_split_line:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_line:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_line:NNnn #1#2#3#4
+{
+  \__spath_split_line:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_line:NNnn {NNnV, NNVn, NNVV}
+\int_new:N \l__spath_split_int
+\int_new:N \l__spath_splitat_int
+\fp_new:N \l__spath_split_fp
+\bool_new:N \l__spath_split_bool
+\tl_new:N \l__spath_split_path_tl
+\tl_new:N \l__spath_split_patha_tl
+\tl_new:N \l__spath_split_pathb_tl
+\tl_new:N \l__spath_split_intoa_tl
+\tl_new:N \l__spath_split_intob_tl
+\dim_new:N \l__spath_splitx_dim
+\dim_new:N \l__spath_splity_dim
+\cs_new_protected_nopar:Npn \__spath_split_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l__spath_splitat_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_split_fp {#2 - floor(#2)}
 
-  \__spath_get:nnNTF {tmp_path} {final point} \l__spath_tmpa_tl
+  % Is split point near one end or other of a component?
+  \fp_compare:nT
   {
-    \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
+    \l__spath_split_fp < 0.01
   }
   {
-    \spath_remove:nn {#1} {final point}
+    % Near the start, so we'll place it at the start
+    \fp_set:Nn \l__spath_split_fp {0}
   }
-
-  \__spath_get:nnNTF {tmp_path} {final action} \l__spath_tmpa_tl
+  \fp_compare:nT
   {
-    \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
+    \l__spath_split_fp > 0.99
   }
   {
-    \spath_remove:nn {#1} {final action}
+    % Near the end, so we'll place it at the end
+    \fp_set:Nn \l__spath_split_fp {0}
+    \int_incr:N \l__spath_splitat_int
   }
 
-  \__spath_get:nnNT {tmp_path} {min bb} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {min bb} \l__spath_tmpb_tl
-    {
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+  \int_zero:N \l__spath_split_int
+  \bool_set_true:N \l__spath_split_bool
 
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}
+  \tl_set:Nn \l__spath_split_path_tl {#1}
+  \tl_clear:N \l__spath_split_patha_tl
 
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
-    }
-  }
+  \dim_zero:N \l__spath_splitx_dim
+  \dim_zero:N \l__spath_splity_dim
 
-  \__spath_get:nnNT {tmp_path} {max bb} \l__spath_tmpa_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_split_path_tl
+    ||
+    \int_compare_p:n { \l__spath_splitat_int == \l__spath_split_int  }
+  }
   {
-    \__spath_get:nnNT {#1} {max bb} \l__spath_tmpb_tl
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_split_path_tl}
+    \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+    \tl_case:Nn \l__spath_tmpc_tl
     {
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}
-
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
+      \c_spath_lineto_tl
       {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+        \int_incr:N \l__spath_split_int
+      }
+      \c_spath_curvetoa_tl
+      {
+        \int_incr:N \l__spath_split_int
       }
-      \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
     }
-  }
-
-  \__spath_get:nnNT {tmp_path} {reverse path} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {reverse path} \l__spath_tmpb_tl
+    \int_compare:nT { \l__spath_split_int < \l__spath_splitat_int  }
     {
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+      \tl_put_right:NV \l__spath_split_patha_tl \l__spath_tmpc_tl
+
+      \tl_put_right:Nx \l__spath_split_patha_tl
+      {{ \tl_head:N \l__spath_split_path_tl }}
+      \dim_set:Nn \l__spath_splitx_dim {\tl_head:N \l__spath_split_path_tl}
+      \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+      \tl_put_right:Nx \l__spath_split_patha_tl
+      {{ \tl_head:N \l__spath_split_path_tl }}
+      \dim_set:Nn \l__spath_splity_dim {\tl_head:N \l__spath_split_path_tl}
+      \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
 
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
     }
   }
 
-  \__spath_get:nnNT {tmp_path} {length} \l__spath_tmpa_tl
+  \tl_clear:N \l__spath_split_pathb_tl
+  \tl_put_right:NV \l__spath_split_pathb_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_split_pathb_tl
   {
-    \__spath_get:nnNT {#1} {length} \l__spath_tmpb_tl
-    {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
-      \spath_put:nnV {#1} {length} \l__spath_tmpa_int
-    }
+    {\dim_use:N \l__spath_splitx_dim}
+    {\dim_use:N \l__spath_splity_dim}
   }
 
-  \__spath_get:nnNT {tmp_path} {real length} \l__spath_tmpa_tl
+  \fp_compare:nTF
+  {
+    \l__spath_split_fp == 0
+  }
   {
-    \__spath_get:nnNT {#1} {real length} \l__spath_tmpb_tl
+    \tl_set_eq:NN \l__spath_split_intob_tl \l__spath_split_pathb_tl
+    \tl_if_empty:NF \l__spath_split_path_tl
     {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl}
-      \spath_put:nnV {#1} {real length} \l__spath_tmpa_int
+      \tl_put_right:NV \l__spath_split_intob_tl \l__spath_tmpc_tl
+      \tl_put_right:NV \l__spath_split_intob_tl \l__spath_split_path_tl
     }
   }
-
-  \__spath_get:nnNT {tmp_path} {number of components} \l__spath_tmpa_tl
   {
-    \__spath_get:nnNT {#1} {number of components} \l__spath_tmpb_tl
+
+    \tl_case:Nn \l__spath_tmpc_tl
     {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
-      \spath_put:nnV {#1} {number of components} \l__spath_tmpa_int
+      \c_spath_lineto_tl
+      {
+        \tl_put_right:NV \l__spath_split_pathb_tl \l__spath_tmpc_tl
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \spath_split_line:NNVV
+        \l__spath_split_intoa_tl
+        \l__spath_split_intob_tl
+        \l__spath_split_pathb_tl
+        \l__spath_split_fp
+
+        \prg_replicate:nn {3} {
+          \tl_set:Nx \l__spath_split_intoa_tl {\tl_tail:N \l__spath_split_intoa_tl}
+        }
+
+        \tl_put_right:NV \l__spath_split_patha_tl \l__spath_split_intoa_tl
+        \tl_put_right:NV \l__spath_split_intob_tl \l__spath_split_path_tl
+      }
+      \c_spath_curvetoa_tl
+      {
+        \tl_put_right:NV \l__spath_split_pathb_tl \l__spath_tmpc_tl
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \prg_replicate:nn {2} {
+
+          \tl_put_right:Nx \l__spath_split_pathb_tl
+          { \tl_head:N \l__spath_split_path_tl }
+          \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+          \tl_put_right:Nx \l__spath_split_pathb_tl
+          {{ \tl_head:N \l__spath_split_path_tl }}
+          \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+          \tl_put_right:Nx \l__spath_split_pathb_tl
+          {{ \tl_head:N \l__spath_split_path_tl }}
+          \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+        }
+
+        \spath_split_curve:NNVV
+        \l__spath_split_intoa_tl
+        \l__spath_split_intob_tl
+        \l__spath_split_pathb_tl \l__spath_split_fp
+
+        \prg_replicate:nn {3} {
+          \tl_set:Nx \l__spath_split_intoa_tl {\tl_tail:N \l__spath_split_intoa_tl}
+        }
+
+        \tl_put_right:NV \l__spath_split_patha_tl \l__spath_split_intoa_tl
+        \tl_put_right:NV \l__spath_split_intob_tl \l__spath_split_path_tl
+      }
     }
   }
 
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_patha_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_intob_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_prepend_no_move:nn #1#2
+\cs_new_protected_nopar:Npn \spath_split_at:NNnn #1#2#3#4
 {
-  \spath_if_exist:nT {#2}
+  \__spath_split_at:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at:NNnn {NNVn, NNVV, NNnV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:NNnn #1#2#3#4
+{
+  \__spath_split_at:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at:NNnn {NNVn, NNVV, NNnV}
+\cs_new_protected_nopar:Npn \spath_split_at:Nnn #1#2#3
+{
+  \__spath_split_at:nn {#2}{#3}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1} \tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_split_at:Nn #1#2
+{
+  \spath_split_at:NVn #1#1{#2}
+}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:Nnn #1#2#3
+{
+  \__spath_split_at:nn {#2}{#3}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1} \tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:Nn #1#2
+{
+  \spath_gsplit_at:NVn #1#1{#2}
+}
+\tl_new:N \l__spath_shorten_fa_tl
+\tl_new:N \l__spath_shorten_path_tl
+\tl_new:N \l__spath_shorten_last_tl
+\tl_new:N \l__spath_shorten_lasta_tl
+\tl_new:N \l__spath_shorten_lastb_tl
+\int_new:N \l__spath_shorten_int
+\fp_new:N \l__spath_shorten_x_fp
+\fp_new:N \l__spath_shorten_y_fp
+\fp_new:N \l__spath_shorten_len_fp
+\cs_new_protected_nopar:Npn \__spath_shorten_at_end:nn #1#2
+{
+  \int_compare:nTF
   {
-    \__spath_get:nnN {#2} {path} \l__spath_tmpa_tl
-    \__spath_get:nnN {#1} {path} \l__spath_tmpb_tl
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
+    \tl_count:n {#1} > 3
+  }
+  {
+    \group_begin:
+    \tl_set:Nn \l__spath_shorten_path_tl {#1}
+    \tl_reverse:N \l__spath_shorten_path_tl
 
-    \spath_if_in:nnTF {#2} {initial point}
-    {
-      \__spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {initial point} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {initial point}
-    }
+    \tl_set:Nx \l__spath_shorten_fa_tl {\tl_item:Nn \l__spath_shorten_path_tl {3}}
 
-    \spath_if_in:nnTF {#2} {initial action}
+    \tl_clear:N \l__spath_shorten_last_tl
+    \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curveto_tl
     {
-      \__spath_get:nnN {#2} {initial action} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {initial action} \l__spath_tmpa_tl
+      \int_set:Nn \l__spath_shorten_int {3}
     }
     {
-      \spath_remove:nn {#1} {initial action}
+      \int_set:Nn \l__spath_shorten_int {1}
     }
 
-    \bool_if:nTF
+    \prg_replicate:nn { \l__spath_shorten_int }
     {
-      \spath_if_in_p:nn {#1} {length}
-      &&
-      \spath_if_in_p:nn {#2} {length}
-    }
-    {
-      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
-    }
-    {
-      \spath_remove:nn {#1} {length}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {real length}
-      &&
-      \spath_if_in_p:nn {#2} {real length}
+      \tl_put_right:Nx \l__spath_shorten_last_tl
+      {
+        {\tl_head:N \l__spath_shorten_path_tl}
+      }
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
+      \tl_put_right:Nx \l__spath_shorten_last_tl
+      {
+        {\tl_head:N \l__spath_shorten_path_tl}
+      }
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
+      \tl_put_right:Nx \l__spath_shorten_last_tl
+      {
+        \tl_head:N \l__spath_shorten_path_tl
+      }
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
     }
+
+    \tl_put_right:Nx \l__spath_shorten_last_tl
     {
-      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl }}
+      {\tl_item:Nn \l__spath_shorten_path_tl {1}}
+      {\tl_item:Nn \l__spath_shorten_path_tl {2}}
     }
+    \tl_put_right:NV \l__spath_shorten_last_tl \c_spath_moveto_tl
+
+    \tl_reverse:N \l__spath_shorten_path_tl
+
+    \fp_set:Nn \l__spath_shorten_x_fp
     {
-      \spath_remove:nn {#1} {real length}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {4}}
+      -
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {1}}
     }
-    \bool_if:nTF
+
+    \fp_set:Nn \l__spath_shorten_y_fp
     {
-      \spath_if_in_p:nn {#1} {number of components}
-      &&
-      \spath_if_in_p:nn {#2} {number of components}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {5}}
+      -
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {2}}
     }
+
+    \fp_set:Nn \l__spath_shorten_len_fp
     {
-      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
+      sqrt( \l__spath_shorten_x_fp * \l__spath_shorten_x_fp +  \l__spath_shorten_y_fp *  \l__spath_shorten_y_fp )
     }
+
+    \fp_compare:nTF
     {
-      \spath_remove:nn {#1} {number of components}
+      \l__spath_shorten_len_fp > #2
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {min bb}
-      &&
-      \spath_if_in_p:nn {#2} {min bb}
-    }
-    {
-      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {min bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+
+      \fp_set:Nn \l__spath_shorten_len_fp
+      {
+        (\l__spath_shorten_len_fp - #2)/ \l__spath_shorten_len_fp
       }
-    }
-    {
-      \spath_remove:nn {#1} {min bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {max bb}
-      &&
-      \spath_if_in_p:nn {#2} {max bb}
-    }
-    {
-      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {max bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+
+      \tl_reverse:N \l__spath_shorten_last_tl
+
+      \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curveto_tl
+      {
+        \fp_set:Nn \l__spath_shorten_len_fp
+        {
+          1 - (1 -\l__spath_shorten_len_fp)/3
+        }
+        \spath_split_curve:NNVV
+        \l__spath_shorten_lasta_tl
+        \l__spath_shorten_lastb_tl
+        \l__spath_shorten_last_tl
+        \l__spath_shorten_len_fp
       }
+      {
+        \spath_split_line:NNVV
+        \l__spath_shorten_lasta_tl
+        \l__spath_shorten_lastb_tl
+        \l__spath_shorten_last_tl
+        \l__spath_shorten_len_fp
+      }
+
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_shorten_lasta_tl {\tl_tail:N \l__spath_shorten_lasta_tl}
+      }
+
+      \tl_put_right:NV \l__spath_shorten_path_tl \l__spath_shorten_lasta_tl
+
     }
     {
-      \spath_remove:nn {#1} {max bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {reverse path}
-      &&
-      \spath_if_in_p:nn {#2} {reverse path}
-    }
-    {
-      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpb_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
-    }
-    {
-      \spath_remove:nn {#1} {reverse path}
+
+      \int_compare:nT
+      {
+        \tl_count:N \l__spath_shorten_path_tl > 3
+      }
+      {
+        \dim_set:Nn \l__spath_tmpa_dim {\fp_to_dim:n {#2 - \l__spath_shorten_len_fp } }
+        \spath_shorten_at_end:NV \l__spath_shorten_path_tl \l__spath_tmpa_dim
+      }
     }
 
+    \tl_gset_eq:NN \g__spath_output_tl \l__spath_shorten_path_tl
+    \group_end:
   }
+  {
+    \tl_gset:Nn \g__spath_output_tl {#1}
+  }
+}
+\cs_new_protected_nopar:Npn \spath_shorten_at_end:Nnn #1#2#3
+{
+  \__spath_shorten_at_end:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_shorten_at_end:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_shorten_at_end:Nn #1#2
+{
+  \spath_shorten_at_end:NVn #1#1{#2}
 }
-\cs_new_nopar:Npn \spath_append_no_move:nn #1#2
+\cs_generate_variant:Nn \spath_shorten_at_end:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_end:Nnn #1#2#3
 {
-  \spath_if_exist:nT {#2}
+  \__spath_shorten_at_end:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gshorten_at_end:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_end:Nn #1#2
+{
+  \spath_gshorten_at_end:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gshorten_at_end:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \__spath_shorten_at_start:nn #1#2
+{
+  \int_compare:nTF
   {
-    \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \spath_get:nnN {#2} {path} \l__spath_tmpb_tl
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-    \spath_if_in:nnTF {#2} {final point}
-    {
-      \__spath_get:nnN {#2} {final point} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {final point}
-    }
-    \spath_if_in:nnTF {#2} {final action}
-    {
-      \__spath_get:nnN {#2} {final action} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {final action}
-    }
-    \bool_if:nTF
+    \tl_count:n {#1} > 3
+  }
+  {
+  \group_begin:
+  \tl_set:Nn \l__spath_shorten_path_tl {#1}
+
+  \tl_set:Nx \l__spath_shorten_fa_tl {\tl_item:Nn \l__spath_shorten_path_tl {4}}
+
+    \tl_clear:N \l__spath_shorten_last_tl
+
+  \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curvetoa_tl
+  {
+    \int_set:Nn \l__spath_shorten_int {3}
+  }
+  {
+    \int_set:Nn \l__spath_shorten_int {1}
+  }
+
+  \tl_set_eq:NN \l__spath_shorten_last_tl \c_spath_moveto_tl
+  \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl }
+
+  \prg_replicate:nn { \l__spath_shorten_int }
+  {
+    \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {1}}
+    \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {2}}
+    \tl_put_right:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {3}}
+
+    \prg_replicate:nn {3}
     {
-      \spath_if_in_p:nn {#1} {length}
-      &&
-      \spath_if_in_p:nn {#2} {length}
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl }
     }
+  }
+  \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {1}}
+  \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {2}}
+
+  \fp_set:Nn \l__spath_shorten_x_fp
+  {
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {5}}
+    -
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {2}}
+  }
+
+  \fp_set:Nn \l__spath_shorten_y_fp
+  {
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {6}}
+    -
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {3}}
+  }
+
+  \fp_set:Nn \l__spath_shorten_len_fp
+  {
+    sqrt( \l__spath_shorten_x_fp * \l__spath_shorten_x_fp +  \l__spath_shorten_y_fp *  \l__spath_shorten_y_fp )
+  }
+
+  \fp_compare:nTF
+  {
+    \l__spath_shorten_len_fp > #2
+  }
+  {
+
+    \fp_set:Nn \l__spath_shorten_len_fp
     {
-      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
+      #2/ \l__spath_shorten_len_fp
     }
+
+    \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curvetoa_tl
     {
-      \spath_remove:nn {#1} {length}
+      \fp_set:Nn \l__spath_shorten_len_fp
+      {
+        \l__spath_shorten_len_fp/3
+      }
+      \spath_split_curve:NNVV
+      \l__spath_shorten_lasta_tl
+      \l__spath_shorten_lastb_tl
+      \l__spath_shorten_last_tl
+      \l__spath_shorten_len_fp
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {real length}
-      &&
-      \spath_if_in_p:nn {#2} {real length}
+      \spath_split_line:NNVV
+      \l__spath_shorten_lasta_tl
+      \l__spath_shorten_lastb_tl
+      \l__spath_shorten_last_tl
+      \l__spath_shorten_len_fp
     }
+
+    \prg_replicate:nn {2}
     {
-      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl }}
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
     }
+
+    \tl_put_left:NV \l__spath_shorten_path_tl \l__spath_shorten_lastb_tl
+
+  }
+  {
+
+    \tl_put_left:NV \l__spath_shorten_path_tl \c_spath_moveto_tl
+
+    \int_compare:nT
     {
-      \spath_remove:nn {#1} {real length}
+      \tl_count:N \l__spath_shorten_path_tl > 3
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {number of components}
-      &&
-      \spath_if_in_p:nn {#2} {number of components}
+      \dim_set:Nn \l__spath_tmpa_dim {\fp_to_dim:n {#2 - \l__spath_shorten_len_fp } }
+      \spath_shorten_at_start:NV \l__spath_shorten_path_tl \l__spath_tmpa_dim
     }
+  }
+
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_shorten_path_tl
+  \group_end:
+  }
+  {
+    \tl_gset:Nn \g__spath_output_tl {#1}
+  }
+}
+\cs_new_protected_nopar:Npn \spath_shorten_at_start:Nnn #1#2#3
+{
+  \__spath_shorten_at_start:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_shorten_at_start:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_shorten_at_start:Nn #1#2
+{
+  \spath_shorten_at_start:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_shorten_at_start:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_start:Nnn #1#2#3
+{
+  \__spath_shorten_at_start:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gshorten_at_start:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_start:Nn #1#2
+{
+  \spath_gshorten_at_start:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gshorten_at_start:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \__spath_point_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l__spath_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_tmpa_fp {#2 - floor(#2)}
+
+  \spath_segments_to_seq:Nn \l__spath_tmpa_seq {#1}
+
+  \int_compare:nTF
+  {
+    \l__spath_tmpa_int < 1
+  }
+  {
+    \spath_initialpoint:Nn \l__spath_tmpc_tl {#1}
+  }
+  {
+    \int_compare:nTF
     {
-      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
+      \l__spath_tmpa_int > \seq_count:N \l__spath_tmpa_seq
     }
     {
-      \spath_remove:nn {#1} {number of components}
+      \spath_finalpoint:Nn \l__spath_tmpc_tl {#1}
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {min bb}
-      &&
-      \spath_if_in_p:nn {#2} {min bb}
-    }
-    {
-      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {min bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+
+      \tl_set:Nx \l__spath_tmpa_tl {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
+
+      \int_compare:nTF
+      {
+        \tl_count:N \l__spath_tmpa_tl > 3
       }
-    }
-    {
-      \spath_remove:nn {#1} {min bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {max bb}
-      &&
-      \spath_if_in_p:nn {#2} {max bb}
-    }
-    {
-      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {max bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {4}}
+      }
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {1}}
+      }
+
+      \tl_clear:N \l__spath_tmpc_tl
+
+      \tl_case:Nn \l__spath_tmpb_tl
+      {
+        \c_spath_moveto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {2}
+            }
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {3}
+            }
+          }
+        }
+
+        \c_spath_lineto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+              }
+            }
+          }
+        }
+
+        \c_spath_closepath_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+              }
+            }
+          }
+        }
+
+        \c_spath_curvetoa_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {2} + 3 * (1 - \l__spath_tmpa_fp)^2 * (\l__spath_tmpa_fp) * \tl_item:Nn \l__spath_tmpa_tl {5} + 3 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp)^2 * \tl_item:Nn \l__spath_tmpa_tl {8} + (\l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {11}
+            }}
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {3} + 3 * (1 - \l__spath_tmpa_fp)^2 * (\l__spath_tmpa_fp) * \tl_item:Nn \l__spath_tmpa_tl {6} + 3 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp)^2 * \tl_item:Nn \l__spath_tmpa_tl {9} + (\l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {12}
+            }}
+          }
+        }
       }
     }
+  }
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpc_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_point_at:Nnn #1#2#3
+{
+  \__spath_point_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_point_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \spath_gpoint_at:Nnn #1#2#3
+{
+  \__spath_point_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gpoint_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \__spath_tangent_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l__spath_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_tmpa_fp {#2 - floor(#2)}
+
+  \spath_segments_to_seq:Nn \l__spath_tmpa_seq {#1}
+
+  \int_compare:nTF
+  {
+    \l__spath_tmpa_int < 1
+  }
+  {
+    \spath_initialpoint:Nn \l__spath_tmpc_tl {#1}
+  }
+  {
+    \int_compare:nTF
     {
-      \spath_remove:nn {#1} {max bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {reverse path}
-      &&
-      \spath_if_in_p:nn {#2} {reverse path}
+      \l__spath_tmpa_int > \seq_count:N \l__spath_tmpa_seq
     }
     {
-      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpa_tl
-      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpb_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
+      \spath_finalpoint:Nn \l__spath_tmpc_tl {#1}
     }
     {
-      \spath_remove:nn {#1} {reverse path}
+
+      \tl_set:Nx \l__spath_tmpa_tl {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
+
+      \int_compare:nTF
+      {
+        \tl_count:N \l__spath_tmpa_tl > 3
+      }
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {4}}
+      }
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {1}}
+      }
+
+      \tl_clear:N \l__spath_tmpc_tl
+
+      \tl_case:Nn \l__spath_tmpb_tl
+      {
+        \c_spath_moveto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {2}
+            }
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {3}
+            }
+          }
+        }
+
+        \c_spath_lineto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+              }
+            }
+          }
+        }
+
+        \c_spath_closepath_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+              }
+            }
+          }
+        }
+
+        \c_spath_curvetoa_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                3*(1 - \l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {5} - \tl_item:Nn \l__spath_tmpa_tl {2})
+                + 6 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp) *  (\tl_item:Nn \l__spath_tmpa_tl {8} - \tl_item:Nn \l__spath_tmpa_tl {5})
+                + 3*(\l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {11} - \tl_item:Nn \l__spath_tmpa_tl {8})
+              }
+            }
+            {\fp_to_dim:n
+              {
+                3*(1 - \l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {6} - \tl_item:Nn \l__spath_tmpa_tl {3})
+                + 6 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp) *  (\tl_item:Nn \l__spath_tmpa_tl {9} - \tl_item:Nn \l__spath_tmpa_tl {6})
+                + 3*(\l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {12} - \tl_item:Nn \l__spath_tmpa_tl {9})
+            }}
+          }
+        }
+      }
     }
   }
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpc_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_bake_round:n #1
+\cs_new_protected_nopar:Npn \spath_tangent_at:Nnn #1#2#3
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \pgf@@processround\l__spath_tmpa_tl\l__spath_tmpb_tl
-  \spath_put:nnV {#1} {path} \l__spath_tmpb_tl
+  \__spath_tangent_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_close_path:n #1
+\cs_generate_variant:Nn \spath_tangent_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \spath_gtangent_at:Nnn #1#2#3
 {
-  \spath_get:nnN {#1} {initial point} \l__spath_tmpb_tl
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-  \spath_if_in:nnT {#1} {reverse path}
+  \__spath_tangent_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtangent_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \__spath_transformation_at:nn #1#2
+{
+  \group_begin:
+  \tl_clear:N \l__spath_tmpa_tl
+  \__spath_tangent_at:nn {#1}{#2}
+  \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_output_tl
+  \fp_set:Nn \l__spath_tmpa_fp { sqrt( (\tl_item:Nn \l__spath_tmpb_tl {1})^2 +  (\tl_item:Nn \l__spath_tmpb_tl {2})^2 ) }
+  \fp_compare:nTF {\l__spath_tmpa_fp = 0}
   {
-    \spath_get:nnN {#1} {final point} \l__spath_tmpb_tl
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
+    \fp_set:Nn \l__spath_tmpa_fp {1}
+    \fp_set:Nn \l__spath_tmpb_fp {0}
   }
+  {
+    \fp_set:Nn \l__spath_tmpb_fp { (\tl_item:Nn \l__spath_tmpb_tl {2}) / \l__spath_tmpa_fp }
+    \fp_set:Nn \l__spath_tmpa_fp { (\tl_item:Nn \l__spath_tmpb_tl {1}) / \l__spath_tmpa_fp }
+  }
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    { \fp_to_decimal:n { \l__spath_tmpa_fp } }
+    { \fp_to_decimal:n { \l__spath_tmpb_fp } }
+    { \fp_to_decimal:n {- \l__spath_tmpb_fp } }
+    { \fp_to_decimal:n { \l__spath_tmpa_fp } }
+  }
+  \__spath_point_at:nn {#1}{#2}
+  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_map_component:Nn #1#2
+\cs_new_protected_nopar:Npn \spath_transformation_at:Nnn #1#2#3
 {
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 {#2}
-  \tl_set:NV \l__spath_tmpa_tl #1
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
+  \__spath_transformation_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_transformation_at:Nnn {NVn, NVV, NnV, NvV}
+\cs_new_protected_nopar:Npn \spath_gtransformation_at:Nnn #1#2#3
+{
+  \__spath_transformation_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtransformation_at:Nnn {NVn, NVV, NnV}
+\tl_new:N \l__spath_split_path_a_tl
+\tl_new:N \l__spath_split_path_b_tl
+\tl_new:N \l__spath_split_path_a_start_tl
+\tl_new:N \l__spath_split_path_b_start_tl
+\tl_new:N \l__spath_split_path_a_end_tl
+\tl_new:N \l__spath_split_path_b_end_tl
+\tl_new:N \l__spath_split_path_a_final_tl
+\tl_new:N \l__spath_split_path_b_final_tl
+
+\tl_new:N \l__spath_split_prev_first_tl
+\tl_new:N \l__spath_split_prev_second_tl
+
+\seq_new:N \l__spath_split_first_seq
+\seq_new:N \l__spath_split_second_seq
+
+\int_new:N \l__spath_split_segment_int
+\cs_new_protected_nopar:Npn \spath_intersect:NN #1#2
+{
+  \pgfintersectionofpaths%
+  {%
+    \pgfsetpath #1
+  }{%
+    \pgfsetpath #2
   }
+}
+\tl_new:N \l__spath_intersecta_tl
+\tl_new:N \l__spath_intersectb_tl
+\cs_new_protected_nopar:Npn \spath_intersect:nn #1#2
+{
+  \tl_set:Nn \l__spath_intersecta_tl {#1}
+  \tl_set:Nn \l__spath_intersectb_tl {#2}
+  \spath_intersect:NN \l__spath_intersecta_tl \l__spath_intersectb_tl
+}
+\cs_new_protected_nopar:Npn \__spath_split_at_intersections:nn #1#2
+{
+  \group_begin:
+
+  % Clear some token lists and sequences
+  \tl_clear:N \l__spath_split_path_a_final_tl
+  \tl_clear:N \l__spath_split_path_b_final_tl
+  \seq_clear:N \l__spath_split_first_seq
+  \seq_clear:N \l__spath_split_second_seq
+
+  \pgfintersectionsortbyfirstpath
+  % Find the intersections of these segments
+  \tl_set:Nn \l__spath_split_path_a_tl {#1}
+  \tl_set:Nn \l__spath_split_path_b_tl {#2}
+  % Remove empty components
+
+  \spath_intersect:NN \l__spath_split_path_a_tl \l__spath_split_path_b_tl
+
+  % If we get intersections
+  \int_compare:nT {\pgfintersectionsolutions > 0}
   {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_if_eq:NNT \l__spath_tmpc_tl \g__spath_moveto_tl
+    % Find the times of the intersections on each path
+    \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
     {
-      \exp_args:NnV \use:c { __spath_map_ \int_use:N \g__spath_map_int :w } \l__spath_tmpb_tl
-\tl_clear:N \l__spath_tmpb_tl
+    \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+      \seq_put_left:NV \l__spath_split_first_seq \l__spath_split_first_tl
     }
-    \tl_if_single:NTF \l__spath_tmpc_tl
+  }
+
+  \spath_intersect:NN \l__spath_split_path_b_tl \l__spath_split_path_a_tl
+
+  % If we get intersections
+  \int_compare:nT {\pgfintersectionsolutions > 0}
+  {
+    % Find the times of the intersections on each path
+    \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
     {
-      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+    \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+      \seq_put_left:NV \l__spath_split_second_seq \l__spath_split_first_tl
+    }
+  }
+
+  \tl_set:Nn \l__spath_split_prev_first_tl {-1}
+
+  \seq_map_inline:Nn \l__spath_split_first_seq
+  {
+    \tl_set:Nn \l__spath_split_first_tl {##1}
+
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_first_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l__spath_split_first_tl) }
+      =
+      \fp_to_int:n {floor( \l__spath_split_prev_first_tl) }
     }
     {
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\l__spath_tmpc_tl}}
+      \tl_set:Nx \l__spath_split_first_tl
+      {
+        \fp_eval:n {
+          floor( \l__spath_split_first_tl )
+          +
+          ( \l__spath_split_first_tl - floor( \l__spath_split_first_tl) )
+          /
+          ( \l__spath_split_prev_first_tl - floor( \l__spath_split_prev_first_tl) )
+        }
+      }
     }
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set_eq:NN \l__spath_split_prev_first_tl \l__spath_tmpa_tl
+
+    \spath_split_at:NNVV \l__spath_split_path_a_start_tl \l__spath_split_path_a_end_tl  \l__spath_split_path_a_tl \l__spath_split_first_tl
+
+    \tl_put_left:NV \l__spath_split_path_a_final_tl \l__spath_split_path_a_end_tl
+    \tl_set_eq:NN \l__spath_split_path_a_tl \l__spath_split_path_a_start_tl
+
+  }
+
+  \tl_set:Nn \l__spath_split_prev_second_tl {-1}
+
+  \seq_map_inline:Nn \l__spath_split_second_seq
+  {
+    \tl_set:Nn \l__spath_split_second_tl {##1}
+
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_second_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l__spath_split_second_tl) }
+      =
+      \fp_to_int:n {floor( \l__spath_split_prev_second_tl) }
+    }
+    {
+      \tl_set:Nx \l__spath_split_second_tl
+      {
+        \fp_eval:n {
+          floor( \l__spath_split_second_tl )
+          +
+          ( \l__spath_split_second_tl - floor( \l__spath_split_second_tl) )
+          /
+          ( \l__spath_split_prev_second_tl - floor( \l__spath_split_prev_second_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l__spath_split_prev_second_tl \l__spath_tmpa_tl
+
+    \spath_split_at:NNVV \l__spath_split_path_b_start_tl \l__spath_split_path_b_end_tl  \l__spath_split_path_b_tl\l__spath_split_second_tl
+
+    \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_end_tl
+    \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_start_tl
+
+  }
+
+  \tl_put_left:NV \l__spath_split_path_a_final_tl \l__spath_split_path_a_tl
+  \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+
+  \tl_if_empty:NT \l__spath_split_path_a_final_tl
+  {
+    \tl_set_eq:NN \l__spath_split_path_a_final_tl \l__spath_split_path_a_tl
   }
+  \tl_if_empty:NT \l__spath_split_path_b_final_tl
+  {
+    \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+  }
+
+  \spath_remove_empty_components:N \l__spath_split_path_a_final_tl
+  \spath_remove_empty_components:N \l__spath_split_path_b_final_tl
+
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_path_a_final_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_path_b_final_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_map_segment_inline:Nn #1#2
+\cs_new_protected_nopar:Npn \spath_split_at_intersections:NNnn #1#2#3#4
 {
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 ##2 {#2}
-  \spath_map_segment_function:Nc #1 { __spath_map_ \int_use:N \g__spath_map_int :w }
+  \__spath_split_at_intersections:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_map_segment_inline:nn #1#2
+\cs_generate_variant:Nn \spath_split_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_new_protected_nopar:Npn \spath_split_at_intersections:NN #1#2
 {
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 ##2 {#2}
-  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
-  \spath_map_segment_function:Nc \l__spath_tmpd_tl { __spath_map_ \int_use:N \g__spath_map_int :w }
+  \spath_split_at_intersections:NNVV #1#2#1#2
 }
-\cs_new_nopar:Npn \spath_map_segment_function:nN #1#2
+\cs_generate_variant:Nn \spath_split_at_intersections:NN {cc}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NNnn #1#2#3#4
 {
-  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
-  \spath_map_segment_function:NN \l__spath_tmpd_tl #2
+  \__spath_split_at_intersections:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_map_segment_function:NN #1#2
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NN #1#2
 {
-  \tl_set_eq:NN \l__spath_tmpa_tl #1
-  \tl_clear:N \l__spath_tmpb_tl
-  \dim_zero:N \l__spath_tmpa_dim
-  \dim_zero:N \l__spath_tmpb_dim
+  \spath_gsplit_at_intersections:NNVV #1#2#1#2
+}
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NN {cc}
+\cs_new_protected_nopar:Npn \__spath_split_at_self_intersections:n #1
+{
+  \group_begin:
 
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
+  % Copy the path
+  \tl_set:Nn \l__spath_split_path_b_tl {#1}
+
+  % Open the path
+  \spath_open:N \l__spath_split_path_b_tl
+  % Remove empty components
+  \spath_remove_empty_components:N \l__spath_split_path_b_tl
+  % Make a copy for later
+  \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+
+  % Clear some token lists and sequences
+  \tl_clear:N \l__spath_split_path_a_tl
+  \seq_clear:N \l__spath_split_first_seq
+  \int_zero:N \l__spath_split_segment_int
+
+  \pgfintersectionsortbyfirstpath
+
+  \bool_do_until:nn
+  {
+    \int_compare_p:n
+    {
+      \tl_count:N \l__spath_split_path_b_tl < 4
+    }
   }
   {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_case:NnF \l__spath_tmpc_tl
+    \tl_clear:N \l__spath_split_path_a_tl
+    \tl_put_right:Nx \l__spath_split_path_a_tl
     {
-      \g__spath_lineto_tl
-      {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl
+      \tl_item:Nn \l__spath_split_path_b_tl {1}
+      {\tl_item:Nn \l__spath_split_path_b_tl {2}}
+      {\tl_item:Nn \l__spath_split_path_b_tl {3}}
+    }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl { \tl_item:Nn \l__spath_split_path_b_tl {4} }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+
+    \int_zero:N \l__spath_tmpa_int
 
+    \tl_case:Nn \l__spath_tmpa_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_clear:N \l__spath_split_path_a_tl
+        \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+        \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+        \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+      }
+      \c_spath_lineto_tl
+      {
+        \int_set:Nn \l__spath_tmpa_int {1}
+      }
+      \c_spath_curvetoa_tl
+      {
+        \int_set:Nn \l__spath_tmpa_int {3}
       }
+    }
 
-      \g__spath_curvetoa_tl
+    \prg_replicate:nn { \l__spath_tmpa_int }
+    {
+      \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+      \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+
+      \tl_put_right:Nx \l__spath_split_path_a_tl
       {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_curvetoa_tl
+        \tl_item:Nn \l__spath_split_path_b_tl {1}
+        {\tl_item:Nn \l__spath_split_path_b_tl {2}}
+        {\tl_item:Nn \l__spath_split_path_b_tl {3}}
+      }
 
-        \prg_replicate:nn {2} {
-          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N               \l__spath_tmpa_tl}}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-          \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N             \l__spath_tmpa_tl}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        }
+      \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+    }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_put_left:NV \l__spath_split_path_b_tl \c_spath_moveto_tl
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_if_empty:NF \l__spath_split_path_a_tl
+    {
+      % Intersect the current segment with the rest of the path
+      \spath_intersect:NN \l__spath_split_path_a_tl \l__spath_split_path_b_tl
 
+      % If we get intersections
+      \int_compare:nT {\pgfintersectionsolutions > 0}
+      {
+        % Find the times of the intersections on each path
+        \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+        {
+          \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+          \fp_compare:nT
+          {
+            \l__spath_split_first_tl < .99
+          }
+          {
+            \tl_set:Nx \l__spath_tmpa_tl {\fp_to_decimal:n {\l__spath_split_first_tl +  \l__spath_split_segment_int}}
+            \seq_put_right:NV \l__spath_split_first_seq \l__spath_tmpa_tl
+          }
+        }
       }
 
-      \g__spath_closepath_tl
+      \spath_intersect:NN \l__spath_split_path_b_tl \l__spath_split_path_a_tl
+
+      % If we get intersections
+      \int_compare:nT {\pgfintersectionsolutions > 0}
       {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
+        % Find the times of the intersections on each path
+        \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
         {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
+          \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+          \fp_compare:nT
+          {
+            \l__spath_split_first_tl > .01
+          }
+          {
+            \tl_set:Nx \l__spath_tmpa_tl {\fp_to_decimal:n {\l__spath_split_first_tl +  \l__spath_split_segment_int + 1}}
+            \seq_put_right:NV \l__spath_split_first_seq \l__spath_tmpa_tl
+          }
         }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl
+      }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    }
+    % Increment the segment counter
+    \int_incr:N \l__spath_split_segment_int
+  }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+  % Sort the sequence by reverse order along the path
+  \seq_sort:Nn \l__spath_split_first_seq
+  {
+    \fp_compare:nNnTF { ##1 } < { ##2 }
+    { \sort_return_swapped: }
+    { \sort_return_same: }
+  }
 
-      }
+  % Restore the original copy of the path
+  \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_final_tl
+
+  % Clear the token lists
+  \tl_clear:N \l__spath_split_path_b_start_tl
+  \tl_clear:N \l__spath_split_path_b_end_tl
+  \tl_clear:N \l__spath_split_path_b_final_tl
 
+  \tl_set:Nn \l__spath_split_prev_first_tl {-1}
+
+  \seq_map_inline:Nn \l__spath_split_first_seq
+  {
+    \tl_set:Nn \l__spath_split_first_tl {##1}
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_first_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l__spath_split_first_tl ) }
+      =
+      \fp_to_int:n {floor( \l__spath_split_prev_first_tl) }
     }
     {
+      \tl_set:Nx \l__spath_split_first_tl
+      {
+        \fp_eval:n {
+          floor( \l__spath_split_first_tl )
+          +
+          ( \l__spath_split_first_tl - floor( \l__spath_split_first_tl) )
+          /
+          ( \l__spath_split_prev_first_tl - floor( \l__spath_split_prev_first_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l__spath_split_prev_first_tl \l__spath_tmpa_tl
 
-      \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpc_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \spath_split_at:NNVV \l__spath_split_path_b_start_tl \l__spath_split_path_b_end_tl  \l__spath_split_path_b_tl \l__spath_split_first_tl
 
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_end_tl
+    \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_start_tl
 
-    }
+  }
 
-    #2 \l__spath_tmpc_tl \l__spath_tmpb_tl
-    \tl_clear:N \l__spath_tmpb_tl
+  \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
 
+  \tl_if_empty:NT \l__spath_split_path_b_final_tl
+  {
+    \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
   }
+
+  \spath_remove_empty_components:N \l__spath_split_path_b_final_tl
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_split_path_b_final_tl
+  \group_end:
 }
-\cs_generate_variant:Nn \spath_map_segment_function:NN {Nc}
-\NewDocumentCommand \MakeSPath { m m }
-{
-  \spath_clear_new:n {#1}
-  \spath_put:nno {#1} {path} {#2}
-}
-\NewDocumentCommand \MakeSPathList { m m }
+\cs_new_protected_nopar:Npn \spath_split_at_self_intersections:Nn #1#2
 {
-  \tl_gclear_new:c {l__spath_list_#1}
-  \int_zero:N \l__spath_tmpa_int
-  \spath_map_component:Nn #2 {
-    \spath_clear_new:n {#1 _ \int_use:N \l__spath_tmpa_int}
-    \spath_put:nnn  {#1 _ \int_use:N \l__spath_tmpa_int} {path} {##1}
-    \tl_gput_right:cx {l__spath_list_#1} {{#1 _ \int_use:N \l__spath_tmpa_int}}
-    \int_incr:N \l__spath_tmpa_int
-  }
+  \__spath_split_at_self_intersections:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \CloneSPath { m m }
+\cs_generate_variant:Nn \spath_split_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_split_at_self_intersections:N #1
 {
-  \spath_clone:nn {#1} {#2}
+  \spath_split_at_self_intersections:NV #1#1
 }
-\NewDocumentCommand \SPathInfo { m m }
+\cs_generate_variant:Nn \spath_split_at_self_intersections:N {c}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:Nn #1#2
 {
-  \spath_get:nn {#1} {#2}
+  \__spath_split_at_self_intersections:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathPrepare { m }
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:N #1
 {
-  \spath_generate_all:n {#1}
+  \spath_gsplit_at_self_intersections:NV #1#1
 }
-\NewDocumentCommand \SPathListPrepare { m }
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:N {c}
+\tl_new:N \l__spath_tmpj_tl
+\cs_new_protected_nopar:Npn \__spath_join_component:nn #1#2
 {
-  \tl_map_inline:cn {l__spath_list_#1}
+  \group_begin:
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \int_compare:nT
+  {
+    #2 == 1
+  }
+  {
+    \tl_clear:N \l__spath_tmpj_tl
+    \seq_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpj_tl
+
+    \prg_replicate:nn {3}
+    {
+      \tl_set:Nx \l__spath_tmpj_tl {\tl_tail:N \l__spath_tmpj_tl}
+    }
+
+    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpj_tl
+  }
+  \bool_if:nT
   {
-    \spath_generate_all:n {##1}
+    \int_compare_p:n
+    {
+      #2 > 1
+    }
+    &&
+    \int_compare_p:n
+    {
+      #2 <= \seq_count:N \l__spath_tmpa_seq
+    }
   }
+  {
+
+    \seq_clear:N \l__spath_tmpb_seq
+    \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+    {
+      \tl_set:Nn \l__spath_tmpj_tl {##2}
+      \int_compare:nT {##1 = #2}
+      {
+        \prg_replicate:nn {3}
+        {
+          \tl_set:Nx \l__spath_tmpj_tl {\tl_tail:N \l__spath_tmpj_tl}
+        }
+      }
+      \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpj_tl
+    }
+
+    \seq_set_eq:NN \l__spath_tmpa_seq \l__spath_tmpb_seq
+  }
+
+  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpa_seq {} }
+  \group_end:
 }
-\NewDocumentCommand \SPathInfoInto { m m m }
+\cs_new_protected_nopar:Npn \spath_join_component:Nnn #1#2#3
 {
-  \tl_clear_new:N #3
-  \spath_get:nnN {#1} {#2} #3
+  \__spath_join_component:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathShow { m }
+\cs_generate_variant:Nn \spath_join_component:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_join_component:Nn #1#2
 {
-  \spath_show:n {#1}
+  \spath_join_component:NVn #1#1{#2}
 }
-\NewDocumentCommand \SPathTranslate { m m m }
+\cs_generate_variant:Nn \spath_join_component:Nn {cn, NV, cV}
+\cs_new_protected_nopar:Npn \spath_gjoin_component:Nnn #1#2#3
 {
-  \spath_translate:nnn {#1} {#2} {#3}
+  \__spath_join_component:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathTranslateInto { m m m m }
+\cs_generate_variant:Nn \spath_gjoin_component:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gjoin_component:Nn #1#2
 {
-  \spath_clone:nn {#1} {#2}
-  \spath_translate:nnn {#2} {#3} {#4}
+  \spath_gjoin_component:NVn #1#1{#2}
 }
-\NewDocumentCommand \SPathScale { m m m }
+\cs_generate_variant:Nn \spath_gjoin_component:Nn {cn, NV, cV}
+\cs_new_protected_nopar:Npn \__spath_spot_weld_components:n #1
 {
-  \spath_scale:nnn {#1} {#2} {#3}
+  \group_begin:
+  \dim_zero:N \l__spath_move_x_dim
+  \dim_zero:N \l__spath_move_y_dim
+
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \seq_clear:N \l__spath_tmpb_seq
+  \dim_set:Nn \l__spath_move_x_dim {\tl_item:nn {#1} {2} + 10 pt}
+  \dim_set:Nn \l__spath_move_y_dim {\tl_item:nn {#1} {3} + 10 pt}
+
+  \int_set:Nn \l__spath_tmpa_int {\seq_count:N \l__spath_tmpa_seq}
+
+  \seq_map_inline:Nn \l__spath_tmpa_seq
+  {
+    \tl_set:Nn \l__spath_tmpa_tl {##1}
+    \bool_if:nT
+    {
+      \dim_compare_p:n
+      {
+        \dim_abs:n {\l__spath_move_x_dim - \tl_item:Nn \l__spath_tmpa_tl {2} } < 0.01pt
+      }
+      &&
+      \dim_compare_p:n
+      {
+        \dim_abs:n {\l__spath_move_y_dim - \tl_item:Nn \l__spath_tmpa_tl {3} } < 0.01pt
+      }
+    }
+    {
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      }
+      \int_decr:N \l__spath_tmpa_int
+    }
+    \tl_reverse:N \l__spath_tmpa_tl
+    \dim_set:Nn \l__spath_move_x_dim {\tl_item:Nn \l__spath_tmpa_tl {2}}
+    \dim_set:Nn \l__spath_move_y_dim {\tl_item:Nn \l__spath_tmpa_tl {1}}
+    \tl_reverse:N \l__spath_tmpa_tl
+    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+  }
+
+  \tl_set:Nx \l__spath_tmpa_tl {\seq_use:Nn \l__spath_tmpb_seq {} }
+  \spath_components_to_seq:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+
+  \spath_initialpoint:Nn \l__spath_tmpa_tl {#1}
+  \spath_finalpoint:Nn \l__spath_tmpb_tl {#1}
+
+  \bool_if:nT
+  {
+    \dim_compare_p:n
+    {
+      \dim_abs:n {\tl_item:Nn \l__spath_tmpa_tl {1} - \tl_item:Nn \l__spath_tmpb_tl {1} } < 0.01pt
+    }
+    &&
+    \dim_compare_p:n
+    {
+      \dim_abs:n {\tl_item:Nn \l__spath_tmpa_tl {2} - \tl_item:Nn \l__spath_tmpb_tl {2} } < 0.01pt
+    }
+  }
+  {
+    \int_compare:nTF
+    {
+      \seq_count:N \l__spath_tmpb_seq > 1
+    }
+    {
+      \seq_pop_left:NN \l__spath_tmpb_seq \l__spath_tmpb_tl
+
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+      }
+      \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpb_tl
+    }
+    {
+      \tl_set:NV \l__spath_tmpb_tl \c_spath_closepath_tl
+      \tl_put_right:Nx \l__spath_tmpb_tl
+      {
+        { \tl_item:Nn \l__spath_tmpa_tl {1} }
+        { \tl_item:Nn \l__spath_tmpa_tl {2} }
+      }
+      \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpb_tl
+    }
+  }
+
+  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpb_seq {}}
+  \group_end:
 }
-\NewDocumentCommand \SPathScaleInto { m m m m }
+\cs_new_protected_nopar:Npn \spath_spot_weld_components:Nn #1#2
 {
-  \spath_clone:nn {#1} {#2}
-  \spath_scale:nnn {#2} {#3} {#4}
+  \__spath_spot_weld_components:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathWeld { m m }
+\cs_generate_variant:Nn \spath_spot_weld_components:Nn {NV, cV, cn}
+\cs_new_protected_nopar:Npn \spath_spot_weld_components:N #1
 {
-  \spath_weld:nn {#1} {#2}
+  \spath_spot_weld_components:NV #1#1
 }
-\NewDocumentCommand \SPathWeldInto { m m m }
+\cs_generate_variant:Nn \spath_spot_weld_components:N {c}
+\cs_new_protected_nopar:Npn \spath_spot_gweld_components:Nn #1#2
 {
-  \spath_clone:nn {#1} {#2}
-  \spath_weld:nn {#2} {#3}
+  \__spath_spot_weld_components:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\tikzset{
-  save~spath/.code={
-    \tikz@addmode{
-      \spath_get_current_path:n {#1}
-    }
-  },
-  restore~spath/.code={
-    \spath_set_current_path:n {#1}
-  }
+\cs_generate_variant:Nn \spath_spot_gweld_components:Nn {NV, cV, cn}
+\cs_new_protected_nopar:Npn \spath_spot_gweld_components:N #1
+{
+  \spath_spot_gweld_components:NV #1#1
 }
-\cs_new_nopar:Npn \spath_split_curve:nnNN #1#2#3#4
+\cs_generate_variant:Nn \spath_spot_gweld_components:N {c}
+\cs_new_protected_nopar:Npn \__spath_convert_to_svg:n #1
 {
   \group_begin:
-  \tl_gclear:N \l__spath_smuggle_tl
-  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl {
-    {\tl_item:nn {#2} {2}}
-    {\tl_item:nn {#2} {3}}
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_put_right:Nn \l__spath_tmpa_tl
+  {
+    <?xml~ version="1.0"~ standalone="no"?>
+    \iow_newline:
+    <!DOCTYPE~ svg~ PUBLIC~ "-//W3C//DTD SVG 1.1//EN"~
+    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+    \iow_newline:
+    <svg~ xmlns="http://www.w3.org/2000/svg"~ version="1.1"~viewBox="
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
+
+  \spath_minbb:Nn \l__spath_tmpb_tl {#1}
+  \spath_maxbb:Nn \l__spath_tmpc_tl {#1}
   \tl_put_right:Nx \l__spath_tmpa_tl
   {
-    {\fp_to_dim:n
+    \dim_to_decimal:n
     {
-      (1 - #1) * \tl_item:nn {#2} {2} + (#1) * \tl_item:nn {#2} {5}
-    }}
-    {\fp_to_dim:n
+      \tl_item:Nn \l__spath_tmpb_tl {1} - 10pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
     {
-      (1 - #1) * \tl_item:nn {#2} {3} + (#1) * \tl_item:nn {#2} {6}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
+      \tl_item:Nn \l__spath_tmpb_tl {2} - 10pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
     {
-      (1 - #1)^2 * \tl_item:nn {#2} {2} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {5} + (#1)^2 * \tl_item:nn {#2} {8}
-    }}
-    {\fp_to_dim:n
+      \tl_item:Nn \l__spath_tmpc_tl {1}
+      -
+      \tl_item:Nn \l__spath_tmpb_tl {1}
+      + 20pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
     {
-      (1 - #1)^2 * \tl_item:nn {#2} {3} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {6} + (#1)^2 * \tl_item:nn {#2} {9}
-    }}
+      \tl_item:Nn \l__spath_tmpc_tl {2}
+      -
+      \tl_item:Nn \l__spath_tmpb_tl {2}
+      + 20pt
+    }
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+
+  \tl_put_right:Nn \l__spath_tmpa_tl
   {
-    {\fp_to_dim:n
-      {
-      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
-    }}
+    ">
+    \iow_newline:
+    <path~ d="
   }
-  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
-  \group_end:
-  \tl_set_eq:NN #3 \l__spath_smuggle_tl
-  \group_begin:
-  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+  \tl_set:Nn \l__spath_tmpc_tl {use:n}
+  \tl_map_inline:Nn #1
   {
-    {\fp_to_dim:n
+    \tl_set:Nn \l__spath_tmpb_tl {##1}
+    \tl_case:NnF \l__spath_tmpb_tl
+    {
+      \c_spath_moveto_tl
       {
-      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
+        \tl_put_right:Nn \l__spath_tmpa_tl {M~}
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_lineto_tl
+      {
+        \tl_put_right:Nn \l__spath_tmpa_tl {L~}
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_closepath_tl
+      {
+        \tl_put_right:Nn \l__spath_tmpa_tl {Z~}
+        \tl_set:Nn \l__spath_tmpc_tl {use_none:n}
+      }
+      \c_spath_curvetoa_tl
+      {
+        \tl_put_right:Nn \l__spath_tmpa_tl {C~}
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_curvetob_tl {
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_curveto_tl {
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+    }
     {
-      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
-    }}
+      \tl_put_right:Nx \l__spath_tmpa_tl {\use:c { \l__spath_tmpc_tl } {\dim_to_decimal:n {##1}} ~}
+    }
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+  \tl_put_right:Nn \l__spath_tmpa_tl
   {
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {5} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {8} + (#1)^2 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {6} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {9} + (#1)^2 * \tl_item:nn {#2} {12}
-    }}
+    "~ fill="none"~ stroke="black"~ />
+    \iow_newline:
+    </svg>
+    \iow_newline:
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_convert_to_svg:Nn #1#2
+{
+  \__spath_convert_to_svg:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_new_protected_nopar:Npn \spath_gconvert_to_svg:Nn #1#2
+{
+  \__spath_convert_to_svg:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\iow_new:N \g__spath_stream
+\cs_new_protected_nopar:Npn \spath_export_to_svg:nn #1#2
+{
+  \spath_convert_path_to_svg:Nn \l__spath_iterp_tl {#2}
+  \iow_open:Nn \g__spath_stream {#1 .svg}
+  \iow_now:Nx \g__spath_stream
   {
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {8} + (#1) * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {9} + (#1) * \tl_item:nn {#2} {12}
-    }}
+    \tl_use:N \l__spath_iterp_tl
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl {
-    {\tl_item:nn {#2} {11}}
-    {\tl_item:nn {#2} {12}}
+  \iow_close:N \g__spath_stream
+}
+\cs_new_protected_nopar:Npn \spath_show:n #1
+{
+  \int_step_inline:nnnn {1} {3} {\tl_count:n {#1}}
+  {
+    \iow_term:x {
+      \tl_item:Nn \l__spath_tmpa_tl {##1}
+      {\tl_item:Nn \l__spath_tmpa_tl {##1+1}}
+      {\tl_item:Nn \l__spath_tmpa_tl {##1+2}}
+    }
   }
-  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
-  \group_end:
-  \tl_set_eq:NN #4 \l__spath_smuggle_tl
 }
+\cs_generate_variant:Nn \spath_show:n {V, v}
 
-\cs_generate_variant:Nn \spath_split_curve:nnNN {nVNN, VVNN}
+\cs_new_protected_nopar:Npn \spath_get_current_path:N #1
+{
+  \pgfsyssoftpath@getcurrentpath #1
+}
+\cs_new_protected_nopar:Npn \spath_gget_current_path:N #1
+{
+  \pgfsyssoftpath@getcurrentpath #1
+  \tl_gset_eq:NN #1 #1
+}
+\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
+{
+  \spath_minbb:Nn \l__spath_tmpa_tl {#1}
+  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
+
+  \spath_maxbb:Nn \l__spath_tmpa_tl {#1}
+  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
+}
+\cs_generate_variant:Nn \spath_protocol_path:n {V}
+\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
+{
+  \spath_protocol_path:n {#1}
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \pgfsyssoftpath@setcurrentpath\l__spath_tmpa_tl
+}
+\cs_new_protected_nopar:Npn \spath_set_current_path:N #1
+{
+  \spath_protocol_path:V #1
+  \pgfsyssoftpath@setcurrentpath #1
+}
+\cs_generate_variant:Nn \spath_set_current_path:N {c}
+\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
+{
+  \spath_set_current_path:n {#1}
+  \pgfusepath{#2}
+}
+\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
+{
+  \path[#1] \pgfextra{
+    \spath_set_current_path:n {#2}
+    \tl_put_right:Nn \tikz@preactions {\def\tikz@actions@path{#2}}
+  };
+}
+\cs_generate_variant:Nn \spath_tikz_path:nn {Vn, VV, nv, Vv, nV}
+\cs_new_protected_nopar:Npn \spath_set_tikz_coords:n #1
+{
+  \spath_finalpoint:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    \exp_not:c {tikz@lastx}=\tl_item:Nn \l__spath_tmpa_tl {1}
+    \exp_not:c {tikz@lasty}=\tl_item:Nn \l__spath_tmpa_tl {2}
+    \exp_not:c {tikz@lastxsaved}=\tl_item:Nn \l__spath_tmpa_tl {1}
+    \exp_not:c {tikz@lastysaved}=\tl_item:Nn \l__spath_tmpa_tl {2}
+  }
+  \tl_use:N \l__spath_tmpa_tl
+}
+\cs_generate_variant:Nn \spath_set_tikz_coords:n {V, v}
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -1500,13 +3130,16 @@ manipulating PGF soft paths}
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
index 9b0e082b144..e987539cb0b 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
@@ -4,10 +4,10 @@
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `calligraphy')
+%% spath3_code.dtx  (with options: `calligraphy')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
@@ -17,10 +17,24 @@
 
 \tl_new:N \l__cal_tmpa_tl
 \tl_new:N \l__cal_tmpb_tl
+\tl_new:N \l__cal_tmp_path_tl
+\tl_new:N \l__cal_tmp_rpath_tl
+\tl_new:N \l__cal_tmp_rpathb_tl
+\tl_new:N \l__cal_tmp_patha_tl
+
+\seq_new:N \l__cal_tmpa_seq
+
 \int_new:N \l__cal_tmpa_int
 \int_new:N \l__cal_tmpb_int
-\int_new:N \l__cal_path_component_int
-\int_new:N \l__cal_label_int
+\int_new:N \g__cal_path_component_int
+\int_new:N \g__cal_label_int
+
+\fp_new:N \l__cal_tmpa_fp
+\fp_new:N \l__cal_tmpb_fp
+\fp_new:N \l__cal_tmpc_fp
+\fp_new:N \l__cal_tmpd_fp
+\fp_new:N \l__cal_tmpe_fp
+
 \dim_new:N \l__cal_tmpa_dim
 \dim_new:N \l__cal_tmpb_dim
 \dim_new:N \l__cal_tmpc_dim
@@ -29,10 +43,12 @@
 \dim_new:N \l__cal_tmpf_dim
 \dim_new:N \l__cal_tmpg_dim
 \dim_new:N \l__cal_tmph_dim
+
 \bool_new:N \l__cal_annotate_bool
 \bool_new:N \l__cal_taper_start_bool
 \bool_new:N \l__cal_taper_end_bool
 \bool_new:N \l__cal_taperable_bool
+
 \dim_new:N \l__cal_taper_width_dim
 \dim_new:N \l__cal_line_width_dim
 
@@ -40,27 +56,35 @@
 \bool_set_true:N \l__cal_taper_end_bool
 
 \cs_generate_variant:Nn \tl_put_right:Nn {Nv}
+
+\msg_new:nnn { calligraphy } { undefined pen } { The~ pen~ "#1"~ is~ not~ defined. }
 \tikzset{
   define~pen/.code={
     \tikzset{pen~name=#1}
     \pgf@relevantforpicturesizefalse
     \tikz@addmode{
       \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
-      \MakeSPathList{calligraphy pen \pgfkeysvalueof{/tikz/pen~name}}{\l__cal_tmpa_tl}
-      \SPathListPrepare{calligraphy pen \pgfkeysvalueof{/tikz/pen~name}}
+      \spath_components_to_seq:NV \l__cal_tmpa_seq \l__cal_tmpa_tl
+      \seq_gclear_new:c {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      \seq_gset_eq:cN {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq} \l__cal_tmpa_seq
       \pgfusepath{discard}%
     }
   },
   define~pen/.default={default},
   use~pen/.code={
     \tikzset{pen~name=#1}
-    \int_gzero:N \l__cal_path_component_int
+    \int_gzero:N \g__cal_path_component_int
     \cs_set_eq:NN \pgfpathmoveto \cal_moveto:n
     \tikz@addmode{
       \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
-      \MakeSPathList{calligraphy path}{\l__cal_tmpa_tl}
-      \SPathListPrepare{calligraphy path}
-      \CalligraphyPathCreate{calligraphy path}{\pgfkeysvalueof{/tikz/pen~name}}
+      \spath_components_to_seq:NV \l__cal_tmpa_seq \l__cal_tmpa_tl
+      \tl_if_exist:cTF {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      {
+        \cal_path_create:Nc \l__cal_tmpa_seq {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      }
+      {
+        \msg_warning:nnx { calligraphy } { undefined pen } { \pgfkeysvalueof{/tikz/pen~name} }
+      }
     }
   },
   use~pen/.default={default},
@@ -132,8 +156,8 @@
     \tl_set:cn {l__cal_stroke_style_#1} {#2}
   },
   this~stroke~style/.code={
-    \tl_clear_new:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_path_component_int}
-    \tl_set:cn {l__cal_stroke_inline_style_ \int_use:N \l__cal_path_component_int} {#1}
+    \tl_clear_new:c {l__cal_stroke_inline_style_ \int_use:N \g__cal_path_component_int}
+    \tl_set:cn {l__cal_stroke_inline_style_ \int_use:N \g__cal_path_component_int} {#1}
   },
   annotate/.style={
     annotate~if,
@@ -151,12 +175,13 @@
     }
   },
   annotate~reset/.code={
-    \int_gzero:N \l__cal_label_int
+    \int_gzero:N \g__cal_label_int
   },
   annotation~style/.initial={draw,->},
   annotation~shift/.initial={(0,1ex)},
   every~annotation~node/.initial={anchor=south~west},
   annotation~node~style/.code~2~args={
+    \tl_clear_new:c {l__cal_annotation_style_ #1 _tl}
     \tl_set:cn {l__cal_annotation_style_ #1 _tl}{#2}
   },
   tl~use:N/.code={
@@ -179,7 +204,7 @@
     {
       \pgfkeyssetvalue{\pgfkeyscurrentpath}{#1}
     }
-  }
+  },
 }
 \NewDocumentCommand \pen { O{} }
 {
@@ -195,100 +220,99 @@
 {
   \path[use~ pen,every~ calligraphy/.try,#1]
 }
-\NewDocumentCommand \CalligraphyPathCreate { m m }
+\cs_new_protected_nopar:Npn \cal_path_create:NN #1#2
 {
   \int_zero:N \l__cal_tmpa_int
-  \tl_map_inline:cn {l__spath_list_#1}
+  \seq_map_inline:Nn #1
   {
-    \int_incr:N \l__cal_tmpa_int
-    \int_zero:N \l__cal_tmpb_int
-    \tl_map_inline:cn {l__spath_list_calligraphy pen #2}
+    \int_compare:nT {\tl_count:n {##1} > 3}
     {
-      \int_incr:N \l__cal_tmpb_int
-      \group_begin:
-      \pgfsys@beginscope
-
-      \cal_apply_style:c {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-      \cal_apply_style:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-      \cal_apply_style:c {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-
-      \spath_clone:nn {##1} {calligraphy temp path}
 
-      \__spath_get:nnN {####1} {initial point} \l__cal_tmpa_tl
-      \spath_translate:nV {calligraphy temp path} \l__cal_tmpa_tl
+      \int_incr:N \l__cal_tmpa_int
+      \int_zero:N \l__cal_tmpb_int
 
-      \__spath_get:nnN {####1} {length} \l__cal_tmpa_tl
+      \tl_set:Nn \l__cal_tmp_path_tl {##1}
+      \spath_open:N \l__cal_tmp_path_tl
+      \spath_reverse:NV \l__cal_tmp_rpath_tl \l__cal_tmp_path_tl
 
-      \int_compare:nTF {\l__cal_tmpa_tl = 1}
+      \seq_map_inline:Nn #2
       {
-        \cal_at_least_three:n {calligraphy temp path}
-
-        \spath_protocol_path:n {calligraphy temp path}
+        \int_incr:N \l__cal_tmpb_int
+        \group_begin:
+        \pgfsys@beginscope
+        \cal_apply_style:c {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
+        \cal_apply_style:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
+        \cal_apply_style:c {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
+
+        \spath_initialpoint:Nn \l__cal_tmpa_tl {####1}
+        \tl_set_eq:NN \l__cal_tmp_patha_tl \l__cal_tmp_path_tl
+        \spath_translate:NV \l__cal_tmp_patha_tl \l__cal_tmpa_tl
+
+        \int_compare:nTF {\tl_count:n {####1} == 3}
+        {
+          \cal_at_least_three:N \l__cal_tmp_patha_tl
+          \spath_protocol_path:V \l__cal_tmp_patha_tl
 
-        \__spath_get:nnN {calligraphy temp path} {path} \l__cal_tmpa_tl
+          \tikz@options
+          \dim_set:Nn \l__cal_line_width_dim {\pgflinewidth}
+          \cal_maybe_taper:N \l__cal_tmp_patha_tl
+        }
+        {
+          \spath_weld:Nn \l__cal_tmp_patha_tl {####1}
+          \spath_weld:NV \l__cal_tmp_patha_tl \l__cal_tmp_rpath_tl
+          \spath_reverse:Nn \l__cal_tmp_rpathb_tl {####1}
+          \spath_weld:NV \l__cal_tmp_patha_tl \l__cal_tmp_rpathb_tl
+
+          \tl_clear:N \l__cal_tmpa_tl
+          \tl_set:Nn \l__cal_tmpa_tl {fill=\pgfkeysvalueof{/tikz/pen~colour},draw=none}
+          \tl_if_exist:cT  {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
+          {
+            \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
+          }
+          \tl_if_exist:cT  {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
+          {
+            \tl_put_right:Nn \l__cal_tmpa_tl {,}
+            \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
+          }
+          \tl_if_exist:cT  {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
+          {
+            \tl_put_right:Nn \l__cal_tmpa_tl {,}
+            \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
+          }
+          \spath_tikz_path:VV \l__cal_tmpa_tl \l__cal_tmp_patha_tl
 
-        \tikz@options
-        \dim_set:Nn \l__cal_line_width_dim {\pgflinewidth}
-        \cal_maybe_taper:N \l__cal_tmpa_tl
+        }
+        \pgfsys@endscope
+        \group_end:
       }
+
+      \bool_if:NT \l__cal_annotate_bool
       {
+        \seq_get_right:NN #2 \l__cal_tmpa_tl
+        \spath_finalpoint:NV \l__cal_tmpa_tl \l__cal_tmpa_tl
+        \spath_translate:NV \l__cal_tmp_path_tl \l__cal_tmpa_tl
+        \tikz@scan@one@point\pgfutil@firstofone\pgfkeysvalueof{/tikz/annotation~shift}
 
-        \spath_weld:nn {calligraphy temp path} {####1}
-        \spath_reverse:n {##1}
-        \spath_reverse:n {####1}
-        \spath_weld:nn {calligraphy temp path} {##1}
-        \spath_weld:nn {calligraphy temp path} {####1}
-        \spath_reverse:n {##1}
-        \spath_reverse:n {####1}
-
-        \tl_clear:N \l__cal_tmpa_tl
-        \tl_set:Nn \l__cal_tmpa_tl {fill=\pgfkeysvalueof{/tikz/pen~colour},draw=none}
-        \tl_if_exist:cT  {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-        {
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-        }
-        \tl_if_exist:cT  {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-        {
-          \tl_put_right:Nn \l__cal_tmpa_tl {,}
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-        }
-        \tl_if_exist:cT  {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-        {
-          \tl_put_right:Nn \l__cal_tmpa_tl {,}
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-        }
-        \spath_tikz_path:Vn \l__cal_tmpa_tl {calligraphy temp path}
+        \spath_translate:Nnn \l__cal_tmp_path_tl {\pgf@x} {\pgf@y}
 
+        \pgfkeysgetvalue{/tikz/annotation~style}{\l__cal_tmpa_tl}
+        \spath_tikz_path:VV \l__cal_tmpa_tl \l__cal_tmp_path_tl
+
+        \spath_finalpoint:NV \l__cal_tmpa_tl \l__cal_tmp_path_tl
+
+        \exp_last_unbraced:NV \pgfqpoint \l__cal_tmpa_tl
+        \begin{scope}[reset~ cm]
+        \node[every~annotation~node/.try,tl~use:c =  {l__cal_annotation_style_ \int_use:N \l__cal_tmpa_int _tl}] at (\pgf@x,\pgf@y) {\int_use:N \l__cal_tmpa_int};
+        \end{scope}
       }
-      \pgfsys@endscope
-      \group_end:
-    }
-    \bool_if:NT \l__cal_annotate_bool
-    {
-      \spath_clone:nn {##1} {calligraphy temp path}
-      \tl_set_eq:Nc \l_tmpa_tl {l__spath_list_calligraphy pen #2}
-      \tl_reverse:N \l_tmpa_tl
-      \tl_set:Nx \l_tmpa_tl {\tl_head:N \l_tmpa_tl}
-      \spath_generate_finalpoint:V \l_tmpa_tl
-      \spath_get:VnN \l_tmpa_tl {final point} \l_tmpa_tl
-      \spath_translate:nV {calligraphy temp path} \l_tmpa_tl
-      \tikz@scan@one@point\pgfutil@firstofone\pgfkeysvalueof{/tikz/annotation~shift}
-      \spath_translate:nnn {calligraphy temp path} {\pgf@x} {\pgf@y}
-
-      \pgfkeysgetvalue{/tikz/annotation~style}{\l_tmpa_tl}
-      \spath_tikz_path:Vn \l_tmpa_tl {calligraphy temp path}
-      \spath_get:nnN {calligraphy temp path} {final point} \l_tmpa_tl
-      \exp_last_unbraced:NV \pgfqpoint \l_tmpa_tl
-      \begin{scope}[reset~ cm]
-      \node[every~annotation~node/.try,tl~use:c =  {l__cal_annotation_style_ \int_use:N \l__cal_tmpa_int _tl}] at (\pgf@x,\pgf@y) {\int_use:N \l__cal_tmpa_int};
-      \end{scope}
     }
   }
 }
+\cs_generate_variant:Nn \cal_path_create:NN {Nc}
 \cs_new_eq:NN \cal_orig_moveto:n \pgfpathmoveto
 \cs_new_nopar:Npn \cal_moveto:n #1
 {
-  \int_gincr:N \l__cal_path_component_int
+  \int_gincr:N \g__cal_path_component_int
   \cal_orig_moveto:n {#1}
 }
 \cs_new_nopar:Npn \cal_apply_style:N #1
@@ -298,154 +322,32 @@
   }
 }
 \cs_generate_variant:Nn \cal_apply_style:N {c}
-\cs_new_nopar:Npn \cal_at_least_three:n #1
+\cs_new_protected_nopar:Npn \cal_at_least_three:Nn #1#2
 {
-  \spath_get:nnN {#1} {real length} \l__cal_tmpa_tl
+  \spath_reallength:Nn \l__cal_tmpa_int {#2}
   \tl_clear:N \l__cal_tmpb_tl
-  \int_compare:nTF {\l__cal_tmpa_tl = 1}
+  \tl_set:Nn \l__cal_tmpb_tl {#2}
+  \int_compare:nTF {\l__cal_tmpa_int = 1}
   {
-    \spath_get:nnN {#1} {path} \l__cal_tmpa_tl
-    \spath_map_segment_inline:Nn \l__cal_tmpa_tl
-    {
-      \tl_case:NnF ##1 {
-        \g__spath_lineto_tl {
-          \cal_split_line_in_three:NN \l__cal_tmpb_tl ##2
-        }
-        \g__spath_curvetoa_tl {
-          \cal_split_curve_in_three:NN \l__cal_tmpb_tl ##2
-        }
-      }
-      {
-        \tl_put_right:NV \l__cal_tmpb_tl ##2
-      }
-    }
-    \spath_put:nnV {#1} {path} \l__cal_tmpb_tl
+    \spath_split_at:Nn \l__cal_tmpb_tl {2/3}
+    \spath_split_at:Nn \l__cal_tmpb_tl {1/2}
   }
   {
-    \int_compare:nT {\l__cal_tmpa_tl = 2}
+    \int_compare:nT {\l__cal_tmpa_int = 2}
     {
-      \spath_get:nnN {#1} {path} \l__cal_tmpa_tl
-      \spath_map_segment_inline:Nn \l__cal_tmpa_tl
-      {
-        \tl_case:NnF ##1 {
-          \g__spath_lineto_tl {
-            \cal_split_line_in_two:NN \l__cal_tmpb_tl ##2
-          }
-          \g__spath_curvetoa_tl {
-            \cal_split_curve_in_two:NN \l__cal_tmpb_tl ##2
-          }
-        }
-        {
-          \tl_put_right:NV \l__cal_tmpb_tl ##2
-        }
-      }
-      \spath_put:nnV {#1} {path} \l__cal_tmpb_tl
+      \spath_split_at:Nn \l__cal_tmpb_tl {1.5}
+      \spath_split_at:Nn \l__cal_tmpb_tl {.5}
     }
   }
+  \tl_set_eq:NN #1 \l__cal_tmpb_tl
 }
-\cs_new_nopar:Npn \cal_split_line_in_two:NN #1#2
+\cs_generate_variant:Nn \cal_at_least_three:Nn {NV}
+\cs_new_protected_nopar:Npn \cal_at_least_three:N #1
 {
-  \tl_set_eq:NN \l__cal_tmpc_tl #2
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpa_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpb_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpc_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-  \dim_set:Nn \l__cal_tmpd_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(\l__cal_tmpa_dim + \l__cal_tmpc_dim)/2}}
-    {\dim_eval:n {(\l__cal_tmpb_dim + \l__cal_tmpd_dim)/2}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-  \tl_put_right:Nx #1 {
-    {\dim_use:N \l__cal_tmpc_dim}
-    {\dim_use:N \l__cal_tmpd_dim}
-  }
+  \cal_at_least_three:NV #1#1
 }
-\cs_new_nopar:Npn \cal_split_line_in_three:NN #1#2
-{
-  \tl_set_eq:NN \l__cal_tmpc_tl #2
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpa_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpb_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpc_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-  \dim_set:Nn \l__cal_tmpd_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(2\l__cal_tmpa_dim + \l__cal_tmpc_dim)/3}}
-    {\dim_eval:n {(2\l__cal_tmpb_dim + \l__cal_tmpd_dim)/3}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(\l__cal_tmpa_dim + 2\l__cal_tmpc_dim)/3}}
-    {\dim_eval:n {(\l__cal_tmpb_dim + 2\l__cal_tmpd_dim)/3}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-  \tl_put_right:Nx #1 {
-    {\dim_use:N \l__cal_tmpc_dim}
-    {\dim_use:N \l__cal_tmpd_dim}
-  }
-}
-\cs_new_nopar:Npn \cal_split_curve_in_two:NN #1#2
-{
-  \spath_split_curve:nVNN {.5} #2 \l_tmpa_tl \l_tmpb_tl
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-  \tl_put_right:NV #1 \l_tmpb_tl
-}
-\cs_new_nopar:Npn \cal_split_curve_in_three:NN #1#2
-{
-  \spath_split_curve:nVNN {1/3} #2 \l_tmpa_tl \l_tmpb_tl
-
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-
-  \spath_split_curve:nVNN {.5} \l_tmpb_tl \l_tmpa_tl \l_tmpb_tl
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-  \tl_put_right:NV #1 \l_tmpb_tl
-}
-\cs_new_nopar:Npn \cal_maybe_taper:N #1
+\cs_generate_variant:Nn \cal_at_least_three:N {c}
+\cs_new_protected_nopar:Npn \cal_maybe_taper:N #1
 {
   \tl_set_eq:NN \l__cal_tmpa_tl #1
 
@@ -458,7 +360,7 @@
 
     \tl_case:NnF \l__cal_tmpb_tl
     {
-      \g__spath_lineto_tl
+      \c_spath_lineto_tl
       {
 
         \bool_set_true:N \l__cal_taperable_bool
@@ -472,9 +374,9 @@
         {
           \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
         }
-        \tl_put_left:NV \l__cal_tmpa_tl \g__spath_moveto_tl
+        \tl_put_left:NV \l__cal_tmpa_tl \c_spath_moveto_tl
       }
-      \g__spath_curvetoa_tl
+      \c_spath_curvetoa_tl
       {
         \bool_set_true:N \l__cal_taperable_bool
         \dim_set:Nn \l__cal_tmpc_dim {\tl_item:Nn \l__cal_tmpa_tl {5}}
@@ -487,7 +389,7 @@
         {
           \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
         }
-        \tl_put_left:NV \l__cal_tmpa_tl \g__spath_moveto_tl
+        \tl_put_left:NV \l__cal_tmpa_tl \c_spath_moveto_tl
       }
     }
     {
@@ -510,7 +412,7 @@
 
     \tl_case:NnF \l__cal_tmpb_tl
     {
-      \g__spath_lineto_tl
+      \c_spath_lineto_tl
       {
 
         \bool_set_true:N \l__cal_taperable_bool
@@ -527,7 +429,7 @@
         }
         \tl_reverse:N \l__cal_tmpa_tl
       }
-      \g__spath_curveto_tl
+      \c_spath_curveto_tl
       {
         \bool_set_true:N \l__cal_taperable_bool
         \dim_set:Nn \l__cal_tmpc_dim {\tl_item:Nn \l__cal_tmpa_tl {-5}}
@@ -560,10 +462,10 @@
   \pgfusepath{stroke}
 
 }
-\cs_new_nopar:Npn \__cal_taper_aux:
+\cs_new_protected_nopar:Npn \__cal_taper_aux:
 {
   \tl_clear:N \l__cal_tmpb_tl
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_moveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_moveto_tl
 
   \fp_set:Nn \l__cal_tmpa_fp
   {
@@ -603,7 +505,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp +             \l__cal_tmpb_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -611,7 +513,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpd_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -619,7 +521,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmpf_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -627,7 +529,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -635,7 +537,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32* \l__cal_tmpc_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -643,7 +545,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32 * \l__cal_tmpc_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -651,7 +553,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -659,7 +561,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmpf_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -667,7 +569,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpd_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -675,7 +577,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -683,7 +585,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32* \l__cal_tmpa_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -691,7 +593,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32 * \l__cal_tmpa_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -704,8 +606,14 @@
   \pgfusepath{fill}
 }
 \tl_set:Nn \l__cal_tmpa_tl {\pgfsyssoftpath@movetotoken{0pt}{0pt}}
-\MakeSPathList{calligraphy pen copperplate}{\l__cal_tmpa_tl}
-\SPathListPrepare{calligraphy pen copperplate}
+\spath_components_to_seq:NV \l__cal_tmpa_seq \l__cal_tmpa_tl
+\seq_gclear_new:N \g__cal_pen_copperplate_seq
+\seq_gset_eq:NN \g__cal_pen_copperplate_seq \l__cal_tmpa_seq
+\DeclareDocumentCommand \CopperplatePath { m }
+{
+  \spath_components_to_seq:NV \l__cal_tmpa_seq #1
+  \cal_path_create:NN \l__cal_tmpa_seq \g__cal_pen_copperplate_seq
+}
 \ExplSyntaxOff
 \expandafter\ifx\csname pgfdeclaredecoration\endcsname\relax
 \else
@@ -745,9 +653,7 @@
       taper
     }%
     \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
+    \CopperplatePath{\cal@tmp@path}
   }
   \state{final}{}
 }
@@ -774,9 +680,7 @@
       taper
     }%
     \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
+    \CopperplatePath{\cal@tmp@path}
   }
   \state{final}{}%
 }
@@ -798,15 +702,13 @@
       taper
     }%
     \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
+    \CopperplatePath{\cal@tmp@path}
   }
   \state{final}{}%
 }
 \fi
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -821,13 +723,16 @@
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
index 0322a679410..5872a71fdf3 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
@@ -4,17 +4,17 @@
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `knots')
+%% spath3_code.dtx  (with options: `knots')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
 %% 
 %%
 \RequirePackage{spath3}
-\usetikzlibrary{intersections}
+\usetikzlibrary{intersections,spath3}
 
 \ExplSyntaxOn
 
@@ -22,8 +22,6 @@
 \tl_new:N \l__knot_tmpb_tl
 \tl_new:N \l__knot_tmpc_tl
 \tl_new:N \l__knot_tmpd_tl
-\tl_new:N \l__knot_tmpe_tl
-\tl_new:N \l__knot_tmpf_tl
 \tl_new:N \l__knot_tmpg_tl
 \tl_new:N \l__knot_redraws_tl
 \tl_new:N \l__knot_clip_width_tl
@@ -31,16 +29,21 @@
 \tl_new:N \l__knot_node_tl
 \tl_new:N \l__knot_aux_tl
 \tl_new:N \l__knot_auxa_tl
+\tl_new:N \l__knot_prefix_tl
+
+\seq_new:N \l__knot_segments_seq
 
 \int_new:N \l__knot_tmpa_int
 \int_new:N \l__knot_strands_int
-\int_new:N \l__knot_intersections_int
-\int_new:N \l__knot_filaments_int
+\int_new:N \g__knot_intersections_int
+\int_new:N \g__knot_filaments_int
 \int_new:N \l__knot_component_start_int
 
+\fp_new:N \l__knot_tmpa_fp
+\fp_new:N \l__knot_tmpb_fp
+
 \dim_new:N \l__knot_tmpa_dim
 \dim_new:N \l__knot_tmpb_dim
-\dim_new:N \l__knot_tmpc_dim
 \dim_new:N \l__knot_tolerance_dim
 \dim_new:N \l__knot_clip_bg_radius_dim
 \dim_new:N \l__knot_clip_draw_radius_dim
@@ -56,10 +59,16 @@
 \bool_new:N \l__knot_skip_bool
 \bool_new:N \l__knot_save_bool
 
-\seq_new:N \l__knot_nodes_seq
+\seq_new:N \g__knot_nodes_seq
 
 \bool_set_true:N \l__knot_ignore_ends_bool
 \tikzset{
+  spath/prefix/knot/.style={
+    spath/set~ prefix=knot strand,
+  },
+  spath/suffix/knot/.style={
+    spath/set~ suffix={},
+  },
   knot/.code={
     \tl_if_eq:nnTF {#1} {none}
     {
@@ -218,7 +227,7 @@
   \int_incr:N \l__knot_strands_int
   \tl_clear_new:c {l__knot_options_strand \int_use:N \l__knot_strands_int}
   \tl_set:cn {l__knot_options_strand \int_use:N \l__knot_strands_int} {#1}
-  \path[#1,save~ spath=knot strand \int_use:N  \l__knot_strands_int]
+  \path[#1,spath/set~ name=knot,spath/save=\int_use:N \l__knot_strands_int]
 }
 \NewDocumentEnvironment{knot} { O{} }
 {
@@ -232,7 +241,7 @@
   \tikzset{knot~ diagram/.cd,every~ knot~ diagram/.try,#1}
   \int_zero:N \l__knot_strands_int
   \tl_clear:N \l__knot_redraws_tl
-  \seq_gclear:N \l__knot_nodes_seq
+  \seq_gclear:N \g__knot_nodes_seq
 }
 \cs_new_protected_nopar:Npn \knot_render:
 {
@@ -245,25 +254,23 @@
     \bool_if:NTF \l__knot_self_intersections_bool
     {
       \knot_split_strands:
-      \int_set_eq:NN \l__knot_tmpa_int \l__knot_filaments_int
+      \int_set_eq:NN \l__knot_tmpa_int \g__knot_filaments_int
       \tl_set:Nn \l__knot_prefix_tl {filament}
     }
     {
       \int_set_eq:NN \l__knot_tmpa_int \l__knot_strands_int
       \tl_set:Nn \l__knot_prefix_tl {strand}
     }
-    \int_gzero:N \l__knot_intersections_int
-    \bool_if:NTF \l__knot_draft_bool
+    \int_gzero:N \g__knot_intersections_int
+    \tl_clear:N \l__knot_node_tl
+    \bool_if:NT \l__knot_draft_bool
     {
       \tl_set:Nn \l__knot_node_tl {
         \exp_not:N \node[coordinate,
-          pin={[node~ contents={\int_use:N \l__knot_intersections_int},knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \l__knot_intersections_int \c_space_tl label/.try]
+          pin={[node~ contents={\int_use:N \g__knot_intersections_int},knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \g__knot_intersections_int \c_space_tl label/.try]
             }]
       }
     }
-    {
-      \tl_set:Nn \l__knot_node_tl {\exp_not:N \node[coordinate]}
-    }
     \int_step_variable:nnnNn {1} {1} {\l__knot_tmpa_int - 1} \l__knot_tmpa_tl
     {
       \int_step_variable:nnnNn {\tl_use:N \l__knot_tmpa_tl + 1} {1}     {\l__knot_tmpa_int} \l__knot_tmpb_tl
@@ -272,7 +279,7 @@
       }
     }
     \tl_use:N \l__knot_redraws_tl
-    \seq_use:Nn \l__knot_nodes_seq {}
+    \seq_use:Nn \g__knot_nodes_seq {}
   }
   \endpgfscope
 }
@@ -280,11 +287,11 @@
 {
   \pgfscope
   \group_begin:
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_strand #1}
-  \tl_put_right:Nn \l_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
-  \spath_bake_round:n {knot strand #1}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot strand #1}
+  \spath_bake_round:c {knot strand #1}
+  \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_strand #1}
+  \tl_put_right:Nn \l__knot_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \spath_tikz_path:Vv \l__knot_tmpa_tl {knot strand #1}
   \group_end:
   \endpgfscope
 }
@@ -293,11 +300,11 @@
 {
   \bool_if:NT \l__knot_draft_bool
   {
-    \spath_get:nnN {knot strand #1} {final point} \l__knot_tmpb_tl
+    \spath_finalpoint:Nv \l__knot_tmpb_tl {knot strand #1}
     \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}}
     \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}}
     \node[knot~ diagram/draft/strand~label] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
-    \spath_get:nnN {knot strand #1} {initial point} \l__knot_tmpb_tl
+    \spath_initialpoint:Nv \l__knot_tmpb_tl {knot strand #1}
     \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}}
     \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}}
     \node[knot~ diagram/draft/strand~label] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
@@ -309,84 +316,86 @@
   }
   {
     \tl_clear:N \l__knot_tmpa_tl
-    \spath_map_segment_function:nN {knot strand #1} \knot_split_self_intersects:NN
-    \spath_put:nnV {knot strand #1} {path} \l__knot_tmpa_tl
+    \spath_segments_to_seq:Nv \l__knot_segments_seq {knot strand #1}
+    \seq_map_function:NN \l__knot_segments_seq \knot_split_self_intersects:N
+    \tl_set_eq:cN {knot strand #1} \l__knot_tmpa_tl
   }
 }
-\cs_new_protected_nopar:Npn \knot_split_self_intersects:NN #1#2
+\cs_new_protected_nopar:Npn \knot_split_self_intersects:N #1
 {
-  \tl_case:NnF #1
+  \tl_set:Nx \l__knot_tmpc_tl {\tl_item:nn {#1} {4}}
+  \tl_case:NnF \l__knot_tmpc_tl
   {
-    \g__spath_curvetoa_tl
+    \c_spath_curvetoa_tl
     {
-      \fp_set:Nn \l_tmpa_fp
+      \fp_set:Nn \l__knot_tmpa_fp
       {
-        (\tl_item:Nn #2 {3} - 3 * \tl_item:Nn #2 {6} + 3 * \tl_item:Nn #2 {9} - \tl_item:Nn #2 {12})
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
         *
-        (3 * \tl_item:Nn #2 {8} - 3 * \tl_item:Nn #2 {11})
+        (3 * \tl_item:nn {#1} {8} - 3 * \tl_item:nn {#1} {11})
         -
-        (\tl_item:Nn #2 {2} - 3 * \tl_item:Nn #2 {5} + 3 * \tl_item:Nn #2 {8} - \tl_item:Nn #2 {11})
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
         *
-        (3 * \tl_item:Nn #2 {9} - 3 * \tl_item:Nn #2 {12})
+        (3 * \tl_item:nn {#1} {9} - 3 * \tl_item:nn {#1} {12})
       }
-      \fp_set:Nn \l_tmpb_fp
+      \fp_set:Nn \l__knot_tmpb_fp
       {
-        (\tl_item:Nn #2 {2} - 3 * \tl_item:Nn #2 {5} + 3 * \tl_item:Nn #2 {8} - \tl_item:Nn #2 {11})
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
         *
-        (3 * \tl_item:Nn #2 {6} - 6 * \tl_item:Nn #2 {9} + 3 * \tl_item:Nn #2 {12})
+        (3 * \tl_item:nn {#1} {6} - 6 * \tl_item:nn {#1} {9} + 3 * \tl_item:nn {#1} {12})
         -
-        (\tl_item:Nn #2 {3} - 3 * \tl_item:Nn #2 {6} + 3 * \tl_item:Nn #2 {9} - \tl_item:Nn #2 {12})
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
         *
-        (3 * \tl_item:Nn #2 {5} - 6 * \tl_item:Nn #2 {8} + 3 * \tl_item:Nn #2 {11})
+        (3 * \tl_item:nn {#1} {5} - 6 * \tl_item:nn {#1} {8} + 3 * \tl_item:nn {#1} {11})
       }
       \fp_compare:nTF
       {
-        \l_tmpb_fp != 0
+        \l__knot_tmpb_fp != 0
       }
       {
-        \fp_set:Nn \l_tmpa_fp {.5 * \l_tmpa_fp / \l_tmpb_fp}
+        \fp_set:Nn \l__knot_tmpa_fp {.5 * \l__knot_tmpa_fp / \l__knot_tmpb_fp}
         \fp_compare:nTF
         {
-          0 < \l_tmpa_fp && \l_tmpa_fp < 1
+          0 < \l__knot_tmpa_fp && \l__knot_tmpa_fp < 1
         }
         {
-          \spath_split_curve:VVNN \l_tmpa_fp #2 \l_tmpa_tl \l_tmpb_tl
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpb_tl
+          \spath_split_curve:NNnV \l__knot_tmpc_tl \l__knot_tmpd_tl {#1} \l__knot_tmpa_fp
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl}
+          \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl}
+          \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl}
+          \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
+          \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpd_tl
         }
         {
-          \tl_set_eq:NN \l_tmpa_tl #2
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
+          \tl_set:Nn \l__knot_tmpc_tl {#1}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
         }
       }
       {
-        \tl_set_eq:NN \l_tmpa_tl #2
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
+        \tl_set:Nn \l__knot_tmpc_tl {#1}
+        \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+        \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+        \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+        \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
       }
     }
-    \g__spath_lineto_tl
+    \c_spath_lineto_tl
     {
-      \tl_set_eq:NN \l_tmpa_tl #2
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
+      \tl_set:Nn \l__knot_tmpc_tl {#1}
+      \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+      \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+      \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+      \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
     }
   }
   {
-    \tl_put_right:NV \l__knot_tmpa_tl #2
+    \tl_put_right:Nn \l__knot_tmpa_tl {#1}
   }
 }
 \cs_new_protected_nopar:Npn \knot_intersections:nn #1#2
@@ -396,8 +405,8 @@
   \tl_put_right:Nn \l__knot_tmpa_tl {#1}
   \tl_set_eq:NN \l__knot_tmpb_tl \l__knot_prefix_tl
   \tl_put_right:Nn \l__knot_tmpb_tl {#2}
-  \spath_get:nnN {knot \tl_use:N \l__knot_tmpa_tl} {path} \l__knot_tmpc_tl
-  \spath_get:nnN {knot \tl_use:N \l__knot_tmpb_tl} {path} \l__knot_tmpd_tl
+  \tl_set_eq:Nc \l__knot_tmpc_tl {knot \tl_use:N \l__knot_tmpa_tl}
+  \tl_set_eq:Nc \l__knot_tmpd_tl {knot \tl_use:N \l__knot_tmpb_tl}
 
   \bool_if:nTF {
     \l__knot_save_bool
@@ -411,10 +420,12 @@
 \pgfintersectionofpaths{\pgfsetpath\l__knot_tmpc_tl}{\pgfsetpath\l__knot_tmpd_tl}
 
   }
+
   \int_compare:nT {\pgfintersectionsolutions > 0}
   {
     \int_step_function:nnnN {1} {1} {\pgfintersectionsolutions} \knot_do_intersection:n
   }
+
   \knot_save_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
   \group_end:
 }
@@ -464,10 +475,10 @@
   \bool_set_false:N \l__knot_skip_bool
   \bool_if:NT \l__knot_self_intersections_bool
   {
-    \tl_set:Nn \l_tmpa_tl {knot previous}
-    \tl_put_right:NV \l_tmpa_tl \l__knot_tmpa_tl
-    \tl_set:Nv \l_tmpa_tl \l_tmpa_tl
-    \tl_if_eq:NNT \l_tmpa_tl \l__knot_tmpb_tl
+    \tl_set:Nn \l__knot_tmpc_tl {knot previous}
+    \tl_put_right:NV \l__knot_tmpc_tl \l__knot_tmpa_tl
+    \tl_set:Nv \l__knot_tmpc_tl \l__knot_tmpc_tl
+    \tl_if_eq:NNT \l__knot_tmpc_tl \l__knot_tmpb_tl
     {
       \knot_test_endpoint:VnT \l__knot_tmpb_tl {final point}
       {
@@ -475,10 +486,10 @@
       }
     }
 
-    \tl_set:Nn \l_tmpa_tl {knot previous}
-    \tl_put_right:NV \l_tmpa_tl \l__knot_tmpb_tl
-    \tl_set:Nv \l_tmpa_tl \l_tmpa_tl
-    \tl_if_eq:NNT \l_tmpa_tl \l__knot_tmpa_tl
+    \tl_set:Nn \l__knot_tmpc_tl {knot previous}
+    \tl_put_right:NV \l__knot_tmpc_tl \l__knot_tmpb_tl
+    \tl_set:Nv \l__knot_tmpc_tl \l__knot_tmpc_tl
+    \tl_if_eq:NNT \l__knot_tmpc_tl \l__knot_tmpa_tl
     {
       \knot_test_endpoint:VnT \l__knot_tmpa_tl {final point}
       {
@@ -508,23 +519,23 @@
   \bool_if:NF \l__knot_skip_bool
   {
 
-    \int_gincr:N \l__knot_intersections_int
+    \int_gincr:N \g__knot_intersections_int
     \bool_if:nF
     {
       \tl_if_exist_p:c {l__knot_ignore_crossing_ \int_use:N
-        \l__knot_intersections_int}
+        \g__knot_intersections_int}
       &&
       ! \tl_if_empty_p:c {l__knot_ignore_crossing_ \int_use:N
-        \l__knot_intersections_int}
+        \g__knot_intersections_int}
     }
     {
       \bool_if:nTF
       {
         \tl_if_exist_p:c {l__knot_crossing_ \int_use:N
-          \l__knot_intersections_int}
+          \g__knot_intersections_int}
         &&
         ! \tl_if_empty_p:c {l__knot_crossing_ \int_use:N
-          \l__knot_intersections_int}
+          \g__knot_intersections_int}
       }
       {
         \tl_set_eq:NN \l__knot_tmpg_tl \l__knot_tmpb_tl
@@ -553,9 +564,10 @@
           \l__knot_prepend_prev_bool || \l__knot_append_next_bool
         }
         {
-          \spath_clone:nn {knot \tl_use:N \l__knot_tmpg_tl}
-          {knot \tl_use:N \l__knot_prefix_tl -1}
+          \tl_clear_new:c {knot \tl_use:N \l__knot_prefix_tl -1}
+          \tl_set_eq:cc {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:N \l__knot_tmpg_tl}
 
+          \tl_clear_new:c {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1}
           \tl_set_eq:cc {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1} {l__knot_options_ \tl_use:N \l__knot_tmpg_tl}
 
           \bool_if:nT
@@ -567,7 +579,7 @@
             !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
           }
           {
-            \spath_prepend_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}
+            \spath_prepend_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}
             \bool_if:nT
             {
               \l__knot_splits_bool
@@ -579,10 +591,9 @@
             {
               \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {initial point}
               {
-                \spath_get:nnN {knot \tl_use:N \l__knot_prefix_tl -1} {path} \l_tmpa_tl
-                \spath_prepend_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}}
-                \spath_get:nnN {knot \tl_use:N \l__knot_prefix_tl -1} {path} \l_tmpa_tl
 
+                \spath_prepend_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}}
+                \tl_set_eq:Nc \l__knot_tmpa_tl {knot \tl_use:N \l__knot_prefix_tl -1}
               }
             }
           }
@@ -595,7 +606,7 @@
             !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
           }
           {
-            \spath_append_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}
+            \spath_append_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}
             \bool_if:nT
             {
               \l__knot_splits_bool
@@ -608,7 +619,7 @@
             {
               \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {final point}
               {
-                \spath_append_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}}
+                \spath_append_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}}
 
               }
             }
@@ -619,13 +630,16 @@
       }
       \pgfscope
       \group_begin:
-      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \l__knot_intersections_int/.try}
-      \knot_draw_crossing:nVV {\tl_use:N \l__knot_tmpg_tl} \l__knot_tmpa_dim \l__knot_tmpb_dim
+      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \g__knot_intersections_int/.try}
+      \knot_draw_crossing:VVV \l__knot_tmpg_tl \l__knot_tmpa_dim \l__knot_tmpb_dim
+      \coordinate (\l__knot_name_tl \c_space_tl \int_use:N \g__knot_intersections_int) at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim);
       \group_end:
       \endpgfscope
     }
-    \seq_gpush:Nx \l__knot_nodes_seq { \l__knot_node_tl (\l__knot_name_tl \c_space_tl \int_use:N \l__knot_intersections_int) at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim) {};}
-
+    \tl_if_empty:NF \l__knot_node_tl
+    {
+      \seq_gpush:Nx \g__knot_nodes_seq { \l__knot_node_tl at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim) {};}
+    }
   }
 }
 
@@ -649,7 +663,7 @@
 }
 \prg_new_protected_conditional:Npnn \knot_test_endpoint:nn #1#2 {T,F,TF}
 {
-  \spath_get:nnN {knot #1} {#2} \l__knot_tmpd_tl
+  \use:c {spath_#2:Nv} \l__knot_tmpd_tl {knot #1}
   \knot_test_endpoint:NTF \l__knot_tmpd_tl
   {
     \prg_return_true:
@@ -662,49 +676,49 @@
 \cs_generate_variant:Nn \knot_test_endpoint:nnT {VnT,vnT}
 \cs_generate_variant:Nn \knot_test_endpoint:nnF {VnF,vnF}
 \cs_generate_variant:Nn \knot_test_endpoint:nnTF {VnTF,vnTF}
-\cs_new_nopar:Npn \knot_draw_crossing:nnn #1#2#3
+\cs_new_protected_nopar:Npn \knot_draw_crossing:nnn #1#2#3
 {
   \group_begin:
   \pgfscope
   \path[knot~ diagram/background~ clip] (#2, #3) circle[radius=\l__knot_clip_bg_radius_dim];
 
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,}
   \tl_if_exist:cT {l__knot_options_ #1}
   {
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_ #1}
+  \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_ #1}
   }
-  \tl_put_right:Nn \l_tmpa_tl {,knotbg,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot #1}
+  \tl_put_right:Nn \l__knot_tmpa_tl {,knotbg,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth}
+  \spath_tikz_path:Vv \l__knot_tmpa_tl {knot #1}
 
   \endpgfscope
 
   \pgfscope
   \path[knot~ diagram/clip] (#2, #3) circle[radius=\l__knot_clip_draw_radius_dim];
 
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,}
   \tl_if_exist:cT {l__knot_options_ #1}
   {
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_ #1}
+  \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_ #1}
   }
-  \tl_put_right:Nn \l_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot #1}
+  \tl_put_right:Nn \l__knot_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \spath_tikz_path:Vv \l__knot_tmpa_tl {knot #1}
 
   \endpgfscope
   \group_end:
 }
 
-\cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV}
+\cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV, VVV}
 
-\cs_new_nopar:Npn \knot_draw_crossing:nn #1#2
+\cs_new_protected_nopar:Npn \knot_draw_crossing:nn #1#2
 {
   \tikz@scan@one@point\pgfutil@firstofone #2 \relax
   \knot_draw_crossing:nVV {#1} \pgf@x \pgf@y
 }
 \cs_new_protected_nopar:Npn \knot_split_strands:
 {
-  \int_gzero:N \l__knot_filaments_int
+  \int_gzero:N \g__knot_filaments_int
   \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_split_strand:n
-  \int_step_function:nnnN {1} {1} {\l__knot_filaments_int} \knot_compute_nexts:n
+  \int_step_function:nnnN {1} {1} {\g__knot_filaments_int} \knot_compute_nexts:n
 }
 \cs_new_protected_nopar:Npn \knot_compute_nexts:n #1
 {
@@ -713,66 +727,70 @@
 }
 \cs_new_protected_nopar:Npn \knot_split_strand:n #1
 {
-  \int_set_eq:NN \l__knot_component_start_int \l__knot_filaments_int
+  \int_set_eq:NN \l__knot_component_start_int \g__knot_filaments_int
   \int_incr:N \l__knot_component_start_int
   \tl_set_eq:Nc \l__knot_tmpa_tl {l__knot_options_strand #1}
-  \spath_map_segment_function:nN {knot strand #1} \knot_save_filament:NN
+  \spath_segments_to_seq:Nv \l__knot_segments_seq {knot strand #1}
+  \seq_map_function:NN \l__knot_segments_seq \knot_save_filament:N
 }
-\cs_new_protected_nopar:Npn \knot_save_filament:NN #1#2
+\cs_new_protected_nopar:Npn \knot_save_filament:N #1
 {
-  \tl_case:NnF #1
+  \tl_set:Nx \l__knot_tmpb_tl {\tl_item:nn {#1} {4}}
+  \tl_case:NnF \l__knot_tmpb_tl
   {
-    \g__spath_moveto_tl
+    \c_spath_moveto_tl
     {
-      \int_compare:nT {\l__knot_component_start_int < \l__knot_filaments_int}
+      \int_compare:nT {\l__knot_component_start_int < \g__knot_filaments_int}
       {
-        \int_set_eq:NN \l__knot_component_start_int \l__knot_filaments_int
+        \int_set_eq:NN \l__knot_component_start_int \g__knot_filaments_int
       }
     }
-    \g__spath_lineto_tl
+    \c_spath_lineto_tl
     {
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} #2
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
+      \int_gincr:N \g__knot_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int}
+      \tl_set:cn {knot filament \int_use:N \g__knot_filaments_int} {#1}
+
+      \tl_clear_new:c {l__knot_options_filament \int_use:N \g__knot_filaments_int}
+      \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
 
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
+      \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int}
+      \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int}
       {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
+        \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}}
       }
     }
-    \g__spath_curvetoa_tl
+    \c_spath_curvetoa_tl
     {
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} #2
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
+      \int_gincr:N \g__knot_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int}
+      \tl_set:cn {knot filament \int_use:N \g__knot_filaments_int} {#1}
+      \tl_clear_new:c {l__knot_options_filament \int_use:N \g__knot_filaments_int}
+      \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
 
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
+      \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int}
+      \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int}
       {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
+        \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}}
       }
     }
-    \g__spath_closepath_tl
+    \c_spath_closepath_tl
     {
-      \tl_show:N #2
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \tl_clear:N \l_tmpa_tl
-      \tl_put_right:Nx {\tl_item:Nn #2 {1}\tl_item:Nn #2 {2}\tl_item:Nn #2 {3}}
-      \tl_put_right:NV \l_tmpa_tl \g__spath_lineto_tl
-      \tl_put_right:Nx {\tl_item:Nn #2 {5}\tl_item:Nn #2 {6}}
-      \tl_show:N \l_tmpa_tl
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} \l_tmpa_tl
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
+      \int_gincr:N \g__knot_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int}
+      \tl_clear:N \l__knot_tmpa_tl
+      \tl_put_right:Nx {\tl_item:nn {#1} {1}\tl_item:nn {#1} {2}\tl_item:nn {#1} {3}}
+      \tl_put_right:NV \l__knot_tmpa_tl \c_spath_lineto_tl
+      \tl_put_right:Nx {\tl_item:nn {#1} {5}\tl_item:nn {#1} {6}}
+
+      \tl_set:cV {knot filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
+      \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
+      \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int}
+      \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int}
       {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
+        \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}}
       }
-      \tl_set:cx {knot previous filament \int_use:N \l__knot_component_start_int} {filament \int_use:N \l__knot_filaments_int}
+      \tl_set:cx {knot previous filament \int_use:N \l__knot_component_start_int} {filament \int_use:N \g__knot_filaments_int}
     }
   }
   {
@@ -990,7 +1008,7 @@
  }
 }
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -1005,13 +1023,16 @@
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
new file mode 100644
index 00000000000..32d0d9fea08
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
@@ -0,0 +1,595 @@
+%%
+%% This is file `tikzlibraryspath3.code.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% spath3_code.dtx  (with options: `tikzspath3')
+%% ----------------------------------------------------------------
+%% spath3 --- Functions for manipulating PGF soft paths
+%% E-mail: loopspace@mathforge.org
+%% Released under the LaTeX Project Public License v1.3c or later
+%% See http://www.latex-project.org/lppl.txt
+%% ----------------------------------------------------------------
+%% 
+\RequirePackage{spath3}
+\RequirePackage{expl3}
+\ExplSyntaxOn
+
+\tl_new:N \l__spath_current_tl
+\tl_new:N \l__spath_reverse_tl
+\tl_new:N \l__spath_prefix_tl
+\tl_new:N \l__spath_suffix_tl
+\tl_new:N \g__spath_smuggle_tl
+\seq_new:N \g__spath_tmpa_seq
+\seq_new:N \g__spath_tmpb_seq
+\bool_new:N \l__spath_draft_bool
+\tl_set:Nn \l__spath_prefix_tl {tikz@intersect@path@name@}
+\tl_set:Nn \l__spath_suffix_tl {}
+\tl_new:N \g__spath_tikzfinish_tl
+\cs_new_protected_nopar:Npn \spath_at_end_of_path:
+{
+  \tl_use:N \g__spath_tikzfinish_tl
+  \tl_gclear:N \g__spath_tikzfinish_tl
+}
+\tl_put_right:Nn \tikz@finish {\spath_at_end_of_path:}
+
+\cs_new_protected_nopar:Npn \spath_save_path:Nn #1#2
+{
+  \tl_gput_right:Nn \g__spath_tikzfinish_tl
+  {
+    \tl_clear_new:N #1
+    \tl_set:Nn #1 {#2}
+  }
+}
+\cs_generate_variant:Nn \spath_save_path:Nn {cn, NV, cV}
+
+\cs_new_protected_nopar:Npn \spath_gsave_path:Nn #1#2
+{
+  \tl_gput_right:Nn \g__spath_tikzfinish_tl
+  {
+    \tl_gclear_new:N #1
+    \tl_gset:Nn #1 {#2}
+  }
+}
+\cs_generate_variant:Nn \spath_gsave_path:Nn {cn, NV, cV}
+\tikzset{
+  spath/.is~family,
+  spath/.cd,
+  set~ prefix/.store~ in=\l__spath_prefix_tl,
+  prefix/.is~choice,
+  prefix/default/.style={
+    /tikz/spath/set~ prefix=tikz@intersect@path@name@
+  },
+  set~ suffix/.store~ in=\l__spath_suffix_tl,
+  suffix/.is~choice,
+  suffix/default/.style={
+    /tikz/spath/set~ suffix={}
+  },
+  set~ name/.style={
+    /tikz/spath/prefix=#1,
+    /tikz/spath/suffix=#1
+  },
+  save/.code={
+    \tikz@addmode{
+      \spath_get_current_path:N \l__spath_tmpa_tl
+      \spath_bake_round:NV \l__spath_tmpa_tl \l__spath_tmpa_tl
+      \spath_save_path:cV {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} \l__spath_tmpa_tl
+    }
+  },
+  clone/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_clear_new:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \tl_set_eq:cc
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  clone~ global/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_gclear_new:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \tl_gset_eq:cc
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  save~ global/.code={
+    \tikz@addmode{
+      \spath_get_current_path:N \l__spath_tmpa_tl
+      \spath_bake_round:NV \l__spath_tmpa_tl \l__spath_tmpa_tl
+      \spath_gsave_path:cV
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \l__spath_tmpa_tl
+    }
+  },
+  save~ to~ aux/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_save_to_aux:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  restore/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_set_current_path:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_set_tikz_coords:v
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  show~current~path/.code={
+    \tikz@addmode{
+      \pgfsyssoftpath@getcurrentpath\l__spath_tmpa_tl
+      \iow_term:n {---~ current~ soft~ path~ ---}
+      \spath_show:V \l__spath_tmpa_tl
+    }
+  },
+  show/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \iow_term:n {---~ soft~ path~ #1~ ---}
+      \spath_show:v {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  append/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_weld:Nv
+      \l__spath_current_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  join~ with/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_append:cv
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+  },
+  spot~ weld/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_spot_weld_components:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_reverse:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  append~ reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_reverse:Nv
+      \l__spath_reverse_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_weld:NV \l__spath_current_tl \l__spath_reverse_tl
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  insert/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_append:Nv
+      \l__spath_current_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  insert~ reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_reverse:Nv
+      \l__spath_reverse_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_append:NV \l__spath_current_tl \l__spath_reverse_tl
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  shorten~ at~ end/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_shorten_at_end:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+  },
+  shorten~ at~ start/.code~ 2~ args ={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_shorten_at_start:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+  },
+  shorten~ at~ both~ ends/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_shorten_at_end:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+      \spath_shorten_at_start:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+  },
+  translate/.code~ n~ args={3}{
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_translate:cnn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{#2}{#3}
+    }
+  },
+  export~ to~ svg/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_export_to_svg:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  transform/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \pgftransformreset
+      \tikzset{#2}
+      \pgfgettransform \l__spath_tmpa_tl
+      \tl_gset:Nn \g__spath_smuggle_tl
+      {
+        \spath_transform:cnnnnnn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+      \tl_gput_right:NV \g__spath_smuggle_tl \l__spath_tmpa_tl
+      \group_end:
+      \tl_use:N \g__spath_smuggle_tl
+    }
+  },
+  transform~global/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \pgftransformreset
+      \tikzset{#2}
+      \pgfgettransform \l__spath_tmpa_tl
+      \tl_gset:Nn \g__spath_smuggle_tl
+      {
+        \spath_gtransform:cnnnnnn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+      \tl_gput_right:NV \g__spath_smuggle_tl \l__spath_tmpa_tl
+      \group_end:
+      \tl_use:N \g__spath_smuggle_tl
+    }
+  },
+  split~ at~ intersections/.code~ n~ args={2}{
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_split_at_intersections:cc
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+  },
+  split~ at~ self~ intersections/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_split_at_self_intersections:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  get~ components~ of/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \clist_clear_new:N #2
+      \spath_components_to_seq:Nv
+      \l__spath_tmpa_seq
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \seq_map_inline:Nn \l__spath_tmpa_seq
+      {
+        \tl_new:c
+        {\tl_use:N \l__spath_prefix_tl anonymous_\int_use:N \g__spath_anon_int \tl_use:N \l__spath_suffix_tl}
+        \tl_set:cn
+        {\tl_use:N \l__spath_prefix_tl anonymous_\int_use:N \g__spath_anon_int \tl_use:N \l__spath_suffix_tl} {##1}
+        \clist_put_right:Nx #2 {anonymous_\int_use:N \g__spath_anon_int}
+        \int_gincr:N \g__spath_anon_int
+      }
+    }
+  },
+  render~ components/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \spath_components_to_seq:Nv
+      \l__spath_tmpa_seq
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+      {
+        \spath_tikz_path:nn
+        {
+          every~ spath~ component/.try,
+          spath ~component~ ##1/.try,
+          spath ~component/.try={##1},
+          every~ #1~ component/.try,
+          #1 ~component~ ##1/.try,
+          #1 ~component/.try={##1},
+        }
+        {
+          ##2
+        }
+      }
+      \group_end:
+    }
+  },
+  insert~ gaps~ after~ components/.code~ n~ args={3}{
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \seq_gclear:N \g__spath_tmpa_seq
+      \seq_gclear:N \g__spath_tmpb_seq
+      \foreach \l__spath_tmpa_tl in {#3}
+      {
+        \seq_gput_right:NV \g__spath_tmpa_seq \l__spath_tmpa_tl
+        \seq_gput_right:Nx \g__spath_tmpb_seq {\int_eval:n { \l__spath_tmpa_tl + 1 }}
+      }
+      \spath_components_to_seq:Nv
+      \l__spath_tmpa_seq
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \seq_clear:N \l__spath_tmpb_seq
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+      {
+        \tl_set:Nn \l__spath_tmpa_tl {##2}
+        \seq_if_in:NnT \g__spath_tmpa_seq {##1}
+        {
+          \spath_shorten_at_end:Nn \l__spath_tmpa_tl {#2/2}
+        }
+        \seq_if_in:NnT \g__spath_tmpb_seq {##1}
+        {
+          \spath_shorten_at_start:Nn \l__spath_tmpa_tl {#2/2}
+        }
+        \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+      }
+      \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpb_seq {} }
+      \group_end:
+      \tl_set_eq:cN
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \g__spath_output_tl
+      \tl_gclear:N \g__spath_output_tl
+    }
+  },
+  join~ components/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \seq_gclear:N \g__spath_tmpa_seq
+      \foreach \l__spath_tmpa_tl in {#2}
+      {
+        \seq_gput_right:NV \g__spath_tmpa_seq \l__spath_tmpa_tl
+      }
+      \seq_gsort:Nn \g__spath_tmpa_seq
+      {
+        \int_compare:nNnTF {##1} > {##2}
+        { \sort_return_same: }
+        { \sort_return_swapped: }
+      }
+      \seq_map_inline:Nn \g__spath_tmpa_seq
+      {
+        \spath_join_component:cn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{##1}
+      }
+    }
+  },
+  remove~ empty~ components/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_remove_empty_components:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  draft~ mode/.is~ choice,
+  draft~ mode/true/.code={
+    \bool_set_true:N \l__spath_draft_bool
+  },
+  draft~ mode/false/.code={
+    \bool_set_false:N \l__spath_draft_bool
+  },
+  maybe~ spot~ weld/.code={
+    \bool_if:NF \l__spath_draft_bool
+    {
+      \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_spot_weld_components:c
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+  },
+  transform~ to/.code~ 2~ args={
+    \group_begin:
+    \tl_if_exist:cTF
+    {
+      \tl_use:N \l__spath_prefix_tl
+      #1
+      \tl_use:N \l__spath_suffix_tl
+    }
+    {
+      \spath_reallength:Nv
+      \l__spath_tmpa_int
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+
+      \tl_set:Nx \l__spath_tmpb_tl
+      {\fp_to_decimal:n {(#2) * (\l__spath_tmpa_int)}}
+      \spath_transformation_at:NvV \l__spath_tmpc_tl
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+      \l__spath_tmpb_tl
+      \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpc_tl
+    }
+    {
+      \tl_gset_eq:NN \g__spath_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
+    }
+    \group_end:
+    \exp_last_unbraced:NV \pgfsettransformentries \g__spath_smuggle_tl
+    \tl_gclear:N \g__spath_smuggle_tl
+  },
+  upright~ transform~ to/.code~ 2~ args={
+    \group_begin:
+    \tl_if_exist:cTF
+    {
+      \tl_use:N \l__spath_prefix_tl
+      #1
+      \tl_use:N \l__spath_suffix_tl
+    }
+    {
+      \spath_reallength:Nv
+      \l__spath_tmpa_int
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+
+      \tl_set:Nx \l__spath_tmpb_tl
+      {\fp_to_decimal:n {(#2) * (\l__spath_tmpa_int)}}
+      \spath_transformation_at:NvV \l__spath_tmpc_tl
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+      \l__spath_tmpb_tl
+      \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpc_tl
+    }
+    {
+      \tl_gset_eq:NN \g__spath_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
+    }
+    \fp_compare:nT { \tl_item:Nn \g__spath_smuggle_tl {4} < 0}
+    {
+      \tl_gset:Nx \g__spath_smuggle_tl
+      {
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {1})} }
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {2})} }
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {3})} }
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {4})} }
+        { \tl_item:Nn \g__spath_smuggle_tl {5} }
+        { \tl_item:Nn \g__spath_smuggle_tl {6} }
+      }
+    }
+    \group_end:
+    \exp_last_unbraced:NV \pgfsettransformentries \g__spath_smuggle_tl
+    \tl_gclear:N \g__spath_smuggle_tl
+  },
+  knot/.style~ n~ args={3}{
+    spath/.cd,
+    split~ at~ self~ intersections=#1,
+    insert~ gaps~ after~ components={#1}{#2}{#3},
+    maybe~ spot~ weld=#1,
+    render~ components=#1
+  },
+}
+\tikzdeclarecoordinatesystem{spath}{%
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_trim_spaces:N \l__spath_tmpa_tl
+
+  \seq_set_split:NnV \l__spath_tmpa_seq {~} \l__spath_tmpa_tl
+  \seq_pop_right:NN \l__spath_tmpa_seq \l__spath_tmpb_tl
+
+  \tl_set:Nx \l__spath_tmpa_tl { \seq_use:Nn \l__spath_tmpa_seq {~} }
+  \tl_if_exist:cTF
+  {
+    \tl_use:N \l__spath_prefix_tl
+    \tl_use:N \l__spath_tmpa_tl
+    \tl_use:N \l__spath_suffix_tl
+  }
+  {
+
+    \tl_set_eq:Nc
+    \l__spath_tmpa_tl
+    {
+      \tl_use:N \l__spath_prefix_tl
+      \tl_use:N \l__spath_tmpa_tl
+      \tl_use:N \l__spath_suffix_tl
+    }
+
+    \tl_if_empty:NTF \l__spath_tmpa_tl
+    {
+      \tl_gset_eq:NN \g__spath_smuggle_tl \pgfpointorigin
+    }
+    {
+      \spath_reallength:NV \l__spath_tmpa_int \l__spath_tmpa_tl
+      \tl_set:Nx \l__spath_tmpb_tl
+      {\fp_to_decimal:n {(\l__spath_tmpb_tl) * (\l__spath_tmpa_int)}}
+      \spath_point_at:NVV \l__spath_tmpc_tl \l__spath_tmpa_tl \l__spath_tmpb_tl
+
+      \tl_clear:N \l__spath_tmpd_tl
+      \tl_put_right:Nn \l__spath_tmpd_tl {\pgf@x=}
+      \tl_put_right:Nx \l__spath_tmpd_tl {\tl_item:Nn \l__spath_tmpc_tl {1}}
+      \tl_put_right:Nn \l__spath_tmpd_tl {\relax}
+      \tl_put_right:Nn \l__spath_tmpd_tl {\pgf@y=}
+      \tl_put_right:Nx \l__spath_tmpd_tl {\tl_item:Nn \l__spath_tmpc_tl {2}}
+      \tl_put_right:Nn \l__spath_tmpd_tl {\relax}
+      \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpd_tl
+    }
+  }
+  {
+    \tl_gset_eq:NN \g__spath_smuggle_tl \pgfpointorigin
+  }
+    \group_end:
+    \tl_use:N \g__spath_smuggle_tl
+}
+
+\ExplSyntaxOff
+%% 
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License (LPPL), either
+%% version 1.3c of this license or (at your option) any later
+%% version.  The latest version of this license is in the file:
+%% 
+%% http://www.latex-project.org/lppl.txt
+%% 
+%% This work is "maintained" (as per LPPL maintenance status) by
+%% Andrew Stacey.
+%% 
+%% This work consists of the files  spath3.dtx
+%%                                  calligraphy_doc.tex
+%%                                  knots_doc.tex
+%%                                  spath3.tex
+%% and the derived files            spath3.ins,
+%%                                  spath3_code.pdf,
+%%                                  spath3.sty,
+%%                                  tikzlibrarycalligraphy.code.tex
+%%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
+%%                                  calligraphy.pdf
+%%                                  knots.pdf
+%%                                  spath3.pdf
+%%                                  README
+%% 
+%%
+%% End of file `tikzlibraryspath3.code.tex'.