summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/tikz-3dtools/3DToolsManual.tex
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/tikz-3dtools/3DToolsManual.tex')
-rw-r--r--Master/texmf-dist/doc/latex/tikz-3dtools/3DToolsManual.tex387
1 files changed, 0 insertions, 387 deletions
diff --git a/Master/texmf-dist/doc/latex/tikz-3dtools/3DToolsManual.tex b/Master/texmf-dist/doc/latex/tikz-3dtools/3DToolsManual.tex
deleted file mode 100644
index 4463f79613f..00000000000
--- a/Master/texmf-dist/doc/latex/tikz-3dtools/3DToolsManual.tex
+++ /dev/null
@@ -1,387 +0,0 @@
-\documentclass[a4paper]{ltxdoc}
-%\input{pgfmanual-dvipdfm.cfg}
-%\input{../../text-en/pgfmanual-en-main-preamble}
-\usepackage[version=latest]{pgf}
-\usepackage{xkeyval,calc,listings,tikz,fp}
-\usepackage[T1]{fontenc}% big thanks to samcarter!
-\usepackage{makeidx}
-\makeindex
-\usepackage{hyperref}
-\hypersetup{%
- colorlinks=true,
- linkcolor=blue,
- filecolor=blue,
- urlcolor=blue,
- citecolor=blue,
- pdfborder=0 0 0,
-}
-\makeatletter % see https://tex.stackexchange.com/q/33946
-\input{pgfmanual.code} %
-\makeatother %
-\input{pgfmanual-en-macros.tex} % link from
-% /usr/local/texlive/2019/texmf-dist/doc/generic/pgf/macros/pgfmanual-en-macros.tex
-% or the equivalent on your installation
-\newenvironment{ltxtikzlibrary}[1]{
- \begin{pgfmanualentry}
- \pgfmanualentryheadline{%
- \pgfmanualpdflabel{#1}{}%
- \textbf{\tikzname\ Library} \texttt{\declare{#1}}}
- \index{#1@\protect\texttt{#1} library}%
- \index{Libraries!#1@\protect\texttt{#1}}%
- \vskip.25em%
- {{\ttfamily\char`\\usetikzlibrary\char`\{\declare{#1}\char`\}\space\space \char`\%\space\space \LaTeX\space only}}\\[.5em]
- \pgfmanualbody
-}
-{
- \end{pgfmanualentry}
-}
-\def\pgfautoxrefs{1}
-\usetikzlibrary{3dtools}
-\begin{document}
-\title{\tikzname\ 3D Tools}
-\author{tallmarmot}
-\date{v1.0}
-\maketitle
-\section{Manual}
-\begin{ltxtikzlibrary}{3dtools}
- This library provides additional tools to create 3d--like pictures.
-\end{ltxtikzlibrary}
-
-TikZ has the |3d| and |tpp| libraries which deal with the projections of
-three--dimensional drawings. This library provides some means to manipulate
-the coordinates. It supports linear combinations of vectors, vector and scalar
-products.
-
-\noindent\textbf{Note:} Hopefully this library is only temporary and its
-contents will be absorbed in slightly extended versions of the |3d| and |calc|
-libraries.
-
-\subsection{Coordinate computations}
-\label{sec:3DCoordinateComputations}
-
-
-The |3dtools| library has some options and styles for coordinate computations.
-\begin{key}{/tikz/3d parse}
- Parses and expression and inserts the result in form of a coordinate.
-\end{key}
-\begin{key}{/tikz/3d coordinate}
- Allow one to define a 3d coordinate from other coordinates.
-\end{key}
-Both keys support both symbolic and explicit coordinates.
-
-\begin{codeexample}[width=6cm]
-\begin{tikzpicture}
- \path (1,2,3) coordinate (A)
- (2,3,-1) coordinate (B)
- (-1,-2,1) coordinate (C)
- [3d parse={0.25*(1,2,3)x(B)}]
- coordinate(D)
- [3d parse={0.25*(C)x(B)}]
- coordinate(E);
- \path foreach \X in {A,...,E}
- {(\X) node[fill,inner sep=1pt,
- label=above:$\X$]{}};
-\end{tikzpicture}
-\end{codeexample}
-
-Notice that, as of now, only the syntax |\path (1,2,3) coordinate (A);| works,
-i.e.\ |\coordinate (A) at (1,2,3);| does \emph{not} work, but leads to error
-messages.
-
-\begin{codeexample}[width=6cm]
-\begin{tikzpicture}
- \path (1,2,3) coordinate (A)
- (2,3,-1) coordinate (B)
- (-1,-2,1) coordinate (C)
- [3d coordinate={(D)=0.25*(1,2,3)x(B)},
- 3d coordinate={(E)=0.25*(C)x(B)},
- 3d coordinate={(F)=(A)-(B)},];
- \path foreach \X in {A,...,E}
- {(\X) node[fill,inner sep=1pt,
- label=above:$\X$]{}};
-\end{tikzpicture}
-\end{codeexample}
-
-The actual parsings are done by the function |\pgfmathtdparse| that allows one
-to parse 3d expressions. The supported vector operations are |+| (addition $+$),
-|-| (subtraction $-$), |*| (multiplication of the vector by a scalar), |x|
-(vector product $\times$) and |o| (scalar product).
-
-\begin{command}{\pgfmathtdparse{\marg{x}}}
- Parses 3d expressions.
-\end{command}
-
-In order to pretty-print the result one may want to use |\pgfmathprintvector|,
-and use the math function |TD| for parsing.
-
-\begin{command}{\pgfmathprintvector\marg{x}}
- Pretty-prints vectors.
-\end{command}
-
-
-\begin{codeexample}[width=6.5cm]
-\pgfmathparse{TD("0.2*(A)
--0.3*(B)+0.6*(C)")}%
-$0.2\,\vec A-0.3\,\vec B+0.6\,\vec C
-=(\pgfmathprintvector\pgfmathresult)$
-\end{codeexample}
-
-The alert reader may wonder why this works, i.e.\ how would \tikzname\ ``know''
-what the coordinates $A$, $B$ and $C$ are. It works because the coordinates in
-\tikzname\ are global, so they get remembered from the above example.
-
-\paragraph{Warning.} The expressions that are used in the coordinates will only
-be evaluated when they are retrieved. So, if you use, say, random numbers, you
-will get each time a \emph{different} result.
-
-\begin{codeexample}[width=4cm]
-\begin{tikzpicture}
- \path[overlay] (rnd,rnd,rnd)
- coordinate (R);
- \node at (0,1)
- {\pgfmathparse{TD("(R)")}%
- $\vec R=(\pgfmathprintvector\pgfmathresult)$};
- \node at (0,0)
- {\pgfmathparse{TD("(R)")}%
- $\vec R=(\pgfmathprintvector\pgfmathresult)$};
-\end{tikzpicture}
-\end{codeexample}
-
-\begin{codeexample}[width=5.2cm]
-\pgfmathparse{TD("(1,0,0)x(0,1,0)")}%
-$(1,0,0)^T\times(0,1,0)^T=
-(\pgfmathprintvector\pgfmathresult)^T$
-\end{codeexample}
-
-
-\begin{codeexample}[width=5.2cm]
-\pgfmathparse{TD("(A)o(B)")}%
-$\vec A\cdot \vec B=
-\pgfmathprintnumber\pgfmathresult$
-\end{codeexample}
-
-
-Notice that, as of now, the only purpose of brackets |(...)| is to delimit
-vectors. Further, the addition |+| and subtraction |-| have a \emph{higher}
-precedence than vector products |x| and scalar products |o|. That is,
-|(A)+(B)o(C)| gets interpreted as $(\vec A+\vec B)\cdot\vec C$, and
-|(A)+(B)x(C)| as $(\vec A+\vec B)\times\vec C$.
-
-
-\begin{codeexample}[width=5.2cm]
-\pgfmathparse{TD("(A)+(B)o(C)")}%
-$(\vec A+\vec B)\cdot\vec C=
-\pgfmathprintnumber\pgfmathresult$
-\end{codeexample}
-
-\begin{codeexample}[width=5.2cm]
-\pgfmathparse{TD("(A)+(B)x(C)")}%
-$(\vec A+\vec B)\times\vec C=
-(\pgfmathprintvector\pgfmathresult)$
-\end{codeexample}
-
-Moreover, any expression can only have either one |o| or one |x|, or none of
-these. Expressions with more of these can be accidentally right.
-
-\subsection{Orthonormal projections}
-\label{sec:3DOrthonormalProjections}
-
-This library can be used together with the |tikz-3dplot| package. It also has
-its own means to install orthonormal projections. Orthonormal projections emerge
-from subjecting 3-dimensional vectors to orthogonal transformations and
-projecting them to 2 dimensions. They are not to be confused with the
-perspective projections, which are more realistic and supported by the |tpp|
-library. Orthonormal projections may be thought of a limit of perspective
-projections at large distances, where large means that the distance of the
-observer is much larger than the dimensions of the objects that get depicted.
-
-\begin{key}{/tikz/3d/install view}
- Installs a 3d orthonormal projection.
-\end{key}
-
-The initial projection is such that $x$ is right an $y$ is up, as if we had no
-third direction.
-
-\begin{codeexample}[width=2cm]
-\begin{tikzpicture}[3d/install view]
- \draw[-stealth] (0,0,0) -- (1,0,0)
- node[pos=1.2] {$x$};
- \draw[-stealth] (0,0,0) -- (0,1,0)
- node[pos=1.2] {$y$};
- \draw[-stealth] (0,0,0) -- (0,0,1)
- node[pos=1.2] {$z$};
-\end{tikzpicture}
-\end{codeexample}
-
-The 3d-like picture emerge by rotating the view. The conventions for the
-parametrization of the orthogonal rotations in terms of three rotation angles
-$\phi$, $\psi$ and $\theta$ are
-\[ O(\phi,\psi,\theta)=\left(\begin{array}{ccc}
- s_{\phi}\,c_{\psi}
-& s_{\psi}
-& -s_{\phi}\,c_{\theta}-c_{\phi}\,s_{\psi}\,s_{\theta} \\
- c_{\phi}\,c_{\theta}-s_{\phi}\,s_{\psi}\,s_{\theta}
-& c_{\psi}\,s_ {\theta}
-& s_{\phi}\,s_{\theta}-c_{\phi}\,c_{\theta}\,s_{\psi} \\
- -s_{\phi}\,s_{\psi}\,c_{\theta}-c_{\phi}\,s_{\theta}
-& c_{\psi}\,c_{\theta}
-& c_{\psi}\,c_{\theta}\end{array}\right)\;.
-\]
-Here, $c_\phi:=\cos\phi$, $s_\phi:=\sin\phi$ and so on.
-\begin{key}{/tikz/3d/phi (initially 0)}
- 3d rotation angle.
-\end{key}
-\begin{key}{/tikz/3d/psi (initially 0)}
- 3d rotation angle.
-\end{key}
-\begin{key}{/tikz/3d/theta (initially 0)}
- 3d rotation angle.
-\end{key}
-The rotation angles can be used to define the view. The conventions are chosen
-in such a way that they resemble those of the |tikz-3dplot| package, which gets
-widely used.
-
-\begin{codeexample}[width=2.5cm]
-\begin{tikzpicture}[3d/install view={phi=110,psi=0,theta=70}]
- \draw[-stealth] (0,0,0) -- (1,0,0)
- node[pos=1.2] {$x$};
- \draw[-stealth] (0,0,0) -- (0,1,0)
- node[pos=1.2] {$y$};
- \draw[-stealth] (0,0,0) -- (0,0,1)
- node[pos=1.2] {$z$};
-\end{tikzpicture}
-\end{codeexample}
-
-\begin{codeexample}[width=2.5cm]
-\begin{tikzpicture}[3d/install view={phi=110,psi=0,theta=70}]
- \draw[-stealth] (0,0,0) -- (1,0,0)
- node[pos=1.2] {$x$};
- \draw[-stealth] (0,0,0) -- (0,1,0)
- node[pos=1.2] {$y$};
- \draw[-stealth] (0,0,0) -- (0,0,1)
- node[pos=1.2] {$z$};
-\end{tikzpicture}
-\end{codeexample}
-
-\subsection{Predefined pics}
-
-\begin{key}{/tikz/pics/3d circle through 3 points=\meta{options} (initially empty)}
- Draws a circle through 3 points in 3 dimensions. If the three
- coordinates are close to linearly dependent, the circle will not be
- drawn.
-\end{key}
-\begin{key}{/tikz/3d circle through 3 points/A (initially {(1,0,0)})}
- First coordinate. Can be either symbolic or explicit. Symbolic
- coordinates need to be defined via
- |\path (x,y,z) coordinate (name);|.
-\end{key}
-\begin{key}{/tikz/3d circle through 3 points/B (initially {(0,1,0)})}
- Second coordinate, like above.
-\end{key}
-\begin{key}{/tikz/3d circle through 3 points/C (initially {(0,0,1)})}
- Third coordinate, like above.
-\end{key}
-\begin{key}{/tikz/3d circle through 3 points/center name (initially {M})}
- Name of the center coordinate that will be derived.
-\end{key}
-\begin{key}{/tikz/3d circle through 3 points/auxiliary coordinate prefix (initially {tmp})}
- In \tikzname the coordinates are global. The code for the circle is more
- comprehensible if named coordinates are introduced. Their names will begin with
- this prefix. Changing the prefix will allow users to avoid overwritin
- existing coordinates.
-\end{key}
-
-\begin{codeexample}[width=2.5cm]
-\begin{tikzpicture}[3d/install view={phi=30,psi=0,theta=70}]
- \foreach \X in {A,B,C}
- {\pgfmathsetmacro{\myx}{3*(rnd-1/2)}
- \pgfmathsetmacro{\myy}{3*(rnd-1/2)}
- \pgfmathsetmacro{\myz}{3*(rnd-1/2)}
- \path (\myx,\myy,\myz) coordinate (\X);}
- \path pic{3d circle through 3 points={%
- A={(A)},B={(B)},C={(C)}}};
- \foreach \X in {A,B,C,M}
- {\fill (\X) circle[radius=1.5pt]
- node[above]{$\X$};}
-\end{tikzpicture}
-\end{codeexample}
-
-To do:
-\begin{itemize}
- \item transform to plane given by three non-degenerate coordinates
- \item transform to plane given by normal and one point
- \item maybe layering/visibility
-\end{itemize}
-
-\subsection{3D--like decorations}
-
-\begin{key}{/tikz/decorations/3d complete coil}
- 3d--like coil where the front is thicker than the back.
-\end{key}
-
-\begin{key}{/tikz/decorations/3d coil closed}
- Indicates that the coil is closed.
-\end{key}
-
-
-\begin{codeexample}[width=8cm]
-\begin{tikzpicture}
-\draw[decoration={3d coil color=red,aspect=0.35, segment length=3.1mm,
-amplitude=3mm,3d complete coil},
-decorate] (0,1) -- (0,6);
-\draw[decoration={3d coil color=blue,3d coil opacity=0.9,aspect=0.5,
-segment length={2*pi*3cm/50}, amplitude=5mm,3d complete coil,
-3d coil closed},
-decorate] (5,3.5) circle[radius=3cm];
-\end{tikzpicture}
-\end{codeexample}
-
-
-\end{document}
-
-
-\tdplotsetmaincoords{70}{110}
-\begin{tikzpicture}
- \begin{scope}[local bounding box=tests,tdplot_main_coords]
- % to work with this library, you need to define the cordinate
- % with \path (<x>,<y>,<z>) coordinate (<name>);
- \path (0,0,0) coordinate (O)
- (1,2,3) coordinate (A)
- (2,3,-1) coordinate (B)
- (-1,-2,1) coordinate (C)
- % you can use 3d parse (clumsy)
- [3d parse={0.25*(A)x(B)}] coordinate(D)
- % you can use 3d coordinate to define a new coordinate from existing ones
- [3d coordinate={(E)=0.2*(A)-0.3*(B)+0.6*(C)}]
- [3d coordinate={(H)=0.2*(A)-0.3*(B)+0.6*(C)}];
- \draw (A) -- (B) -- (C) -- (D) -- (E) -- cycle;
- \end{scope}
- %\RawCoord yields the components
- \edef\tempD{\RawCoord(D)}
- \edef\tempE{\RawCoord(E)}
- \edef\tempH{\RawCoord(H)}
- \node[below right,align=left] at (tests.south west)
- {$(D)=\tempD$,\\ $(E)=\tempE$,\\ $(H)=\tempH$};
-\end{tikzpicture}
-
-\noindent% clumsy parser
-$\tdparse{(A)+0.3*(B)>(A)+0.3(B)}=(\pgfmathresult)$
-
-\noindent% parsing inside \pgfmathparse. You need to wrap the argument in "..."
-\pgfmathparse{TD("0.2*(A)-0.3*(B)+0.6*(C)")}%
-$0.2\,\vec A-0.3\,\vec B+0.6\vec C=(\pgfmathresult)$
-
-%one can parse with the same parser vector products
-\noindent\pgfmathparse{TD("0.5*(A)x(B)")}%
-$0.5\,\vec A\times\vec B=(\pgfmathresult)$
-%(note, however, that something like (A)x(B)x(C) does NOT work)
-
-%as well as scalar products
-\noindent\pgfmathparse{TD("(A)+(C)o(B)")}%
-$\left(\begin{array}{@{}c@{}}1\\ 0\\ 0\end{array}\right)$
-%(note, however, that + and - have higher precedence than o)\end{document}
-
-
-\end{document}
-
-\endinput