spath3 (12apr13)

git-svn-id: svn://tug.org/texlive/trunk@29898 c570f23f-e606-0410-a88d-b1316a301751

3 files changed, 3020 insertions, 0 deletions

diff --git a/Master/texmf-dist/tex/latex/spath3/spath3.sty b/Master/texmf-dist/tex/latex/spath3/spath3.sty
new file mode 100644
index 00000000000..a1f4b190fe8
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/spath3/spath3.sty
@@ -0,0 +1,1395 @@
+%%
+%% This is file `spath3.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% spath3.dtx  (with options: `spath3')
+%% ----------------------------------------------------------------
+%% 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
+%% ----------------------------------------------------------------
+%% 
+\NeedsTeXFormat{LaTeX2e}
+\RequirePackage{expl3}
+\RequirePackage{pgf}
+\ProvidesExplPackage {spath3} {2013/04/09} {1.0} {Functions for
+manipulating PGF soft paths}
+\RequirePackage{xparse}
+\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
+\int_new:N \l__spath_tmpa_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_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_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_get:cn {l__spath_#1} {#2}
+}
+\cs_new_nopar:Npn \__spath_get:nnN #1#2#3
+{
+  \prop_get:cnN {l__spath_#1} {#2} #3
+}
+\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: }
+}
+\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}
+  { \__prop_get_true:Nnnn #3 }
+  { \prg_return_false: }
+}
+\cs_generate_variant:Nn \spath_put:nnn {nnV, nnx, nno}
+\cs_generate_variant:Nn \__spath_get:nn {Vn}
+\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:
+  }
+}
+\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
+    }
+  }
+}
+\cs_new_protected_nopar:Npn \spath_get_current_path:n #1
+{
+  \pgfsyssoftpath@getcurrentpath\l__knot_tmpa_tl
+  \spath_clear_new:n {#1}
+  \spath_put:nnV {#1} {path} \l__knot_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}
+}
+\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
+}
+\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}
+\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}
+}
+\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 {nnV}
+\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 }}
+}
+\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}
+}
+\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}
+}
+\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
+}
+\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_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:Nnn \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
+}
+\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
+}
+\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
+}
+\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
+}
+\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
+}
+\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:Nnn \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
+
+}
+\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}
+\cs_new_nopar:Npn \spath_translate:nn #1#2
+{
+  \spath_translate:nnn {#1} #2
+}
+
+\cs_generate_variant:Nn \spath_translate:nn {nV}
+\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
+
+      \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_new_nopar:Npn \spath_reverse:n #1
+{
+  \spath_if_in:nnF {#1} {reverse path} {
+    \cs_use:c {spath_generate_reverse path}
+  }
+  \spath_swap:nnn {#1} {path} {reverse path}
+  \spath_swap:nnn {#1} {initial point} {final point}
+  \spath_swap:nnn {#1} {initial action} {final action}
+}
+\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:nnV {#1} {#2}}
+  {\spath_put:nnV {#1} {#2} \l__spath_tmpb_tl}
+  \tl_if_empty:NTF \l__spath_tmpa_tl
+  {\spath_remove:nnV {#1} {#3}}
+  {\spath_put:nnV {#1} {#3} \l__spath_tmpa_tl}
+}
+\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
+    }
+  }
+
+}
+\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}
+    }
+
+  }
+}
+\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}
+    }
+  }
+}
+\cs_new_nopar:Npn \spath_map_component:Nn #1#2
+{
+  \int_gincr:N \g__prg_map_int
+  \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_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 { __prg_map_ \int_use:N \g__prg_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}
+  }
+}
+\cs_new_nopar:Npn \spath_map_segment_inline:Nn #1#2
+{
+  \int_gincr:N \g__prg_map_int
+  \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 ##2 {#2}
+  \spath_map_segment_function:Nc #1 { __prg_map_ \int_use:N \g__prg_map_int :w }
+}
+\cs_new_nopar:Npn \spath_map_segment_inline:nn #1#2
+{
+  \int_gincr:N \g__prg_map_int
+  \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 ##2 {#2}
+  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
+  \spath_map_segment_function:Nc \l__spath_tmpd_tl { __prg_map_ \int_use:N \g__prg_map_int :w }
+}
+\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
+}
+\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:Nnn \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}
+
+      }
+    }
+    {
+
+      \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}
+\NewDocumentCommand \MakeSPath { m m }
+{
+  \spath_clear_new:n {#1}
+  \spath_put:nno {#1} {path} {#2}
+}
+\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
+  }
+}
+\NewDocumentCommand \CloneSPath { m m }
+{
+  \spath_clone:nn {#1} {#2}
+}
+\NewDocumentCommand \SPathInfo { m m }
+{
+  \spath_get:nn {#1} {#2}
+}
+\NewDocumentCommand \SPathPrepare { m }
+{
+  \spath_generate_all:n {#1}
+}
+\NewDocumentCommand \SPathListPrepare { m }
+{
+  \tl_map_inline:cn {l__spath_list_#1}
+  {
+    \spath_generate_all:n {##1}
+  }
+}
+\NewDocumentCommand \SPathInfoInto { m m m }
+{
+  \tl_set:Nn \l_tmpa_tl #3
+  \spath_get:nnV {#1} {#2} \l_tmpa_tl
+}
+\NewDocumentCommand \SPathShow { m m }
+{
+  \spath_show:n {#1}
+}
+\NewDocumentCommand \SPathTranslate { m m m }
+{
+  \spath_translate:nnn {#1} {#2} {#3}
+}
+\NewDocumentCommand \SPathTranslateInto { m m m m }
+{
+  \spath_clone:nn {#1} {#2}
+  \spath_translate:nnn {#2} {#3} {#4}
+}
+\NewDocumentCommand \SPathScale { m m m }
+{
+  \spath_translate:nnn {#1} {#2} {#3}
+}
+\NewDocumentCommand \SPathScaleInto { m m m m }
+{
+  \spath_clone:nn {#1} {#2}
+  \spath_translate:nnn {#2} {#3} {#4}
+}
+\NewDocumentCommand \SPathWeld { m m }
+{
+  \spath_weld:nn {#1} {#2}
+}
+\NewDocumentCommand \SPathWeldInto { m m m }
+{
+  \spath_clone:nn {#1} {#2}
+  \spath_weld:nn {#2} {#3}
+}
+\tikzset{
+  save~spath/.code={
+    \tikz@addmode{
+      \spath_get_current_path:n {#1}
+    }
+  },
+  restore~spath/.code={
+    \spath_set_current_path:n {#1}
+  },
+}
+\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} {3}}
+    {\tl_item:nn {#2} {4}}
+  }
+  \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}
+%% 
+%% Copyright (C) 2011 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
+%%                                  knot_doc.tex
+%% and the derived files            spath3.ins,
+%%                                  spath3.pdf,
+%%                                  spath3.sty,
+%%                                  tikzlibrarycalligraphy.code.tex
+%%                                  tikzlibraryknots.code.tex
+%%                                  calligraphy_doc.pdf
+%%                                  knots_doc.pdf
+%%                                  README.txt
+%% 
+%%
+%% End of file `spath3.sty'.
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
new file mode 100644
index 00000000000..9e4c80c6672
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
@@ -0,0 +1,749 @@
+%%
+%% This is file `tikzlibrarycalligraphy.code.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% spath3.dtx  (with options: `calligraphy')
+%% ----------------------------------------------------------------
+%% 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
+%% ----------------------------------------------------------------
+%% 
+\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
+\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_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
+\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}
+  },
+}
+\NewDocumentCommand \pen { O{} }
+{
+  \path[define~ pen,#1]
+}
+
+\NewDocumentCommand \definepen { O{} }
+{
+  \tikz \path[define~ pen,#1]
+}
+
+\NewDocumentCommand \calligraphy { O{} }
+{
+  \path[use~ pen,#1]
+}
+\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:
+      \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__spath_tmpa_tl
+      \spath_translate:nV {calligraphy temp path} \l__spath_tmpa_tl
+
+      \__spath_get:nnN {####1} {length} \l__spath_tmpa_tl
+
+      \int_compare:nTF {\l__spath_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__spath_tmpa_tl
+
+        \tikz@options
+        \dim_set:Nn \l__cal_line_width_dim {\pgflinewidth}
+        \cal_maybe_taper:N \l__spath_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}
+
+        \spath_set_current_path:n {calligraphy temp path}
+
+        \tikz@options
+        \pgfsetfillcolor{\pgfkeysvalueof{/tikz/pen~colour}}
+        \pgfusepath{fill}
+      }
+      \group_end:
+    }
+  }
+}
+\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}
+}
+\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}
+\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:Nnn ##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:Nnn ##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
+    }
+  }
+}
+\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}
+  }
+}
+\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
+{
+  \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:Nnn \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:Nnn \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}
+
+}
+\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}
+}
+\tl_set:Nn \l__cal_tmpa_tl {\pgfsyssoftpath@movetotoken{0pt}{0pt}}
+\MakeSPathList{calligraphy pen copperplate}{\l__cal_tmpa_tl}
+\SPathListPrepare{calligraphy pen copperplate}
+\ExplSyntaxOff
+\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}{}
+}
+\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}{}%
+}
+\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}{}%
+}
+\fi
+%% 
+%% Copyright (C) 2011 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
+%%                                  knot_doc.tex
+%% and the derived files            spath3.ins,
+%%                                  spath3.pdf,
+%%                                  spath3.sty,
+%%                                  tikzlibrarycalligraphy.code.tex
+%%                                  tikzlibraryknots.code.tex
+%%                                  calligraphy_doc.pdf
+%%                                  knots_doc.pdf
+%%                                  README.txt
+%% 
+%%
+%% End of file `tikzlibrarycalligraphy.code.tex'.
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
new file mode 100644
index 00000000000..2cc0806f588
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
@@ -0,0 +1,876 @@
+%%
+%% This is file `tikzlibraryknots.code.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% spath3.dtx  (with options: `knots')
+%% ----------------------------------------------------------------
+%% 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
+%% ----------------------------------------------------------------
+%% 
+%%
+\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
+
+\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_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_set_true:N \l__knot_ignore_ends_bool
+\tikzset{
+  knot/.code={
+    \tl_if_eq:nnTF {#1} {none}
+    {
+      \tikz@addmode{\tikz@mode@doublefalse}
+    }
+    {
+      \tikz@addmode{\tikz@mode@doubletrue}
+      \tl_if_empty:nTF {#1}
+      {
+        \pgfsetinnerstrokecolor{\tikz@strokecolor}
+      }
+      {
+        \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},
+  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_radius_dim {#1}
+  },
+  clip~ radius=10pt,
+  end~ tolerance/.code={
+    \dim_set:Nn \l__knot_tolerance_dim {#1}
+  },
+  end~ tolerance=14pt,
+  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}
+  },
+  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
+  },
+}
+\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}
+\NewDocumentCommand \flipcrossings {m}
+{
+  \tikzset{knot~ diagram/flip~ crossing/.list={#1}}%
+}
+\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]
+}
+\NewDocumentEnvironment{knot} { O{} }
+{
+  \knot_initialise:n {#1}
+}
+{
+  \knot_render:
+}
+\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
+}
+\cs_new_protected_nopar:Npn \knot_render:
+{
+  \pgfscope
+  \pgftransformreset
+  \int_step_function:nnnN {1} {1} {\l__knot_strands_int}  \knot_draw_strand:n
+  \bool_if:NF \l__knot_super_draft_bool
+  {
+    \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_draw_labels:n
+    \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}
+    }
+    \int_gzero:N \l__knot_intersections_int
+    \bool_if:NTF \l__knot_draft_bool
+    {
+      \tl_set:Nn \l__knot_node_tl
+      {\node[coordinate,pin={[knot~ diagram/draft/crossing~ label]{\int_use:N \l__knot_intersections_int}}]}
+    }
+    {
+      \tl_set:Nn \l__knot_node_tl {\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
+      {
+        \knot_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
+      }
+    }
+    \tl_use:N \l__knot_redraws_tl
+  }
+  \endpgfscope
+}
+\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_tikz_path:Vn \l_tmpa_tl {knot strand #1}
+  \group_end:
+  \endpgfscope
+}
+\cs_generate_variant:Nn \tl_put_right:Nn {Nv}
+\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
+  }
+}
+\cs_new_protected_nopar:Npn \knot_split_self_intersects:NN #1#2
+{
+  \tl_case:Nnn #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
+  }
+}
+\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
+
+  \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
+  }
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \knot_do_intersection:n #1
+{
+  \pgfpointintersectionsolution{#1}
+  \dim_set:Nn \l__knot_tmpa_dim {\pgf@x}
+  \dim_set:Nn \l__knot_tmpb_dim {\pgf@y}
+  \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
+    {
+      \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
+      }
+    }
+  }
+  \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
+    }
+  }
+  \bool_if:NF \l__knot_skip_bool
+  {
+
+    \int_gincr:N \l__knot_intersections_int
+    \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
+    }
+    \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
+      }
+      \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
+        {
+          \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}}
+          \bool_if:NT \l__knot_splits_bool
+          {
+            \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
+
+            }
+          }
+        }
+        \bool_if:NT \l__knot_append_next_bool
+        {
+          \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
+          {
+            \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}
+      }
+    }
+    \group_begin:
+    \tikzset{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:
+    \tl_use:N \l__knot_node_tl (\l__knot_name_tl \c_space_tl \int_use:N \l__knot_intersections_int) at (\l__knot_tmpa_dim, \l__knot_tmpb_dim) {};
+  }
+}
+
+\cs_generate_variant:Nn \knot_intersections:nn {VV}
+\prg_new_conditional:Npnn \knot_test_endpoint:N #1 {p,T,F,TF}
+{
+  \dim_compare:nTF
+  {
+    \dim_abs:n {\pgf@x - \tl_item:Nn #1 {1}}
+    +
+    \dim_abs:n {\pgf@y - \tl_item:Nn #1 {2}}
+    <
+    \l__knot_tolerance_dim
+  }
+  {
+    \prg_return_true:
+  }
+  {
+    \prg_return_false:
+  }
+}
+\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}
+\cs_new_nopar:Npn \knot_draw_crossing:nnn #1#2#3
+{
+  \group_begin:
+  \pgfscope
+  \clip (#2, #3) circle[radius=\l__knot_clip_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
+  \clip (#2, #3) circle[radius=1.1\l__knot_clip_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_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
+}
+\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}
+}
+\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
+  \spath_map_segment_function:nN {knot strand #1} \knot_save_filament:NN
+}
+\cs_new_protected_nopar:Npn \knot_save_filament:NN #1#2
+{
+  \tl_case:Nnn #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_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_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_close_tl
+    {
+      \int_gincr:N \l__knot_filaments_int
+      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
+      \tl_set_eq:NN \l_tmpa_tl #2
+      \tl_set:Nx \l_tmpa_tl {\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_set:Nx \l_tmpa_tl {\tl_item:Nn #2 {5}\tl_item:Nn #2 {6}}
+      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} \l_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}
+    }
+  }
+  {
+  }
+}
+\NewDocumentCommand \redraw { m m }
+{
+  \tikz@scan@one@point\pgfutil@firstofone #2 \relax
+  \tl_put_right:Nn \l__knot_redraws_tl {\knot_draw_crossing:nnn}
+  \tl_put_right:Nx \l__knot_redraws_tl {
+    {strand #1} {\dim_use:N \pgf@x} {\dim_use:N \pgf@y}
+  }
+}
+\ExplSyntaxOff
+\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%
+  }%
+}
+\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%
+  }
+}
+\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{
+    \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}}
+ }
+}
+\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{
+    \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}}
+ }
+}
+\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{
+    \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}}
+ }
+}
+\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{
+    \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}}
+ }
+}
+%% 
+%% Copyright (C) 2011 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
+%%                                  knot_doc.tex
+%% and the derived files            spath3.ins,
+%%                                  spath3.pdf,
+%%                                  spath3.sty,
+%%                                  tikzlibrarycalligraphy.code.tex
+%%                                  tikzlibraryknots.code.tex
+%%                                  calligraphy_doc.pdf
+%%                                  knots_doc.pdf
+%%                                  README.txt
+%% 
+%%
+%% End of file `tikzlibraryknots.code.tex'.