spath3 (23jan21)

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

4 files changed, 3606 insertions, 1452 deletions

diff --git a/Master/texmf-dist/tex/latex/spath3/spath3.sty b/Master/texmf-dist/tex/latex/spath3/spath3.sty
index 43fd64cf5e2..155441947b0 100644
--- a/Master/texmf-dist/tex/latex/spath3/spath3.sty
+++ b/Master/texmf-dist/tex/latex/spath3/spath3.sty
@@ -4,10 +4,10 @@
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `spath3')
+%% spath3_code.dtx  (with options: `spath3')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
@@ -15,335 +15,610 @@
 \NeedsTeXFormat{LaTeX2e}
 \RequirePackage{expl3}
 \RequirePackage{pgf}
-\ProvidesExplPackage {spath3} {2019/02/12} {1.2} {Functions for
+\ProvidesExplPackage {spath3} {2021/01/19} {2.0} {Functions for
 manipulating PGF soft paths}
 \RequirePackage{xparse}
+\cs_new_protected:Nn \__spath_tl_put_right_braced:Nn
+{
+  \tl_put_right:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_put_right_braced:Nn { NV, cV, cv, Nx, cx }
+
+\cs_new_protected:Nn \__spath_tl_gput_right_braced:Nn
+{
+  \tl_gput_right:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_gput_right_braced:Nn { NV, cV, cv, Nx, cx }
+\cs_new_protected:Nn \__spath_tl_put_left_braced:Nn
+{
+  \tl_put_left:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_put_left_braced:Nn { NV, cV, cv, Nx, cx }
+
+\cs_new_protected:Nn \__spath_tl_gput_left_braced:Nn
+{
+  \tl_gput_left:Nn #1 { { #2 } }
+}
+\cs_generate_variant:Nn \__spath_tl_gput_left_braced:Nn { NV, cV, cv, Nx, cx }
 \tl_new:N \l__spath_tmpa_tl
 \tl_new:N \l__spath_tmpb_tl
 \tl_new:N \l__spath_tmpc_tl
 \tl_new:N \l__spath_tmpd_tl
-\tl_new:N \l__spath_smuggle_tl
+\tl_new:N \l__spath_tmpe_tl
+
+\seq_new:N \l__spath_tmpa_seq
+\seq_new:N \l__spath_tmpb_seq
+
+\tl_new:N \g__spath_output_tl
+\int_new:N \g__spath_output_int
+\seq_new:N \g__spath_output_seq
+
 \dim_new:N \l__spath_tmpa_dim
 \dim_new:N \l__spath_tmpb_dim
+\dim_new:N \l__spath_move_x_dim
+\dim_new:N \l__spath_move_y_dim
 \fp_new:N \l__spath_tmpa_fp
 \fp_new:N \l__spath_tmpb_fp
 \int_new:N \l__spath_tmpa_int
-\int_new:N \g__spath_map_int
-\tl_new:N \g__spath_moveto_tl
-\tl_new:N \g__spath_lineto_tl
-\tl_new:N \g__spath_curveto_tl
-\tl_new:N \g__spath_curvetoa_tl
-\tl_new:N \g__spath_curvetob_tl
-\tl_new:N \g__spath_closepath_tl
-\tl_set:Nn \g__spath_moveto_tl {\pgfsyssoftpath@movetotoken}
-\tl_set:Nn \g__spath_lineto_tl {\pgfsyssoftpath@linetotoken}
-\tl_set:Nn \g__spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
-\tl_set:Nn \g__spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
-\tl_set:Nn \g__spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
-\tl_set:Nn \g__spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
-\tl_new:N \g__spath_attributes
-\tl_new:N \g__spath_moveable_attributes
-\tl_new:N \g__spath_path_attributes
-\tl_set:Nn \g__spath_attributes {
-  {path}
-  {reverse path}
-  {length}
-  {real length}
-  {number of components}
-  {initial point}
-  {final point}
-  {initial action}
-  {final action}
-  {min bb}
-  {max bb}
-}
-\tl_set:Nn \g__spath_moveable_attributes {
-  {initial point}
-  {final point}
-  {min bb}
-  {max bb}
-}
-\tl_set:Nn \g__spath_path_attributes {
-  {path}
-  {reverse path}
-}
-\cs_new_nopar:Npn \spath_new:n #1
-{
-  \prop_new:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_clear:n #1
-{
-  \prop_gclear:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_clear_new:n #1
-{
-  \prop_gclear_new:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_show:n #1
-{
-  \prop_show:c {l__spath_#1}
-}
-\cs_new_nopar:Npn \spath_put:nnn #1#2#3
-{
-  \prop_gput:cnn {l__spath_#1} {#2} {#3}
-}
-\cs_new_nopar:Npn \spath_remove:nn #1#2
-{
-  \prop_gremove:cn {l__spath_#1} {#2}
-}
-\cs_new_nopar:Npn \__spath_get:nn #1#2
-{
-  \prop_item:cn {l__spath_#1} {#2}
-}
-\cs_new_nopar:Npn \__spath_get:nnN #1#2#3
+
+\bool_new:N \g__spath_output_bool
+\bool_new:N \l__spath_closed_bool
+\tl_const:Nn \c_spath_moveto_tl {\pgfsyssoftpath@movetotoken}
+\tl_const:Nn \c_spath_lineto_tl {\pgfsyssoftpath@linetotoken}
+\tl_const:Nn \c_spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
+\tl_const:Nn \c_spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
+\tl_const:Nn \c_spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
+\tl_const:Nn \c_spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
+\int_new:N \g__spath_anon_int
+\int_gzero:N \g__spath_anon_int
+\tl_new:N \l__spath_itera_tl
+\tl_new:N \l__spath_iterb_tl
+\tl_new:N \l__spath_iterc_tl
+\tl_new:N \l__spath_iterd_tl
+\tl_new:N \l__spath_iterp_tl
+\dim_new:N \l__spath_itera_dim
+\dim_new:N \l__spath_iterb_dim
+\seq_new:N \l__spath_iter_seq
+\msg_new:nnn { spath3 } { unknown path construction } { The~ path~ construction~ element~ #1~ is~ not~ currently~ supported.}
+\cs_new_protected_nopar:Npn \__spath_segments_to_seq:n #1
 {
-  \prop_get:cnN {l__spath_#1} {#2} #3
+  \group_begin:
+  \tl_set:Nn \l__spath_itera_tl {#1}
+  \tl_clear:N \l__spath_iterb_tl
+  \seq_clear:N \l__spath_iter_seq
+  \dim_zero:N \l__spath_itera_dim
+  \dim_zero:N \l__spath_iterb_dim
+
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_itera_tl
+  }
+  {
+    \tl_set:Nx \l__spath_iterc_tl {\tl_head:N \l__spath_itera_tl}
+    \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+    \tl_case:NnF \l__spath_iterc_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_set:Nx \l__spath_iterd_tl {\tl_head:N \l__spath_itera_tl}
+        \tl_if_eq:NNF \l__spath_iterd_tl \c_spath_moveto_tl
+        {
+          \tl_clear:N \l__spath_iterb_tl
+        }
+
+      }
+
+      \c_spath_lineto_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl
+        {
+          {\dim_use:N \l__spath_itera_dim}
+          {\dim_use:N \l__spath_iterb_dim}
+        }
+        \tl_put_right:NV \l__spath_iterb_tl \c_spath_lineto_tl
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      }
+
+      \c_spath_curvetoa_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl
+        {
+          {\dim_use:N \l__spath_itera_dim}
+          {\dim_use:N \l__spath_iterb_dim}
+        }
+        \tl_put_right:NV \l__spath_iterb_tl \c_spath_curvetoa_tl
+
+        \prg_replicate:nn {2} {
+          \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+          \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+          \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N               \l__spath_itera_tl}}
+          \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+          \tl_put_right:Nx \l__spath_iterb_tl {\tl_head:N             \l__spath_itera_tl}
+          \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+        }
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      }
+
+      \c_spath_closepath_tl
+      {
+        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_iterb_tl
+        {
+          {\dim_use:N \l__spath_itera_dim}
+          {\dim_use:N \l__spath_iterb_dim}
+        }
+        \tl_put_right:NV \l__spath_iterb_tl \c_spath_lineto_tl
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+        \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+        \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+        \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      }
+
+    }
+    {
+
+      \tl_set_eq:NN \l__spath_iterb_tl \l__spath_iterc_tl
+      \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+      \dim_set:Nn \l__spath_itera_dim {\tl_head:N \l__spath_itera_tl}
+      \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+      \tl_put_right:Nx \l__spath_iterb_tl {{\tl_head:N \l__spath_itera_tl}}
+      \dim_set:Nn \l__spath_iterb_dim {\tl_head:N \l__spath_itera_tl}
+      \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+
+    }
+
+    \tl_if_empty:NF \l__spath_iterb_tl
+    {
+      \seq_put_right:NV \l__spath_iter_seq \l__spath_iterb_tl
+    }
+    \tl_clear:N \l__spath_iterb_tl
+  }
+
+  \seq_gclear:N \g__spath_output_seq
+  \seq_gset_eq:NN \g__spath_output_seq \l__spath_iter_seq
+  \group_end:
 }
-\prg_new_conditional:Npnn \spath_if_in:nn #1#2 {p, T, F, TF}
+\cs_new_protected_nopar:Npn \spath_segments_to_seq:Nn #1#2
 {
-  \prop_if_in:cnTF {l__spath_#1} {#2}
-  { \prg_return_true: }
-  { \prg_return_false: }
+  \__spath_segments_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_set_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \__prop_split:NnTF {cnTF}
-\prg_new_protected_conditional:Npnn \__spath_get:nnN #1#2#3 {T, F, TF}
+\cs_generate_variant:Nn \spath_segments_to_seq:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \spath_segments_gto_seq:Nn #1#2
 {
-  \__prop_split:cnTF {l__spath_#1} {#2}
-  {
-    \tl_set:Nn #3 {##2}
-    \prg_return_true:
-  }
-  { \prg_return_false: }
+  \__spath_segments_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_gset_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \spath_put:nnn {nnV, nnx, nno}
-\cs_generate_variant:Nn \__spath_get:nn {Vn}
-\cs_generate_variant:Nn \__spath_get:nnN {VnN}
-\prg_new_conditional:Npnn \spath_if_exist:n #1 {p,T,F,TF}
+\cs_generate_variant:Nn \spath_segments_gto_seq:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \__spath_components_to_seq:n #1
 {
-  \prop_if_exist:cTF {l__spath_#1}
-  {
-    \prg_return_true:
-  }
-  {
-    \prg_return_false:
+  \group_begin:
+  \tl_set:Nn \l__spath_itera_tl {#1}
+  \seq_clear:N \l__spath_iter_seq
+  \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+  \tl_put_right:NV \l__spath_itera_tl \c_spath_moveto_tl
+  \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
+  \bool_do_until:nn {
+    \tl_if_empty_p:N \l__spath_itera_tl
   }
-}
-\cs_new_nopar:Npn \spath_clone:nn #1 #2
-{
-  \spath_clear_new:n {#2}
-  \tl_map_inline:Nn \g__spath_attributes
   {
-    \spath_if_in:nnT {#1} {##1}
+    \tl_set:Nx \l__spath_iterc_tl {\tl_head:N \l__spath_itera_tl}
+    \tl_if_eq:NNT \l__spath_iterc_tl \c_spath_moveto_tl
+    {
+      \seq_put_right:NV \l__spath_iter_seq \l__spath_iterb_tl
+      \tl_clear:N \l__spath_iterb_tl
+    }
+    \tl_if_single:NTF \l__spath_iterc_tl
+    {
+      \tl_put_right:NV \l__spath_iterb_tl \l__spath_iterc_tl
+    }
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \spath_put:nnV {#2} {##1} \l__spath_tmpa_tl
+      \tl_put_right:Nx \l__spath_iterb_tl {{\l__spath_iterc_tl}}
     }
+    \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
   }
-}
-\cs_new_protected_nopar:Npn \spath_get_current_path:n #1
-{
-  \pgfsyssoftpath@getcurrentpath\l__spath_tmpa_tl
-  \spath_clear_new:n {#1}
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-}
-\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
-{
-  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
 
-  \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \pgfsyssoftpath@setcurrentpath\l__spath_tmpa_tl
-  \pgfsyssoftpath@flushcurrentpath
-}
-\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
-{
-  \spath_set_current_path:n {#1}
-  \pgfusepath{#2}
+  \seq_gclear:N \g__spath_output_seq
+  \seq_gset_eq:NN \g__spath_output_seq \l__spath_iter_seq
+  \group_end:
 }
-\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
+\cs_new_protected_nopar:Npn \spath_components_to_seq:Nn #1#2
 {
-  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
-
-  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
+  \__spath_components_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_set_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
+\cs_generate_variant:Nn \spath_components_to_seq:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_gto_seq:Nn #1#2
 {
-  \path[#1] \pgfextra{
-    \spath_get:nnN {#2} {path} \l__spath_tmpa_tl
-    \pgfsyssoftpath@setcurrentpath \l__spath_tmpa_tl
-  };
+  \__spath_components_to_seq:n {#2}
+  \seq_clear_new:N #1
+  \seq_gset_eq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \spath_tikz_path:nn {Vn}
-\cs_new_nopar:Npn \spath_get:nn #1#2
+\cs_generate_variant:Nn \spath_components_gto_seq:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_to_clist:Nn #1#2
 {
-  \spath_if_in:nnF {#1} {#2}
-  {
-    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
-  }
-  \__spath_get:nn {#1} {#2}
+  \__spath_components_to_seq:n {#2}
+  \clist_clear_new:N #1
+  \clist_set_from_seq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_new_nopar:Npn \spath_get:nnN #1#2#3
+\cs_generate_variant:Nn \spath_components_to_clist:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_components_gto_clist:Nn #1#2
 {
-  \spath_if_in:nnF {#1} {#2}
-  {
-    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
-  }
-  \__spath_get:nnN {#1} {#2} #3
+  \__spath_components_to_seq:n {#2}
+  \clist_clear_new:N #1
+  \clist_gset_from_seq:NN #1 \g__spath_output_seq
+  \seq_gclear:N \g__spath_output_seq
 }
-\cs_generate_variant:Nn \spath_get:nnN {VnN}
-\cs_new_nopar:Npn \spath_generate_length:n #1
+\cs_generate_variant:Nn \spath_components_gto_clist:Nn {NV, cn, cV, cv, Nv}
+\cs_new_protected_nopar:Npn \spath_length:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \spath_put:nnx {#1} {length} {\int_eval:n {\tl_count:N \l__spath_tmpa_tl /3 }}
+  \int_eval:n {\tl_count:n {#1} / 3}
 }
-\cs_new_nopar:Npn \spath_generate_reallength:n #1
+\cs_generate_variant:Nn \spath_length:n {V}
+\cs_new_protected_nopar:Npn \__spath_reallength:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
   \int_set:Nn \l__spath_tmpa_int {0}
-  \tl_map_inline:Nn \l__spath_tmpa_tl {
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@linetotoken}
+  \tl_map_inline:nn {#1} {
+    \tl_set:Nn \l__spath_tmpc_tl {##1}
+    \tl_case:NnT \l__spath_tmpc_tl
     {
-      \int_incr:N \l__spath_tmpa_int
+      \c_spath_lineto_tl {}
+      \c_spath_curveto_tl {}
+      \c_spath_closepath_tl {}
     }
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@curvetotoken}
     {
       \int_incr:N \l__spath_tmpa_int
     }
   }
-  \spath_put:nnx {#1} {real length} {\int_use:N \l__spath_tmpa_int}
+  \int_gzero:N \g__spath_output_int
+  \int_gset_eq:NN \g__spath_output_int \l__spath_tmpa_int
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_reallength:Nn #1#2
+{
+  \__spath_reallength:n {#2}
+  \int_set_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
+}
+\cs_generate_variant:Nn \spath_reallength:Nn {NV, cn, cV, Nv, cv}
+\cs_new_protected_nopar:Npn \spath_greallength:Nn #1#2
+{
+  \__spath_reallength:n {#2}
+  \int_gset_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
 }
-\cs_new_nopar:Npn \spath_generate_numberofcomponents:n #1
+\cs_generate_variant:Nn \spath_greallength:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \__spath_numberofcomponents:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
   \int_set:Nn \l__spath_tmpa_int {0}
-  \tl_map_inline:Nn \l__spath_tmpa_tl {
-    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@movetotoken}
+  \tl_map_inline:nn {#1} {
+    \tl_set:Nn \l__spath_tmpa_tl {##1}
+    \tl_case:Nn \l__spath_tmpa_tl
     {
-      \int_incr:N \l__spath_tmpa_int
+      \c_spath_moveto_tl
+      {
+        \int_incr:N \l__spath_tmpa_int
+      }
     }
   }
-  \spath_put:nnx {#1} {number of components} {\int_use:N \l__spath_tmpa_int}
+  \int_gzero:N \g__spath_output_int
+  \int_gset_eq:NN \g__spath_output_int \l__spath_tmpa_int
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_generate_initialpoint:n #1
+\cs_new_protected_nopar:Npn \spath_numberofcomponents:Nn #1#2
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-  \spath_put:nnV {#1} {initial point} \l__spath_tmpb_tl
+  \__spath_numberofcomponents:n {#2}
+  \int_set_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
+}
+\cs_generate_variant:Nn \spath_numberofcomponents:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gnumberofcomponents:Nn #1#2
+{
+  \__spath_numberofcomponents:n {#2}
+  \int_gset_eq:NN #1 \g__spath_output_int
+  \int_gzero:N \g__spath_output_int
 }
-\cs_new_nopar:Npn \spath_generate_finalpoint:n #1
+\cs_generate_variant:Nn \spath_gnumberofcomponents:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \__spath_initialpoint:n #1
 {
+  \group_begin:
   \tl_clear:N \l__spath_tmpb_tl
-  \spath_if_in:nnTF {#1} {reverse path}
+  \tl_set:Nx \l__spath_tmpb_tl
   {
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+    { \tl_item:nn {#1} {2} }
+    { \tl_item:nn {#1} {3} }
   }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_initialpoint:Nn #1#2
+{
+  \__spath_initialpoint:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_initialpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_ginitialpoint:Nn #1#2
+{
+  \__spath_initialpoint:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_ginitialpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \__spath_finalpoint:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_reverse:N \l__spath_tmpa_tl
+  \tl_clear:N \l__spath_tmpb_tl
+  \tl_set:Nx \l__spath_tmpb_tl
   {
-    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \tl_reverse:N \l__spath_tmpa_tl
-    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+    { \tl_item:Nn \l__spath_tmpa_tl {2} }
+    { \tl_item:Nn \l__spath_tmpa_tl {1} }
   }
-  \spath_put:nnV {#1} {final point} \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalpoint:Nn #1#2
+{
+  \__spath_finalpoint:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_finalpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_gfinalpoint:Nn #1#2
+{
+  \__spath_finalpoint:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_generate_variant:Nn \spath_generate_finalpoint:n {V}
-\cs_new_nopar:Npn \spath_generate_reversepath:n #1
+\cs_generate_variant:Nn \spath_gfinalpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \__spath_reverse:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+
   \tl_clear:N \l__spath_tmpb_tl
+  \tl_clear:N \l__spath_tmpd_tl
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_left:Nx \l__spath_tmpb_tl
+
+  \tl_put_left:Nx \l__spath_tmpd_tl
   {
     {\dim_use:N \l__spath_tmpa_dim}
     {\dim_use:N \l__spath_tmpb_dim}
   }
+
+  \bool_set_false:N \l__spath_closed_bool
+
   \bool_until_do:nn {
     \tl_if_empty_p:N \l__spath_tmpa_tl
   }
   {
     \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nn \l__spath_tmpd_tl {}
-    \tl_case:NnF \l__spath_tmpc_tl
+
+    \tl_case:NnTF \l__spath_tmpc_tl
     {
-      \g__spath_moveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl }
-      \g__spath_lineto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl }
-      \g__spath_curveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl }
-      \g__spath_curvetoa_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl }
-      \g__spath_curvetob_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl }
+      \c_spath_moveto_tl {
+
+        \bool_if:NT \l__spath_closed_bool
+        {
+          \tl_put_right:NV \l__spath_tmpd_tl \c_spath_closepath_tl
+          \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpd_tl}
+          \tl_put_right:Nx \l__spath_tmpd_tl
+          {
+            { \tl_head:N \l__spath_tmpd_tl }
+            { \tl_head:N \l__spath_tmpe_tl }
+          }
+        }
+        \bool_set_false:N \l__spath_closed_bool
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_moveto_tl
+        \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
+        \tl_clear:N \l__spath_tmpd_tl
+      }
+      \c_spath_lineto_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_lineto_tl
+      }
+      \c_spath_curveto_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_curvetoa_tl
+      }
+      \c_spath_curvetoa_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_curveto_tl
+      }
+      \c_spath_curvetob_tl {
+        \tl_put_left:NV \l__spath_tmpd_tl \c_spath_curvetob_tl
+      }
     }
     {
-      \tl_show:N \l__spath_tmpc_tl
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+      \tl_put_left:Nx \l__spath_tmpd_tl
+      {
+        {\dim_use:N \l__spath_tmpa_dim}
+        {\dim_use:N \l__spath_tmpb_dim}
+      }
+
     }
-    \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_put_left:Nx \l__spath_tmpb_tl
     {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
+      \tl_if_eq:NNTF \l__spath_tmpc_tl \c_spath_closepath_tl
+      {
+        \bool_set_true:N \l__spath_closed_bool
+      }
+      {
+        \msg_warning:nnx { spath3 } { unknown path construction } {\l__spath_tmpc_tl }
+      }
+
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
     }
   }
-  \tl_put_left:NV \l__spath_tmpb_tl \g__spath_moveto_tl
-  \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
+
+  \bool_if:NT \l__spath_closed_bool
+  {
+    \tl_put_right:NV \l__spath_tmpd_tl \c_spath_closepath_tl
+    \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpd_tl}
+    \tl_put_right:Nx \l__spath_tmpd_tl
+    {
+      { \tl_head:N \l__spath_tmpd_tl }
+      { \tl_head:N \l__spath_tmpe_tl }
+    }
+  }
+
+  \bool_set_false:N \l__spath_closed_bool
+  \tl_put_left:NV \l__spath_tmpd_tl \c_spath_moveto_tl
+  \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
+
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_generate_initialaction:n #1
+\cs_new_protected_nopar:Npn \spath_reverse:Nn #1#2
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_if_empty:NF \l__spath_tmpa_tl {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-  }
-  \spath_put:nnV {#1} {initial action} \l__spath_tmpb_tl
+  \__spath_reverse:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_generate_finalaction:n #1
+\cs_generate_variant:Nn \spath_reverse:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_reverse:N #1
 {
-  \tl_clear:N \l__spath_tmpb_tl
-  \spath_if_in:nnTF {#1} {reverse path}
+  \spath_reverse:NV #1#1
+}
+\cs_generate_variant:Nn \spath_reverse:N {c}
+\cs_new_protected_nopar:Npn \spath_greverse:Nn #1#2
+{
+  \__spath_reverse:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_greverse:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \spath_greverse:N #1
+{
+  \spath_greverse:NV #1#1
+}
+\cs_generate_variant:Nn \spath_greverse:N {c}
+\cs_new_protected_nopar:Npn \__spath_initialaction:n #1
+{
+  \group_begin:
+  \tl_clear:N \l__spath_tmpa_tl
+  \int_compare:nT
   {
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_count:n {#1} > 3
   }
   {
-    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \tl_reverse:N \l__spath_tmpa_tl
+    \tl_set:Nx \l__spath_tmpa_tl
+    {
+      \tl_item:Nn {#1} {4}
+    }
   }
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_if_empty:NF \l__spath_tmpa_tl {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_initialaction:Nn #1#2
+{
+  \__spath_initialaction:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_initialaction:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_ginitialaction:Nn #1#2
+{
+  \__spath_initialaction:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_ginitialaction:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_finalaction:n #1
+{
+  \group_begin:
+  \tl_clear:N \l__spath_tmpb_tl
+  \int_compare:nT
+  {
+    \tl_count:n {#1} > 3
   }
-  \tl_if_eq:NNT \l__spath_tmpa_tl \g__spath_curvetoa_tl
   {
-    \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_curveto_tl
+    \tl_set:Nn \l__spath_tmpa_tl {#1}
+    \tl_reverse:N \l__spath_tmpa_tl
+    \tl_set:Nx \l__spath_tmpb_tl
+    {
+      \tl_item:Nn \l__spath_tmpa_tl {3}
+    }
+    \tl_if_eq:NNT \l__spath_tmpb_tl \c_spath_curvetoa_tl
+    {
+      \tl_set_eq:NN \l__spath_tmpb_tl \c_spath_curveto_tl
+    }
   }
-  \spath_put:nnV {#1} {final action} \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalaction:Nn #1#2
+{
+  \__spath_finalaction:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_generate_minbb:n #1
+\cs_generate_variant:Nn \spath_finalaction:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gfinalaction:Nn #1#2
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \__spath_finalaction:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gfinalaction:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_minbb:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
@@ -365,11 +640,27 @@ manipulating PGF soft paths}
     {\dim_use:N \l__spath_tmpa_dim}
     {\dim_use:N \l__spath_tmpb_dim}
   }
-  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_minbb:Nn #1#2
+{
+  \__spath_minbb:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_minbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gminbb:Nn #1#2
+{
+  \__spath_minbb:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_generate_maxbb:n #1
+\cs_generate_variant:Nn \spath_gminbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \__spath_maxbb:n #1
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
   \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
@@ -391,1101 +682,2440 @@ manipulating PGF soft paths}
     {\dim_use:N \l__spath_tmpa_dim}
     {\dim_use:N \l__spath_tmpb_dim}
   }
-  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
-}
-\tl_new:N \l__spath_rp_tl
-\int_new:N \l__spath_l_int
-\int_new:N \l__spath_rl_int
-\int_new:N \l__spath_nc_int
-\tl_new:N \l__spath_ip_tl
-\tl_new:N \l__spath_fp_tl
-\tl_new:N \l__spath_ia_tl
-\tl_new:N \l__spath_fa_tl
-\dim_new:N \l__spath_minx_dim
-\dim_new:N \l__spath_miny_dim
-\dim_new:N \l__spath_maxx_dim
-\dim_new:N \l__spath_maxy_dim
-
-\cs_new_nopar:Npn \spath_generate_all:n #1
-{
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-
-  \tl_clear:N \l__spath_rp_tl
-  \int_set:Nn \l__spath_l_int {1}
-  \int_zero:N \l__spath_rl_int
-  \int_set:Nn \l__spath_nc_int {1}
-  \tl_clear:N \l__spath_ip_tl
-  \tl_clear:N \l__spath_fp_tl
-  \tl_clear:N \l__spath_ia_tl
-  \tl_clear:N \l__spath_fa_tl
-  \dim_zero:N \l__spath_minx_dim
-  \dim_zero:N \l__spath_miny_dim
-  \dim_zero:N \l__spath_maxx_dim
-  \dim_zero:N \l__spath_maxy_dim
-
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-  \tl_clear:N \l__spath_ip_tl
-  \tl_put_right:Nx \l__spath_ip_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_maxbb:Nn #1#2
+{
+  \__spath_maxbb:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_maxbb:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gmaxbb:Nn #1#2
+{
+  \__spath_maxbb:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gmaxbb:Nn {NV, cn, cV}
+\int_set:Nn \l__spath_tmpa_int {\char_value_catcode:n {`@}}
+\char_set_catcode_letter:N @
+\cs_new_protected_nopar:Npn \spath_save_to_aux:Nn #1#2 {
+  \tl_if_empty:nF {#2}
   {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
+    \tl_clear:N \l__spath_tmpa_tl
+    \tl_put_right:Nn \l__spath_tmpa_tl {
+      \ExplSyntaxOn
+      \tl_clear:N #1
+      \tl_set:Nn #1 {#2}
+      \ExplSyntaxOff
+    }
+    \protected@write\@auxout{}{
+      \tl_to_str:N \l__spath_tmpa_tl
+    }
   }
-
-  \dim_set_eq:NN \l__spath_minx_dim \l__spath_tmpa_dim
-  \dim_set_eq:NN \l__spath_miny_dim \l__spath_tmpb_dim
-  \dim_set_eq:NN \l__spath_maxx_dim \l__spath_tmpa_dim
-  \dim_set_eq:NN \l__spath_maxy_dim \l__spath_tmpb_dim
-
-  \tl_put_left:Nx \l__spath_rp_tl
+}
+\char_set_catcode:nn {`@} {\l__spath_tmpa_int}
+\cs_generate_variant:Nn \spath_save_to_aux:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_save_to_aux:N #1
+{
+  \tl_if_exist:NT #1
   {
-    {\dim_use:N \l__spath_tmpa_dim}
-    {\dim_use:N \l__spath_tmpb_dim}
+    \spath_save_to_aux:NV #1#1
   }
-
-  \tl_set:Nx \l__spath_ia_tl {\tl_head:N \l__spath_tmpa_tl}
-
+}
+\cs_new_protected_nopar:Npn \__spath_translate:nnn #1#2#3
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
   \bool_until_do:nn {
     \tl_if_empty_p:N \l__spath_tmpa_tl
   }
   {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nn \l__spath_tmpd_tl {}
-    \tl_set_eq:NN \l__spath_fa_tl \l__spath_tmpc_tl
-    \int_incr:N \l__spath_l_int
-
-    \tl_case:NnF \l__spath_tmpc_tl
-    {
-      \g__spath_moveto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl
-        \int_incr:N \l__spath_nc_int
-      }
-      \g__spath_lineto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl
-        \int_incr:N \l__spath_rl_int
-      }
-      \g__spath_curveto_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl
-        \int_incr:N \l__spath_rl_int
-      }
-      \g__spath_curvetoa_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl
-      }
-      \g__spath_curvetob_tl {
-        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl
-      }
-    }
-    {
-      \tl_show:N \l__spath_tmpc_tl
-    }
-    \tl_put_left:NV \l__spath_rp_tl \l__spath_tmpd_tl
+    \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \dim_set:Nn \l__spath_minx_dim {\dim_min:nn { \l__spath_minx_dim} {\l__spath_tmpa_dim}}
-    \dim_set:Nn \l__spath_miny_dim {\dim_min:nn { \l__spath_miny_dim} {\l__spath_tmpb_dim}}
-    \dim_set:Nn \l__spath_maxx_dim {\dim_max:nn { \l__spath_maxx_dim} {\l__spath_tmpa_dim}}
-    \dim_set:Nn \l__spath_maxy_dim {\dim_max:nn { \l__spath_maxy_dim} {\l__spath_tmpb_dim}}
+    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \tl_put_left:Nx \l__spath_rp_tl
+    \tl_put_right:Nx \l__spath_tmpb_tl
     {
       {\dim_use:N \l__spath_tmpa_dim}
       {\dim_use:N \l__spath_tmpb_dim}
     }
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_translate:Nnnn #1#2#3#4
+{
+  \__spath_translate:nnn {#2}{#3}{#4}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_translate:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_translate:Nnn #1#2#3
+{
+  \spath_translate:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_translate:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nnnn #1#2#3#4
+{
+  \__spath_translate:nnn {#2}{#3}{#4}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nnn #1#2#3
+{
+  \spath_gtranslate:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_translate:Nn #1#2
+{
+  \spath_translate:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_translate:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gtranslate:Nn #1#2
+{
+  \spath_gtranslate:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_gtranslate:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_scale:nnn #1#2#3
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
+  }
+  {
+    \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-    \tl_set:Nx \l__spath_fp_tl
+    \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+    \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+    \tl_put_right:Nx \l__spath_tmpb_tl
     {
-      {\dim_use:N \l__spath_tmpa_dim}
-      {\dim_use:N \l__spath_tmpb_dim}
+      {\fp_to_dim:N \l__spath_tmpa_fp}
+      {\fp_to_dim:N \l__spath_tmpb_fp}
     }
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_scale:Nnnn #1#2#3#4
+{
+  \__spath_scale:nnn {#2}{#3}{#4}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_scale:Nnnn {NVnn, Nnxx}
+\cs_new_protected_nopar:Npn \spath_scale:Nnn #1#2#3
+{
+  \spath_scale:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_scale:Nnn {cnn, cVV, NVV}
+\cs_new_protected_nopar:Npn \spath_gscale:Nnnn #1#2#3#4
+{
+  \__spath_scale:nnn {#2}{#3}{#4}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gscale:Nnnn {NVnn, Nnxx}
+\cs_new_protected_nopar:Npn \spath_gscale:Nnn #1#2#3
+{
+  \spath_gscale:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gscale:Nnn {cnn, cVV, NVV}
+\cs_new_protected_nopar:Npn \spath_scale:Nn #1#2
+{
+  \spath_scale:Nnn #1 #2
+}
+
+\cs_generate_variant:Nn \spath_scale:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gscale:Nn #1#2
+{
+  \spath_gscale:Nnn #1 #2
+}
 
+\cs_generate_variant:Nn \spath_gscale:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_transform:nnnnnnn #1#2#3#4#5#6#7
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
   }
+  {
+    \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpd_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-  \tl_put_left:NV \l__spath_rp_tl \g__spath_moveto_tl
+    \fp_set:Nn \l__spath_tmpa_fp {\l__spath_tmpc_tl * #2 + \l__spath_tmpd_tl * #4 + #6}
+    \fp_set:Nn \l__spath_tmpb_fp {\l__spath_tmpc_tl * #3 + \l__spath_tmpd_tl * #5 + #7}
+    \tl_put_right:Nx \l__spath_tmpb_tl
+    {
+      {\fp_to_dim:N \l__spath_tmpa_fp}
+      {\fp_to_dim:N \l__spath_tmpb_fp}
+    }
+  }
 
-  \spath_put:nnV {#1} {reverse path} \l__spath_rp_tl
-  \spath_put:nnV {#1} {length} \l__spath_l_int
-  \spath_put:nnV {#1} {real length} \l__spath_rl_int
-  \spath_put:nnV {#1} {number of components} \l__spath_nc_int
-  \spath_put:nnV {#1} {initial point} \l__spath_ip_tl
-  \spath_put:nnV {#1} {final point} \l__spath_fp_tl
-  \spath_put:nnV {#1} {initial action} \l__spath_ia_tl
-  \spath_put:nnV {#1} {final action} \l__spath_fa_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_transform:Nnnnnnnn #1#2#3#4#5#6#7#8
+{
+  \__spath_transform:nnnnnnn {#2}{#3}{#4}{#5}{#6}{#7}{#8}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_transform:Nnnnnnnn {NVnnnnnn, Nnxxxxxx, cnnnnnnn}
+\cs_new_protected_nopar:Npn \spath_transform:Nnnnnnn #1#2#3#4#5#6#7
+{
+  \spath_transform:NVnnnnnn #1#1{#2}{#3}{#4}{#5}{#6}{#7}
+}
+\cs_generate_variant:Nn \spath_transform:Nnnnnnn {cnnnnnn}
+\cs_new_protected_nopar:Npn \spath_transform:Nnn #1#2#3
+{
+  \spath_transform:Nnnnnnnn #1{#2}#3
+}
+\cs_generate_variant:Nn \spath_transform:Nnn {cnn, cVn, NVn, NnV}
+\cs_new_protected_nopar:Npn \spath_transform:Nn #1#2
+{
+  \spath_transform:NVnnnnnn #1#1#2
+}
+\cs_generate_variant:Nn \spath_transform:Nn {cn, cV, NV}
 
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnnnnnnn #1#2#3#4#5#6#7#8
+{
+  \__spath_transform:nnnnnnn {#2}{#3}{#4}{#5}{#6}{#7}{#8}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnnnnnnn {NVnnnnnn, Nnxxxxxx, cnnnnnnn}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnnnnnn #1#2#3#4#5#6#7
+{
+  \spath_gtransform:NVnnnnnn #1#1{#2}{#3}{#4}{#5}{#6}{#7}
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnnnnnn {cnnnnnn}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nnn #1#2#3
+{
+  \spath_gtransform:Nnnnnnnn #1{#2}#3
+}
+\cs_generate_variant:Nn \spath_gtransform:Nnn {cnn, cVn, NVn, NnV}
+\cs_new_protected_nopar:Npn \spath_gtransform:Nn #1#2
+{
+  \spath_gtransform:NVnnnnnn #1#1#2
+}
+\cs_generate_variant:Nn \spath_gtransform:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \__spath_weld:nn #1#2
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nn \l__spath_tmpb_tl {#2}
+
+  \spath_finalpoint:NV \l__spath_tmpc_tl \l__spath_tmpa_tl
+  \spath_initialpoint:NV \l__spath_tmpd_tl \l__spath_tmpb_tl
+
+  \dim_set:Nn \l__spath_tmpa_dim
   {
-    {\dim_use:N \l__spath_minx_dim}
-    {\dim_use:N \l__spath_miny_dim}
+    \tl_item:Nn \l__spath_tmpc_tl {1}
+    -
+    \tl_item:Nn \l__spath_tmpd_tl {1}
+  }
+  \dim_set:Nn \l__spath_tmpb_dim
+  {
+    \tl_item:Nn \l__spath_tmpc_tl {2}
+    -
+    \tl_item:Nn \l__spath_tmpd_tl {2}
   }
-  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
 
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_put_right:Nx \l__spath_tmpb_tl
+  \spath_translate:NVV \l__spath_tmpb_tl \l__spath_tmpa_dim \l__spath_tmpb_dim
+
+  \prg_replicate:nn {3}
   {
-    {\dim_use:N \l__spath_maxx_dim}
-    {\dim_use:N \l__spath_maxy_dim}
+    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
   }
-  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
 
+  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_translate:nnn #1#2#3
+\cs_new_protected_nopar:Npn \spath_weld:Nnn #1#2#3
 {
-  \tl_map_inline:Nn \g__spath_moveable_attributes
-  {
-    \spath_if_in:nnT {#1} {##1}
-    {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
+  \__spath_weld:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_weld:Nnn {NVV,NVn}
+\cs_new_protected_nopar:Npn \spath_weld:Nn #1#2
+{
+  \spath_weld:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_weld:Nn {NV, Nv, cV, cv}
+\cs_new_protected_nopar:Npn \spath_gweld:Nnn #1#2#3
+{
+  \__spath_weld:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gweld:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gweld:Nn #1#2
+{
+  \spath_gweld:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gweld:Nn {NV, Nv, cV, cv}
+\cs_new_protected_nopar:Npn \__spath_append_no_move:nn #1#2
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nn \l__spath_tmpb_tl {#2}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
 
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
+  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_append_no_move:Nnn #1#2#3
+{
+  \__spath_append_no_move:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_append_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_append_no_move:Nn #1#2
+{
+  \spath_append_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_append_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_gappend_no_move:Nnn #1#2#3
+{
+  \__spath_append_no_move:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gappend_no_move:Nn #1#2
+{
+  \spath_gappend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_append:Nnn #1#2#3
+{
+  \tl_set:Nn #1 {#2}
+  \tl_put_right:Nn #1 {#3}
+}
+\cs_generate_variant:Nn \spath_append:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_append:Nn #1#2
+{
+  \spath_append:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_append:Nn {NV, Nv}
+\cs_new_protected_nopar:Npn \spath_gappend:Nnn #1#2#3
+{
+  \tl_gset:Nn #1 {#2}
+  \tl_gput_right:Nn #1 {#3}
+}
+\cs_generate_variant:Nn \spath_gappend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gappend:Nn #1#2
+{
+  \spath_gappend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gappend:Nn {NV, Nv}
+\cs_new_protected_nopar:Npn \spath_prepend_no_move:Nnn #1#2#3
+{
+  \spath_append_no_move:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_prepend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_prepend_no_move:Nn #1#2
+{
+  \spath_prepend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_prepend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_gprepend_no_move:Nnn #1#2#3
+{
+  \spath_gappend_no_move:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend_no_move:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gprepend_no_move:Nn #1#2
+{
+  \spath_gprepend_no_move:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend_no_move:Nn {NV, cv}
+\cs_new_protected_nopar:Npn \spath_prepend:Nnn #1#2#3
+{
+  \spath_append:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_prepend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_prepend:Nn #1#2
+{
+  \spath_prepend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_prepend:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gprepend:Nnn #1#2#3
+{
+  \spath_gappend:Nnn #1{#3}{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend:Nnn {NVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gprepend:Nn #1#2
+{
+  \spath_gprepend:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gprepend:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_bake_round:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \pgf@@processround \l__spath_tmpa_tl\l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_bake_round:Nn #1#2
+{
+  \__spath_bake_round:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_bake_round:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_bake_round:N #1
+{
+  \spath_bake_round:NV #1#1
+}
+\cs_generate_variant:Nn \spath_bake_round:N {c}
+\cs_new_protected_nopar:Npn \spath_gbake_round:Nn #1#2
+{
+  \__spath_bake_round:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gbake_round:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gbake_round:N #1
+{
+  \spath_gbake_round:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gbake_round:N {c}
+\cs_new_protected_nopar:Npn \__spath_close:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \spath_initialpoint:NV \l__spath_tmpb_tl \l__spath_tmpa_tl
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_closepath_tl
+  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_close:Nn #1#2
+{
+  \__spath_close:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_close:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_close:N #1
+{
+  \spath_close:NV #1#1
+}
+\cs_generate_variant:Nn \spath_close:N {c}
+\cs_new_protected_nopar:Npn \spath_gclose:Nn #1#2
+{
+  \__spath_close:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gclose:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gclose:N #1
+{
+  \spath_gclose:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gclose:N {c}
+\cs_new_protected_nopar:Npn \__spath_open:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
   }
-  \tl_map_inline:Nn \g__spath_path_attributes
   {
-    \spath_if_in:nnT {#1} {##1}
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+    \tl_case:NnF \l__spath_tmpc_tl
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
-      {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \c_spath_closepath_tl {
 
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
+        \bool_if:nF
+        {
+          \dim_compare_p:n
+          {
+            \l__spath_move_x_dim == \l__spath_tmpa_dim
+          }
+          &&
+          \dim_compare_p:n
+          {
+            \l__spath_move_y_dim == \l__spath_tmpb_dim
+          }
+        }
+        {
+          \tl_put_right:NV \l__spath_tmpb_tl \c_spath_lineto_tl
+
+          \tl_put_right:Nx \l__spath_tmpb_tl {
+            { \dim_use:N \l__spath_move_x_dim }
+            { \dim_use:N \l__spath_move_y_dim }
+          }
+        }
+
+        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
         \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      }
 
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
+      \c_spath_moveto_tl {
+        \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+
+        \dim_set:Nn \l__spath_move_x_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+        \dim_set:Nn \l__spath_move_y_dim {\tl_head:N \l__spath_tmpa_tl}
         \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
+        \tl_put_right:Nx \l__spath_tmpb_tl {
+          { \dim_use:N \l__spath_move_x_dim }
+          { \dim_use:N \l__spath_move_y_dim }
         }
+
+        \dim_set_eq:NN \l__spath_tmpa_dim \l__spath_move_x_dim
+        \dim_set_eq:NN \l__spath_tmpb_dim \l__spath_move_y_dim
+      }
+    }
+    {
+      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+
+      \tl_put_right:Nx \l__spath_tmpb_tl {
+        { \dim_use:N \l__spath_tmpa_dim }
+        { \dim_use:N \l__spath_tmpb_dim }
       }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
     }
   }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
 }
-
-\cs_generate_variant:Nn \spath_translate:nnn {nxx}
-\cs_new_nopar:Npn \spath_translate:nn #1#2
+\cs_new_protected_nopar:Npn \spath_open:Nn #1#2
 {
-  \spath_translate:nnn {#1} #2
+  \__spath_open:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-
-\cs_generate_variant:Nn \spath_translate:nn {nV}
-\cs_new_nopar:Npn \spath_scale:nnn #1#2#3
+\cs_generate_variant:Nn \spath_open:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_open:N #1
+{
+  \spath_open:NV #1#1
+}
+\cs_new_protected_nopar:Npn \spath_gopen:Nn #1#2
+{
+  \__spath_open:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gopen:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gopen:N #1
+{
+  \spath_gopen:NV #1#1
+}
+\cs_new_protected_nopar:Npn \__spath_remove_empty_components:n #1
 {
-  \tl_map_inline:Nn \g__spath_moveable_attributes
+  \group_begin:
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \tl_clear:N \l__spath_tmpa_tl
+  \seq_map_inline:Nn \l__spath_tmpa_seq
   {
-    \spath_if_in:nnT {#1} {##1}
+    \int_compare:nF
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-
-      \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\fp_to_dim:N \l__spath_tmpa_fp}
-        {\fp_to_dim:N \l__spath_tmpb_fp}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
+      \tl_count:n {##1} == 3
+    }
+    {
+      \tl_put_right:Nn \l__spath_tmpa_tl {##1}
     }
   }
-  \tl_map_inline:Nn \g__spath_path_attributes
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_remove_empty_components:Nn #1#2
+{
+  \__spath_remove_empty_components:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_remove_empty_components:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_remove_empty_components:N #1
+{
+  \spath_remove_empty_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_remove_empty_components:N {c}
+\cs_new_protected_nopar:Npn \spath_gremove_empty_components:Nn #1#2
+{
+  \__spath_remove_empty_components:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gremove_empty_components:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gremove_empty_components:N #1
+{
+  \spath_gremove_empty_components:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gremove_empty_components:N {c}
+\prg_new_protected_conditional:Npnn \spath_if_eq:nn #1#2 { T, F, TF }
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nn \l__spath_tmpb_tl {#2}
+  \bool_gset_true:N \g__spath_tmpa_bool
+  \int_compare:nNnTF {\tl_count:N \l__spath_tmpa_tl} = {\tl_count:N \l__spath_tmpb_tl}
   {
-    \spath_if_in:nnT {#1} {##1}
+    \int_step_inline:nnnn {1} {3} {\tl_count:N \l__spath_tmpa_tl}
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
+      \tl_set:Nx \l__spath_tmpc_tl {\tl_item:Nn \l__spath_tmpa_tl {##1}}
+      \tl_set:Nx \l__spath_tmpd_tl {\tl_item:Nn \l__spath_tmpb_tl {##1}}
+      \tl_if_eq:NNF \l__spath_tmpc_tl \l__spath_tmpd_tl
+      {
+        \bool_gset_false:N \g__spath_tmpa_bool
       }
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_item:Nn \l__spath_tmpa_tl {##1+1}}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_item:Nn \l__spath_tmpb_tl {##1+1}}
+      \dim_compare:nF { \dim_abs:n { \l__spath_tmpa_dim - \l__spath_tmpb_dim} < 0.001pt }
       {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\fp_to_dim:N \l__spath_tmpa_fp}
-          {\fp_to_dim:N \l__spath_tmpb_fp}
-        }
+        \bool_gset_false:N \g__spath_tmpa_bool
+      }
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_item:Nn \l__spath_tmpa_tl {##1+2}}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_item:Nn \l__spath_tmpb_tl {##1+2}}
+      \dim_compare:nF { \dim_abs:n { \l__spath_tmpa_dim - \l__spath_tmpb_dim} < 0.001pt }
+      {
+        \bool_gset_false:N \g__spath_tmpa_bool
       }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
     }
   }
+  {
+    \bool_gset_false:N \g__spath_tmpa_bool
+  }
+  \group_end:
+  \bool_if:NTF \g__spath_tmpa_bool
+  {
+    \prg_return_true:
+  }
+  {
+    \prg_return_false:
+  }
 }
-\cs_generate_variant:Nn \spath_scale:nnn {nxx}
-\cs_new_nopar:Npn \spath_scale:nn #1#2
+\prg_generate_conditional_variant:Nnn \spath_if_eq:nn {VV, Vn, nV, vv} {TF, T, F}
+\cs_new_protected_nopar:Npn \__spath_split_curve:nn #1#2
 {
-  \spath_scale:nnn {#1} #2
-}
+  \group_begin:
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {2}}
+    {\tl_item:nn {#1} {3}}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetoa_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
 
-\cs_generate_variant:Nn \spath_scale:nn {nV}
-\cs_new_nopar:Npn \spath_transform:nnnnnnn #1#2#3#4#5#6#7
-{
-  \tl_map_inline:Nn \g__spath_moveable_attributes
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetob_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
   {
-    \spath_if_in:nnT {#1} {##1}
+    {\fp_to_dim:n
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
-      \fp_set:Nn \l__spath_tmpa_fp {\l__spath_tmpa_tl * #2 + \l__spath_tmpb_tl * #3 + #6}
-      \fp_set:Nn \l__spath_tmpb_fp {\l__spath_tmpa_tl * #4 + \l__spath_tmpb_tl * #5 + #7}
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\fp_to_dim:N \l__spath_tmpa_fp}
-        {\fp_to_dim:N \l__spath_tmpb_fp}
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
+      (1 - #2)^2 * \tl_item:nn {#1} {2} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {5} + (#2)^2 * \tl_item:nn {#1} {8}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {3} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {6} + (#2)^2 * \tl_item:nn {#1} {9}
+    }}
   }
-  \tl_map_inline:Nn \g__spath_path_attributes
+
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
   {
-    \spath_if_in:nnT {#1} {##1}
+    {\fp_to_dim:n
+      {
+      (1 - #2)^3 * \tl_item:nn {#1} {2} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {5} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {8} + (#2)^3 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
     {
-      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
-      \tl_clear:N \l__spath_tmpb_tl
-      \bool_until_do:nn {
-        \tl_if_empty_p:N \l__spath_tmpa_tl
-      }
+      (1 - #2)^3 * \tl_item:nn {#1} {3} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {6} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {9} + (#2)^3 * \tl_item:nn {#1} {12}
+    }}
+  }
+
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
+
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
       {
-        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      (1 - #2)^3 * \tl_item:nn {#1} {2} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {5} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {8} + (#2)^3 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^3 * \tl_item:nn {#1} {3} + 3 * (1 - #2)^2 * (#2) * \tl_item:nn {#1} {6} + 3 * (1 - #2) * (#2)^2 * \tl_item:nn {#1} {9} + (#2)^3 * \tl_item:nn {#1} {12}
+    }}
+  }
 
-        \fp_set:Nn \l__spath_tmpa_fp {\l_tmpa_tl * #2 + \l_tmpb_tl * #3 + #6}
-        \fp_set:Nn \l__spath_tmpb_fp {\l_tmpa_tl * #4 + \l_tmpb_tl * #5 + #7}
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\fp_to_dim:N \l__spath_tmpa_fp}
-          {\fp_to_dim:N \l__spath_tmpb_fp}
-        }
-      }
-      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
-    }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetoa_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {5} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {8} + (#2)^2 * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2)^2 * \tl_item:nn {#1} {6} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {9} + (#2)^2 * \tl_item:nn {#1} {12}
+    }}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curvetob_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {8} + (#2) * \tl_item:nn {#1} {11}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {9} + (#2) * \tl_item:nn {#1} {12}
+    }}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_curveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {11}}
+    {\tl_item:nn {#1} {12}}
   }
-}
 
-\cs_generate_variant:Nn \spath_transform:nnnnnnn {nxxxxxx}
-\cs_new_nopar:Npn \spath_transform:nn #1#2
-{
-  \spath_transform:nnnnnnn {#1} #2
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
 }
-
-\cs_generate_variant:Nn \spath_transform:nn {nV}
-\cs_new_nopar:Npn \spath_reverse:n #1
+\cs_new_protected_nopar:Npn \spath_split_curve:NNnn #1#2#3#4
 {
-  \spath_if_in:nnF {#1} {reverse path} {
-    \use:c {spath_generate_reverse path:n} {#1}
-  }
-  \spath_swap:nnn {#1} {path} {reverse path}
-  \spath_swap:nnn {#1} {initial point} {final point}
-  \spath_swap:nnn {#1} {initial action} {final action}
+  \__spath_split_curve:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_swap:nnn #1#2#3
+\cs_generate_variant:Nn \spath_split_curve:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_curve:NNnn #1#2#3#4
 {
-  \__spath_get:nnNF {#1} {#2} \l__spath_tmpa_tl {\tl_clear:N \l__spath_tmpa_tl}
-  \__spath_get:nnNF {#1} {#3} \l__spath_tmpb_tl {\tl_clear:N \l__spath_tmpb_tl}
-  \tl_if_empty:NTF \l__spath_tmpb_tl
-  {\spath_remove:nn {#1} {#2}}
-  {\spath_put:nnV {#1} {#2} \l__spath_tmpb_tl}
-  \tl_if_empty:NTF \l__spath_tmpa_tl
-  {\spath_remove:nn {#1} {#3}}
-  {\spath_put:nnV {#1} {#3} \l__spath_tmpa_tl}
+  \__spath_split_curve:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_weld:nn #1#2
+\cs_generate_variant:Nn \spath_gsplit_curve:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \__spath_split_line:nn #1#2
 {
-  \spath_clone:nn {#2} {tmp_path}
-  \spath_get:nnN {#1} {final point} \l__spath_tmpa_tl
-
-  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-  \spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
-
-  \dim_sub:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \dim_sub:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-  \spath_translate:nxx {tmp_path} {\dim_use:N \l__spath_tmpa_dim} {\dim_use:N \l__spath_tmpb_dim}
+  \group_begin:
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {2}}
+    {\tl_item:nn {#1} {3}}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_lineto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
 
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \__spath_get:nnN {tmp_path} {path} \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_set_eq:NN \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl
+  {
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {2} + (#2) * \tl_item:nn {#1} {5}
+    }}
+    {\fp_to_dim:n
+    {
+      (1 - #2) * \tl_item:nn {#1} {3} + (#2) * \tl_item:nn {#1} {6}
+    }}
+  }
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_lineto_tl
+  \tl_put_right:Nx \l__spath_tmpa_tl {
+    {\tl_item:nn {#1} {5}}
+    {\tl_item:nn {#1} {6}}
+  }
 
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_line:NNnn #1#2#3#4
+{
+  \__spath_split_line:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_line:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_line:NNnn #1#2#3#4
+{
+  \__spath_split_line:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_line:NNnn {NNnV, NNVn, NNVV}
+\int_new:N \l__spath_split_int
+\int_new:N \l__spath_splitat_int
+\fp_new:N \l__spath_split_fp
+\bool_new:N \l__spath_split_bool
+\tl_new:N \l__spath_split_path_tl
+\tl_new:N \l__spath_split_patha_tl
+\tl_new:N \l__spath_split_pathb_tl
+\tl_new:N \l__spath_split_intoa_tl
+\tl_new:N \l__spath_split_intob_tl
+\dim_new:N \l__spath_splitx_dim
+\dim_new:N \l__spath_splity_dim
+\cs_new_protected_nopar:Npn \__spath_split_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l__spath_splitat_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_split_fp {#2 - floor(#2)}
 
-  \__spath_get:nnNTF {tmp_path} {final point} \l__spath_tmpa_tl
+  % Is split point near one end or other of a component?
+  \fp_compare:nT
   {
-    \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
+    \l__spath_split_fp < 0.01
   }
   {
-    \spath_remove:nn {#1} {final point}
+    % Near the start, so we'll place it at the start
+    \fp_set:Nn \l__spath_split_fp {0}
   }
-
-  \__spath_get:nnNTF {tmp_path} {final action} \l__spath_tmpa_tl
+  \fp_compare:nT
   {
-    \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
+    \l__spath_split_fp > 0.99
   }
   {
-    \spath_remove:nn {#1} {final action}
+    % Near the end, so we'll place it at the end
+    \fp_set:Nn \l__spath_split_fp {0}
+    \int_incr:N \l__spath_splitat_int
   }
 
-  \__spath_get:nnNT {tmp_path} {min bb} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {min bb} \l__spath_tmpb_tl
-    {
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+  \int_zero:N \l__spath_split_int
+  \bool_set_true:N \l__spath_split_bool
 
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}
+  \tl_set:Nn \l__spath_split_path_tl {#1}
+  \tl_clear:N \l__spath_split_patha_tl
 
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
-      {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
-      }
-      \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
-    }
-  }
+  \dim_zero:N \l__spath_splitx_dim
+  \dim_zero:N \l__spath_splity_dim
 
-  \__spath_get:nnNT {tmp_path} {max bb} \l__spath_tmpa_tl
+  \bool_until_do:nn {
+    \tl_if_empty_p:N \l__spath_split_path_tl
+    ||
+    \int_compare_p:n { \l__spath_splitat_int == \l__spath_split_int  }
+  }
   {
-    \__spath_get:nnNT {#1} {max bb} \l__spath_tmpb_tl
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_split_path_tl}
+    \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+    \tl_case:Nn \l__spath_tmpc_tl
     {
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}
-
-      \tl_clear:N \l__spath_tmpb_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl
+      \c_spath_lineto_tl
       {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+        \int_incr:N \l__spath_split_int
+      }
+      \c_spath_curvetoa_tl
+      {
+        \int_incr:N \l__spath_split_int
       }
-      \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
     }
-  }
-
-  \__spath_get:nnNT {tmp_path} {reverse path} \l__spath_tmpa_tl
-  {
-    \__spath_get:nnNT {#1} {reverse path} \l__spath_tmpb_tl
+    \int_compare:nT { \l__spath_split_int < \l__spath_splitat_int  }
     {
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+      \tl_put_right:NV \l__spath_split_patha_tl \l__spath_tmpc_tl
+
+      \tl_put_right:Nx \l__spath_split_patha_tl
+      {{ \tl_head:N \l__spath_split_path_tl }}
+      \dim_set:Nn \l__spath_splitx_dim {\tl_head:N \l__spath_split_path_tl}
+      \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+      \tl_put_right:Nx \l__spath_split_patha_tl
+      {{ \tl_head:N \l__spath_split_path_tl }}
+      \dim_set:Nn \l__spath_splity_dim {\tl_head:N \l__spath_split_path_tl}
+      \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
 
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
     }
   }
 
-  \__spath_get:nnNT {tmp_path} {length} \l__spath_tmpa_tl
+  \tl_clear:N \l__spath_split_pathb_tl
+  \tl_put_right:NV \l__spath_split_pathb_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_split_pathb_tl
   {
-    \__spath_get:nnNT {#1} {length} \l__spath_tmpb_tl
-    {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
-      \spath_put:nnV {#1} {length} \l__spath_tmpa_int
-    }
+    {\dim_use:N \l__spath_splitx_dim}
+    {\dim_use:N \l__spath_splity_dim}
   }
 
-  \__spath_get:nnNT {tmp_path} {real length} \l__spath_tmpa_tl
+  \fp_compare:nTF
+  {
+    \l__spath_split_fp == 0
+  }
   {
-    \__spath_get:nnNT {#1} {real length} \l__spath_tmpb_tl
+    \tl_set_eq:NN \l__spath_split_intob_tl \l__spath_split_pathb_tl
+    \tl_if_empty:NF \l__spath_split_path_tl
     {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl}
-      \spath_put:nnV {#1} {real length} \l__spath_tmpa_int
+      \tl_put_right:NV \l__spath_split_intob_tl \l__spath_tmpc_tl
+      \tl_put_right:NV \l__spath_split_intob_tl \l__spath_split_path_tl
     }
   }
-
-  \__spath_get:nnNT {tmp_path} {number of components} \l__spath_tmpa_tl
   {
-    \__spath_get:nnNT {#1} {number of components} \l__spath_tmpb_tl
+
+    \tl_case:Nn \l__spath_tmpc_tl
     {
-      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
-      \spath_put:nnV {#1} {number of components} \l__spath_tmpa_int
+      \c_spath_lineto_tl
+      {
+        \tl_put_right:NV \l__spath_split_pathb_tl \l__spath_tmpc_tl
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \spath_split_line:NNVV
+        \l__spath_split_intoa_tl
+        \l__spath_split_intob_tl
+        \l__spath_split_pathb_tl
+        \l__spath_split_fp
+
+        \prg_replicate:nn {3} {
+          \tl_set:Nx \l__spath_split_intoa_tl {\tl_tail:N \l__spath_split_intoa_tl}
+        }
+
+        \tl_put_right:NV \l__spath_split_patha_tl \l__spath_split_intoa_tl
+        \tl_put_right:NV \l__spath_split_intob_tl \l__spath_split_path_tl
+      }
+      \c_spath_curvetoa_tl
+      {
+        \tl_put_right:NV \l__spath_split_pathb_tl \l__spath_tmpc_tl
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \tl_put_right:Nx \l__spath_split_pathb_tl
+        {{ \tl_head:N \l__spath_split_path_tl }}
+        \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+        \prg_replicate:nn {2} {
+
+          \tl_put_right:Nx \l__spath_split_pathb_tl
+          { \tl_head:N \l__spath_split_path_tl }
+          \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+          \tl_put_right:Nx \l__spath_split_pathb_tl
+          {{ \tl_head:N \l__spath_split_path_tl }}
+          \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+
+          \tl_put_right:Nx \l__spath_split_pathb_tl
+          {{ \tl_head:N \l__spath_split_path_tl }}
+          \tl_set:Nx \l__spath_split_path_tl {\tl_tail:N \l__spath_split_path_tl }
+        }
+
+        \spath_split_curve:NNVV
+        \l__spath_split_intoa_tl
+        \l__spath_split_intob_tl
+        \l__spath_split_pathb_tl \l__spath_split_fp
+
+        \prg_replicate:nn {3} {
+          \tl_set:Nx \l__spath_split_intoa_tl {\tl_tail:N \l__spath_split_intoa_tl}
+        }
+
+        \tl_put_right:NV \l__spath_split_patha_tl \l__spath_split_intoa_tl
+        \tl_put_right:NV \l__spath_split_intob_tl \l__spath_split_path_tl
+      }
     }
   }
 
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_patha_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_intob_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_prepend_no_move:nn #1#2
+\cs_new_protected_nopar:Npn \spath_split_at:NNnn #1#2#3#4
 {
-  \spath_if_exist:nT {#2}
+  \__spath_split_at:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at:NNnn {NNVn, NNVV, NNnV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:NNnn #1#2#3#4
+{
+  \__spath_split_at:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at:NNnn {NNVn, NNVV, NNnV}
+\cs_new_protected_nopar:Npn \spath_split_at:Nnn #1#2#3
+{
+  \__spath_split_at:nn {#2}{#3}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1} \tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_at:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_split_at:Nn #1#2
+{
+  \spath_split_at:NVn #1#1{#2}
+}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:Nnn #1#2#3
+{
+  \__spath_split_at:nn {#2}{#3}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1} \tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_at:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at:Nn #1#2
+{
+  \spath_gsplit_at:NVn #1#1{#2}
+}
+\tl_new:N \l__spath_shorten_fa_tl
+\tl_new:N \l__spath_shorten_path_tl
+\tl_new:N \l__spath_shorten_last_tl
+\tl_new:N \l__spath_shorten_lasta_tl
+\tl_new:N \l__spath_shorten_lastb_tl
+\int_new:N \l__spath_shorten_int
+\fp_new:N \l__spath_shorten_x_fp
+\fp_new:N \l__spath_shorten_y_fp
+\fp_new:N \l__spath_shorten_len_fp
+\cs_new_protected_nopar:Npn \__spath_shorten_at_end:nn #1#2
+{
+  \int_compare:nTF
   {
-    \__spath_get:nnN {#2} {path} \l__spath_tmpa_tl
-    \__spath_get:nnN {#1} {path} \l__spath_tmpb_tl
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
+    \tl_count:n {#1} > 3
+  }
+  {
+    \group_begin:
+    \tl_set:Nn \l__spath_shorten_path_tl {#1}
+    \tl_reverse:N \l__spath_shorten_path_tl
 
-    \spath_if_in:nnTF {#2} {initial point}
-    {
-      \__spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {initial point} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {initial point}
-    }
+    \tl_set:Nx \l__spath_shorten_fa_tl {\tl_item:Nn \l__spath_shorten_path_tl {3}}
 
-    \spath_if_in:nnTF {#2} {initial action}
+    \tl_clear:N \l__spath_shorten_last_tl
+    \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curveto_tl
     {
-      \__spath_get:nnN {#2} {initial action} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {initial action} \l__spath_tmpa_tl
+      \int_set:Nn \l__spath_shorten_int {3}
     }
     {
-      \spath_remove:nn {#1} {initial action}
+      \int_set:Nn \l__spath_shorten_int {1}
     }
 
-    \bool_if:nTF
+    \prg_replicate:nn { \l__spath_shorten_int }
     {
-      \spath_if_in_p:nn {#1} {length}
-      &&
-      \spath_if_in_p:nn {#2} {length}
-    }
-    {
-      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
-    }
-    {
-      \spath_remove:nn {#1} {length}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {real length}
-      &&
-      \spath_if_in_p:nn {#2} {real length}
+      \tl_put_right:Nx \l__spath_shorten_last_tl
+      {
+        {\tl_head:N \l__spath_shorten_path_tl}
+      }
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
+      \tl_put_right:Nx \l__spath_shorten_last_tl
+      {
+        {\tl_head:N \l__spath_shorten_path_tl}
+      }
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
+      \tl_put_right:Nx \l__spath_shorten_last_tl
+      {
+        \tl_head:N \l__spath_shorten_path_tl
+      }
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
     }
+
+    \tl_put_right:Nx \l__spath_shorten_last_tl
     {
-      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl }}
+      {\tl_item:Nn \l__spath_shorten_path_tl {1}}
+      {\tl_item:Nn \l__spath_shorten_path_tl {2}}
     }
+    \tl_put_right:NV \l__spath_shorten_last_tl \c_spath_moveto_tl
+
+    \tl_reverse:N \l__spath_shorten_path_tl
+
+    \fp_set:Nn \l__spath_shorten_x_fp
     {
-      \spath_remove:nn {#1} {real length}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {4}}
+      -
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {1}}
     }
-    \bool_if:nTF
+
+    \fp_set:Nn \l__spath_shorten_y_fp
     {
-      \spath_if_in_p:nn {#1} {number of components}
-      &&
-      \spath_if_in_p:nn {#2} {number of components}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {5}}
+      -
+      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {2}}
     }
+
+    \fp_set:Nn \l__spath_shorten_len_fp
     {
-      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
+      sqrt( \l__spath_shorten_x_fp * \l__spath_shorten_x_fp +  \l__spath_shorten_y_fp *  \l__spath_shorten_y_fp )
     }
+
+    \fp_compare:nTF
     {
-      \spath_remove:nn {#1} {number of components}
+      \l__spath_shorten_len_fp > #2
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {min bb}
-      &&
-      \spath_if_in_p:nn {#2} {min bb}
-    }
-    {
-      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {min bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+
+      \fp_set:Nn \l__spath_shorten_len_fp
+      {
+        (\l__spath_shorten_len_fp - #2)/ \l__spath_shorten_len_fp
       }
-    }
-    {
-      \spath_remove:nn {#1} {min bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {max bb}
-      &&
-      \spath_if_in_p:nn {#2} {max bb}
-    }
-    {
-      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {max bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+
+      \tl_reverse:N \l__spath_shorten_last_tl
+
+      \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curveto_tl
+      {
+        \fp_set:Nn \l__spath_shorten_len_fp
+        {
+          1 - (1 -\l__spath_shorten_len_fp)/3
+        }
+        \spath_split_curve:NNVV
+        \l__spath_shorten_lasta_tl
+        \l__spath_shorten_lastb_tl
+        \l__spath_shorten_last_tl
+        \l__spath_shorten_len_fp
       }
+      {
+        \spath_split_line:NNVV
+        \l__spath_shorten_lasta_tl
+        \l__spath_shorten_lastb_tl
+        \l__spath_shorten_last_tl
+        \l__spath_shorten_len_fp
+      }
+
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_shorten_lasta_tl {\tl_tail:N \l__spath_shorten_lasta_tl}
+      }
+
+      \tl_put_right:NV \l__spath_shorten_path_tl \l__spath_shorten_lasta_tl
+
     }
     {
-      \spath_remove:nn {#1} {max bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {reverse path}
-      &&
-      \spath_if_in_p:nn {#2} {reverse path}
-    }
-    {
-      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpb_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
-    }
-    {
-      \spath_remove:nn {#1} {reverse path}
+
+      \int_compare:nT
+      {
+        \tl_count:N \l__spath_shorten_path_tl > 3
+      }
+      {
+        \dim_set:Nn \l__spath_tmpa_dim {\fp_to_dim:n {#2 - \l__spath_shorten_len_fp } }
+        \spath_shorten_at_end:NV \l__spath_shorten_path_tl \l__spath_tmpa_dim
+      }
     }
 
+    \tl_gset_eq:NN \g__spath_output_tl \l__spath_shorten_path_tl
+    \group_end:
   }
+  {
+    \tl_gset:Nn \g__spath_output_tl {#1}
+  }
+}
+\cs_new_protected_nopar:Npn \spath_shorten_at_end:Nnn #1#2#3
+{
+  \__spath_shorten_at_end:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_shorten_at_end:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_shorten_at_end:Nn #1#2
+{
+  \spath_shorten_at_end:NVn #1#1{#2}
 }
-\cs_new_nopar:Npn \spath_append_no_move:nn #1#2
+\cs_generate_variant:Nn \spath_shorten_at_end:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_end:Nnn #1#2#3
 {
-  \spath_if_exist:nT {#2}
+  \__spath_shorten_at_end:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gshorten_at_end:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_end:Nn #1#2
+{
+  \spath_gshorten_at_end:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gshorten_at_end:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \__spath_shorten_at_start:nn #1#2
+{
+  \int_compare:nTF
   {
-    \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-    \spath_get:nnN {#2} {path} \l__spath_tmpb_tl
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-    \spath_if_in:nnTF {#2} {final point}
-    {
-      \__spath_get:nnN {#2} {final point} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {final point}
-    }
-    \spath_if_in:nnTF {#2} {final action}
-    {
-      \__spath_get:nnN {#2} {final action} \l__spath_tmpa_tl
-      \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
-    }
-    {
-      \spath_remove:nn {#1} {final action}
-    }
-    \bool_if:nTF
+    \tl_count:n {#1} > 3
+  }
+  {
+  \group_begin:
+  \tl_set:Nn \l__spath_shorten_path_tl {#1}
+
+  \tl_set:Nx \l__spath_shorten_fa_tl {\tl_item:Nn \l__spath_shorten_path_tl {4}}
+
+    \tl_clear:N \l__spath_shorten_last_tl
+
+  \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curvetoa_tl
+  {
+    \int_set:Nn \l__spath_shorten_int {3}
+  }
+  {
+    \int_set:Nn \l__spath_shorten_int {1}
+  }
+
+  \tl_set_eq:NN \l__spath_shorten_last_tl \c_spath_moveto_tl
+  \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl }
+
+  \prg_replicate:nn { \l__spath_shorten_int }
+  {
+    \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {1}}
+    \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {2}}
+    \tl_put_right:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {3}}
+
+    \prg_replicate:nn {3}
     {
-      \spath_if_in_p:nn {#1} {length}
-      &&
-      \spath_if_in_p:nn {#2} {length}
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl }
     }
+  }
+  \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {1}}
+  \__spath_tl_put_right_braced:Nx \l__spath_shorten_last_tl {\tl_item:Nn \l__spath_shorten_path_tl {2}}
+
+  \fp_set:Nn \l__spath_shorten_x_fp
+  {
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {5}}
+    -
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {2}}
+  }
+
+  \fp_set:Nn \l__spath_shorten_y_fp
+  {
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {6}}
+    -
+    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {3}}
+  }
+
+  \fp_set:Nn \l__spath_shorten_len_fp
+  {
+    sqrt( \l__spath_shorten_x_fp * \l__spath_shorten_x_fp +  \l__spath_shorten_y_fp *  \l__spath_shorten_y_fp )
+  }
+
+  \fp_compare:nTF
+  {
+    \l__spath_shorten_len_fp > #2
+  }
+  {
+
+    \fp_set:Nn \l__spath_shorten_len_fp
     {
-      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
+      #2/ \l__spath_shorten_len_fp
     }
+
+    \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curvetoa_tl
     {
-      \spath_remove:nn {#1} {length}
+      \fp_set:Nn \l__spath_shorten_len_fp
+      {
+        \l__spath_shorten_len_fp/3
+      }
+      \spath_split_curve:NNVV
+      \l__spath_shorten_lasta_tl
+      \l__spath_shorten_lastb_tl
+      \l__spath_shorten_last_tl
+      \l__spath_shorten_len_fp
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {real length}
-      &&
-      \spath_if_in_p:nn {#2} {real length}
+      \spath_split_line:NNVV
+      \l__spath_shorten_lasta_tl
+      \l__spath_shorten_lastb_tl
+      \l__spath_shorten_last_tl
+      \l__spath_shorten_len_fp
     }
+
+    \prg_replicate:nn {2}
     {
-      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl }}
+      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
     }
+
+    \tl_put_left:NV \l__spath_shorten_path_tl \l__spath_shorten_lastb_tl
+
+  }
+  {
+
+    \tl_put_left:NV \l__spath_shorten_path_tl \c_spath_moveto_tl
+
+    \int_compare:nT
     {
-      \spath_remove:nn {#1} {real length}
+      \tl_count:N \l__spath_shorten_path_tl > 3
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {number of components}
-      &&
-      \spath_if_in_p:nn {#2} {number of components}
+      \dim_set:Nn \l__spath_tmpa_dim {\fp_to_dim:n {#2 - \l__spath_shorten_len_fp } }
+      \spath_shorten_at_start:NV \l__spath_shorten_path_tl \l__spath_tmpa_dim
     }
+  }
+
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_shorten_path_tl
+  \group_end:
+  }
+  {
+    \tl_gset:Nn \g__spath_output_tl {#1}
+  }
+}
+\cs_new_protected_nopar:Npn \spath_shorten_at_start:Nnn #1#2#3
+{
+  \__spath_shorten_at_start:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_shorten_at_start:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_shorten_at_start:Nn #1#2
+{
+  \spath_shorten_at_start:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_shorten_at_start:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_start:Nnn #1#2#3
+{
+  \__spath_shorten_at_start:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gshorten_at_start:Nnn {NVV, cnn, cVV, NVn}
+\cs_new_protected_nopar:Npn \spath_gshorten_at_start:Nn #1#2
+{
+  \spath_gshorten_at_start:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gshorten_at_start:Nn {cn, cV, NV}
+\cs_new_protected_nopar:Npn \__spath_point_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l__spath_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_tmpa_fp {#2 - floor(#2)}
+
+  \spath_segments_to_seq:Nn \l__spath_tmpa_seq {#1}
+
+  \int_compare:nTF
+  {
+    \l__spath_tmpa_int < 1
+  }
+  {
+    \spath_initialpoint:Nn \l__spath_tmpc_tl {#1}
+  }
+  {
+    \int_compare:nTF
     {
-      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
-      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
-          \l__spath_tmpb_tl - 1}}
+      \l__spath_tmpa_int > \seq_count:N \l__spath_tmpa_seq
     }
     {
-      \spath_remove:nn {#1} {number of components}
+      \spath_finalpoint:Nn \l__spath_tmpc_tl {#1}
     }
-    \bool_if:nTF
     {
-      \spath_if_in_p:nn {#1} {min bb}
-      &&
-      \spath_if_in_p:nn {#2} {min bb}
-    }
-    {
-      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {min bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+
+      \tl_set:Nx \l__spath_tmpa_tl {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
+
+      \int_compare:nTF
+      {
+        \tl_count:N \l__spath_tmpa_tl > 3
       }
-    }
-    {
-      \spath_remove:nn {#1} {min bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {max bb}
-      &&
-      \spath_if_in_p:nn {#2} {max bb}
-    }
-    {
-      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
-      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
-      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {1}} {\tl_item:Nn
-          \l__spath_tmpb_tl {1}}}
-      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
-          \l__spath_tmpa_tl {2}} {\tl_item:Nn
-          \l__spath_tmpb_tl {2}}}
-      \spath_put:nnx {#1} {max bb} {
-        {\dim_use:N \l__spath_tmpa_dim}
-        {\dim_use:N \l__spath_tmpb_dim}
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {4}}
+      }
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {1}}
+      }
+
+      \tl_clear:N \l__spath_tmpc_tl
+
+      \tl_case:Nn \l__spath_tmpb_tl
+      {
+        \c_spath_moveto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {2}
+            }
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {3}
+            }
+          }
+        }
+
+        \c_spath_lineto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+              }
+            }
+          }
+        }
+
+        \c_spath_closepath_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp) * ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+                +
+                \l__spath_tmpa_fp * ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+              }
+            }
+          }
+        }
+
+        \c_spath_curvetoa_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {2} + 3 * (1 - \l__spath_tmpa_fp)^2 * (\l__spath_tmpa_fp) * \tl_item:Nn \l__spath_tmpa_tl {5} + 3 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp)^2 * \tl_item:Nn \l__spath_tmpa_tl {8} + (\l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {11}
+            }}
+            {\fp_to_dim:n
+              {
+                (1 - \l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {3} + 3 * (1 - \l__spath_tmpa_fp)^2 * (\l__spath_tmpa_fp) * \tl_item:Nn \l__spath_tmpa_tl {6} + 3 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp)^2 * \tl_item:Nn \l__spath_tmpa_tl {9} + (\l__spath_tmpa_fp)^3 * \tl_item:Nn \l__spath_tmpa_tl {12}
+            }}
+          }
+        }
       }
     }
+  }
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpc_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_point_at:Nnn #1#2#3
+{
+  \__spath_point_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_point_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \spath_gpoint_at:Nnn #1#2#3
+{
+  \__spath_point_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gpoint_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \__spath_tangent_at:nn #1#2
+{
+  \group_begin:
+  \int_set:Nn \l__spath_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_tmpa_fp {#2 - floor(#2)}
+
+  \spath_segments_to_seq:Nn \l__spath_tmpa_seq {#1}
+
+  \int_compare:nTF
+  {
+    \l__spath_tmpa_int < 1
+  }
+  {
+    \spath_initialpoint:Nn \l__spath_tmpc_tl {#1}
+  }
+  {
+    \int_compare:nTF
     {
-      \spath_remove:nn {#1} {max bb}
-    }
-    \bool_if:nTF
-    {
-      \spath_if_in_p:nn {#1} {reverse path}
-      &&
-      \spath_if_in_p:nn {#2} {reverse path}
+      \l__spath_tmpa_int > \seq_count:N \l__spath_tmpa_seq
     }
     {
-      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpa_tl
-      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpb_tl
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
-      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
+      \spath_finalpoint:Nn \l__spath_tmpc_tl {#1}
     }
     {
-      \spath_remove:nn {#1} {reverse path}
+
+      \tl_set:Nx \l__spath_tmpa_tl {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
+
+      \int_compare:nTF
+      {
+        \tl_count:N \l__spath_tmpa_tl > 3
+      }
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {4}}
+      }
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {1}}
+      }
+
+      \tl_clear:N \l__spath_tmpc_tl
+
+      \tl_case:Nn \l__spath_tmpb_tl
+      {
+        \c_spath_moveto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {2}
+            }
+            {
+              \tl_item:Nn \l__spath_tmpa_tl {3}
+            }
+          }
+        }
+
+        \c_spath_lineto_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+              }
+            }
+          }
+        }
+
+        \c_spath_closepath_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {5} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {2} )
+              }
+            }
+            {\fp_to_dim:n
+              {
+                ( \tl_item:Nn \l__spath_tmpa_tl {6} )
+                -
+                ( \tl_item:Nn \l__spath_tmpa_tl {3} )
+              }
+            }
+          }
+        }
+
+        \c_spath_curvetoa_tl
+        {
+          \tl_set:Nx \l__spath_tmpc_tl
+          {
+            {\fp_to_dim:n
+              {
+                3*(1 - \l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {5} - \tl_item:Nn \l__spath_tmpa_tl {2})
+                + 6 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp) *  (\tl_item:Nn \l__spath_tmpa_tl {8} - \tl_item:Nn \l__spath_tmpa_tl {5})
+                + 3*(\l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {11} - \tl_item:Nn \l__spath_tmpa_tl {8})
+              }
+            }
+            {\fp_to_dim:n
+              {
+                3*(1 - \l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {6} - \tl_item:Nn \l__spath_tmpa_tl {3})
+                + 6 * (1 - \l__spath_tmpa_fp) * (\l__spath_tmpa_fp) *  (\tl_item:Nn \l__spath_tmpa_tl {9} - \tl_item:Nn \l__spath_tmpa_tl {6})
+                + 3*(\l__spath_tmpa_fp)^2 * (\tl_item:Nn \l__spath_tmpa_tl {12} - \tl_item:Nn \l__spath_tmpa_tl {9})
+            }}
+          }
+        }
+      }
     }
   }
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpc_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_bake_round:n #1
+\cs_new_protected_nopar:Npn \spath_tangent_at:Nnn #1#2#3
 {
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \pgf@@processround\l__spath_tmpa_tl\l__spath_tmpb_tl
-  \spath_put:nnV {#1} {path} \l__spath_tmpb_tl
+  \__spath_tangent_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_close_path:n #1
+\cs_generate_variant:Nn \spath_tangent_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \spath_gtangent_at:Nnn #1#2#3
 {
-  \spath_get:nnN {#1} {initial point} \l__spath_tmpb_tl
-  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
-  \spath_if_in:nnT {#1} {reverse path}
+  \__spath_tangent_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtangent_at:Nnn {NVn, NVV, NnV}
+\cs_new_protected_nopar:Npn \__spath_transformation_at:nn #1#2
+{
+  \group_begin:
+  \tl_clear:N \l__spath_tmpa_tl
+  \__spath_tangent_at:nn {#1}{#2}
+  \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_output_tl
+  \fp_set:Nn \l__spath_tmpa_fp { sqrt( (\tl_item:Nn \l__spath_tmpb_tl {1})^2 +  (\tl_item:Nn \l__spath_tmpb_tl {2})^2 ) }
+  \fp_compare:nTF {\l__spath_tmpa_fp = 0}
   {
-    \spath_get:nnN {#1} {final point} \l__spath_tmpb_tl
-    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
-    \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
-    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
-    \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
+    \fp_set:Nn \l__spath_tmpa_fp {1}
+    \fp_set:Nn \l__spath_tmpb_fp {0}
   }
+  {
+    \fp_set:Nn \l__spath_tmpb_fp { (\tl_item:Nn \l__spath_tmpb_tl {2}) / \l__spath_tmpa_fp }
+    \fp_set:Nn \l__spath_tmpa_fp { (\tl_item:Nn \l__spath_tmpb_tl {1}) / \l__spath_tmpa_fp }
+  }
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    { \fp_to_decimal:n { \l__spath_tmpa_fp } }
+    { \fp_to_decimal:n { \l__spath_tmpb_fp } }
+    { \fp_to_decimal:n {- \l__spath_tmpb_fp } }
+    { \fp_to_decimal:n { \l__spath_tmpa_fp } }
+  }
+  \__spath_point_at:nn {#1}{#2}
+  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_map_component:Nn #1#2
+\cs_new_protected_nopar:Npn \spath_transformation_at:Nnn #1#2#3
 {
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 {#2}
-  \tl_set:NV \l__spath_tmpa_tl #1
-  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
+  \__spath_transformation_at:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_transformation_at:Nnn {NVn, NVV, NnV, NvV}
+\cs_new_protected_nopar:Npn \spath_gtransformation_at:Nnn #1#2#3
+{
+  \__spath_transformation_at:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gtransformation_at:Nnn {NVn, NVV, NnV}
+\tl_new:N \l__spath_split_path_a_tl
+\tl_new:N \l__spath_split_path_b_tl
+\tl_new:N \l__spath_split_path_a_start_tl
+\tl_new:N \l__spath_split_path_b_start_tl
+\tl_new:N \l__spath_split_path_a_end_tl
+\tl_new:N \l__spath_split_path_b_end_tl
+\tl_new:N \l__spath_split_path_a_final_tl
+\tl_new:N \l__spath_split_path_b_final_tl
+
+\tl_new:N \l__spath_split_prev_first_tl
+\tl_new:N \l__spath_split_prev_second_tl
+
+\seq_new:N \l__spath_split_first_seq
+\seq_new:N \l__spath_split_second_seq
+
+\int_new:N \l__spath_split_segment_int
+\cs_new_protected_nopar:Npn \spath_intersect:NN #1#2
+{
+  \pgfintersectionofpaths%
+  {%
+    \pgfsetpath #1
+  }{%
+    \pgfsetpath #2
   }
+}
+\tl_new:N \l__spath_intersecta_tl
+\tl_new:N \l__spath_intersectb_tl
+\cs_new_protected_nopar:Npn \spath_intersect:nn #1#2
+{
+  \tl_set:Nn \l__spath_intersecta_tl {#1}
+  \tl_set:Nn \l__spath_intersectb_tl {#2}
+  \spath_intersect:NN \l__spath_intersecta_tl \l__spath_intersectb_tl
+}
+\cs_new_protected_nopar:Npn \__spath_split_at_intersections:nn #1#2
+{
+  \group_begin:
+
+  % Clear some token lists and sequences
+  \tl_clear:N \l__spath_split_path_a_final_tl
+  \tl_clear:N \l__spath_split_path_b_final_tl
+  \seq_clear:N \l__spath_split_first_seq
+  \seq_clear:N \l__spath_split_second_seq
+
+  \pgfintersectionsortbyfirstpath
+  % Find the intersections of these segments
+  \tl_set:Nn \l__spath_split_path_a_tl {#1}
+  \tl_set:Nn \l__spath_split_path_b_tl {#2}
+  % Remove empty components
+
+  \spath_intersect:NN \l__spath_split_path_a_tl \l__spath_split_path_b_tl
+
+  % If we get intersections
+  \int_compare:nT {\pgfintersectionsolutions > 0}
   {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_if_eq:NNT \l__spath_tmpc_tl \g__spath_moveto_tl
+    % Find the times of the intersections on each path
+    \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
     {
-      \exp_args:NnV \use:c { __spath_map_ \int_use:N \g__spath_map_int :w } \l__spath_tmpb_tl
-\tl_clear:N \l__spath_tmpb_tl
+    \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+      \seq_put_left:NV \l__spath_split_first_seq \l__spath_split_first_tl
     }
-    \tl_if_single:NTF \l__spath_tmpc_tl
+  }
+
+  \spath_intersect:NN \l__spath_split_path_b_tl \l__spath_split_path_a_tl
+
+  % If we get intersections
+  \int_compare:nT {\pgfintersectionsolutions > 0}
+  {
+    % Find the times of the intersections on each path
+    \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
     {
-      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+    \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+      \seq_put_left:NV \l__spath_split_second_seq \l__spath_split_first_tl
+    }
+  }
+
+  \tl_set:Nn \l__spath_split_prev_first_tl {-1}
+
+  \seq_map_inline:Nn \l__spath_split_first_seq
+  {
+    \tl_set:Nn \l__spath_split_first_tl {##1}
+
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_first_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l__spath_split_first_tl) }
+      =
+      \fp_to_int:n {floor( \l__spath_split_prev_first_tl) }
     }
     {
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\l__spath_tmpc_tl}}
+      \tl_set:Nx \l__spath_split_first_tl
+      {
+        \fp_eval:n {
+          floor( \l__spath_split_first_tl )
+          +
+          ( \l__spath_split_first_tl - floor( \l__spath_split_first_tl) )
+          /
+          ( \l__spath_split_prev_first_tl - floor( \l__spath_split_prev_first_tl) )
+        }
+      }
     }
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set_eq:NN \l__spath_split_prev_first_tl \l__spath_tmpa_tl
+
+    \spath_split_at:NNVV \l__spath_split_path_a_start_tl \l__spath_split_path_a_end_tl  \l__spath_split_path_a_tl \l__spath_split_first_tl
+
+    \tl_put_left:NV \l__spath_split_path_a_final_tl \l__spath_split_path_a_end_tl
+    \tl_set_eq:NN \l__spath_split_path_a_tl \l__spath_split_path_a_start_tl
+
+  }
+
+  \tl_set:Nn \l__spath_split_prev_second_tl {-1}
+
+  \seq_map_inline:Nn \l__spath_split_second_seq
+  {
+    \tl_set:Nn \l__spath_split_second_tl {##1}
+
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_second_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l__spath_split_second_tl) }
+      =
+      \fp_to_int:n {floor( \l__spath_split_prev_second_tl) }
+    }
+    {
+      \tl_set:Nx \l__spath_split_second_tl
+      {
+        \fp_eval:n {
+          floor( \l__spath_split_second_tl )
+          +
+          ( \l__spath_split_second_tl - floor( \l__spath_split_second_tl) )
+          /
+          ( \l__spath_split_prev_second_tl - floor( \l__spath_split_prev_second_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l__spath_split_prev_second_tl \l__spath_tmpa_tl
+
+    \spath_split_at:NNVV \l__spath_split_path_b_start_tl \l__spath_split_path_b_end_tl  \l__spath_split_path_b_tl\l__spath_split_second_tl
+
+    \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_end_tl
+    \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_start_tl
+
+  }
+
+  \tl_put_left:NV \l__spath_split_path_a_final_tl \l__spath_split_path_a_tl
+  \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+
+  \tl_if_empty:NT \l__spath_split_path_a_final_tl
+  {
+    \tl_set_eq:NN \l__spath_split_path_a_final_tl \l__spath_split_path_a_tl
   }
+  \tl_if_empty:NT \l__spath_split_path_b_final_tl
+  {
+    \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+  }
+
+  \spath_remove_empty_components:N \l__spath_split_path_a_final_tl
+  \spath_remove_empty_components:N \l__spath_split_path_b_final_tl
+
+  \tl_gclear:N \g__spath_output_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_path_a_final_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_split_path_b_final_tl
+  \group_end:
 }
-\cs_new_nopar:Npn \spath_map_segment_inline:Nn #1#2
+\cs_new_protected_nopar:Npn \spath_split_at_intersections:NNnn #1#2#3#4
 {
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 ##2 {#2}
-  \spath_map_segment_function:Nc #1 { __spath_map_ \int_use:N \g__spath_map_int :w }
+  \__spath_split_at_intersections:nn {#3}{#4}
+  \tl_set:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_set:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_map_segment_inline:nn #1#2
+\cs_generate_variant:Nn \spath_split_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_new_protected_nopar:Npn \spath_split_at_intersections:NN #1#2
 {
-  \int_gincr:N \g__spath_map_int
-  \cs_gset:cpn { __spath_map_ \int_use:N \g__spath_map_int :w } ##1 ##2 {#2}
-  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
-  \spath_map_segment_function:Nc \l__spath_tmpd_tl { __spath_map_ \int_use:N \g__spath_map_int :w }
+  \spath_split_at_intersections:NNVV #1#2#1#2
 }
-\cs_new_nopar:Npn \spath_map_segment_function:nN #1#2
+\cs_generate_variant:Nn \spath_split_at_intersections:NN {cc}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NNnn #1#2#3#4
 {
-  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
-  \spath_map_segment_function:NN \l__spath_tmpd_tl #2
+  \__spath_split_at_intersections:nn {#3}{#4}
+  \tl_gset:Nx #1 {\tl_item:Nn \g__spath_output_tl {1}}
+  \tl_gset:Nx #2 {\tl_item:Nn \g__spath_output_tl {2}}
+  \tl_gclear:N \g__spath_output_tl
 }
-\cs_new_nopar:Npn \spath_map_segment_function:NN #1#2
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NN #1#2
 {
-  \tl_set_eq:NN \l__spath_tmpa_tl #1
-  \tl_clear:N \l__spath_tmpb_tl
-  \dim_zero:N \l__spath_tmpa_dim
-  \dim_zero:N \l__spath_tmpb_dim
+  \spath_gsplit_at_intersections:NNVV #1#2#1#2
+}
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NN {cc}
+\cs_new_protected_nopar:Npn \__spath_split_at_self_intersections:n #1
+{
+  \group_begin:
 
-  \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_tmpa_tl
+  % Copy the path
+  \tl_set:Nn \l__spath_split_path_b_tl {#1}
+
+  % Open the path
+  \spath_open:N \l__spath_split_path_b_tl
+  % Remove empty components
+  \spath_remove_empty_components:N \l__spath_split_path_b_tl
+  % Make a copy for later
+  \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+
+  % Clear some token lists and sequences
+  \tl_clear:N \l__spath_split_path_a_tl
+  \seq_clear:N \l__spath_split_first_seq
+  \int_zero:N \l__spath_split_segment_int
+
+  \pgfintersectionsortbyfirstpath
+
+  \bool_do_until:nn
+  {
+    \int_compare_p:n
+    {
+      \tl_count:N \l__spath_split_path_b_tl < 4
+    }
   }
   {
-    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
-    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \tl_case:NnF \l__spath_tmpc_tl
+    \tl_clear:N \l__spath_split_path_a_tl
+    \tl_put_right:Nx \l__spath_split_path_a_tl
     {
-      \g__spath_lineto_tl
-      {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl
+      \tl_item:Nn \l__spath_split_path_b_tl {1}
+      {\tl_item:Nn \l__spath_split_path_b_tl {2}}
+      {\tl_item:Nn \l__spath_split_path_b_tl {3}}
+    }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_tmpa_tl { \tl_item:Nn \l__spath_split_path_b_tl {4} }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+
+    \int_zero:N \l__spath_tmpa_int
 
+    \tl_case:Nn \l__spath_tmpa_tl
+    {
+      \c_spath_moveto_tl
+      {
+        \tl_clear:N \l__spath_split_path_a_tl
+        \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+        \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+        \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+      }
+      \c_spath_lineto_tl
+      {
+        \int_set:Nn \l__spath_tmpa_int {1}
+      }
+      \c_spath_curvetoa_tl
+      {
+        \int_set:Nn \l__spath_tmpa_int {3}
       }
+    }
 
-      \g__spath_curvetoa_tl
+    \prg_replicate:nn { \l__spath_tmpa_int }
+    {
+      \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+      \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+
+      \tl_put_right:Nx \l__spath_split_path_a_tl
       {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
-        {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
-        }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_curvetoa_tl
+        \tl_item:Nn \l__spath_split_path_b_tl {1}
+        {\tl_item:Nn \l__spath_split_path_b_tl {2}}
+        {\tl_item:Nn \l__spath_split_path_b_tl {3}}
+      }
 
-        \prg_replicate:nn {2} {
-          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N               \l__spath_tmpa_tl}}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-          \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N             \l__spath_tmpa_tl}
-          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-        }
+      \tl_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
+    }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_put_left:NV \l__spath_split_path_b_tl \c_spath_moveto_tl
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_if_empty:NF \l__spath_split_path_a_tl
+    {
+      % Intersect the current segment with the rest of the path
+      \spath_intersect:NN \l__spath_split_path_a_tl \l__spath_split_path_b_tl
 
+      % If we get intersections
+      \int_compare:nT {\pgfintersectionsolutions > 0}
+      {
+        % Find the times of the intersections on each path
+        \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
+        {
+          \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+          \fp_compare:nT
+          {
+            \l__spath_split_first_tl < .99
+          }
+          {
+            \tl_set:Nx \l__spath_tmpa_tl {\fp_to_decimal:n {\l__spath_split_first_tl +  \l__spath_split_segment_int}}
+            \seq_put_right:NV \l__spath_split_first_seq \l__spath_tmpa_tl
+          }
+        }
       }
 
-      \g__spath_closepath_tl
+      \spath_intersect:NN \l__spath_split_path_b_tl \l__spath_split_path_a_tl
+
+      % If we get intersections
+      \int_compare:nT {\pgfintersectionsolutions > 0}
       {
-        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
-        \tl_put_right:Nx \l__spath_tmpb_tl
+        % Find the times of the intersections on each path
+        \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
         {
-          {\dim_use:N \l__spath_tmpa_dim}
-          {\dim_use:N \l__spath_tmpb_dim}
+          \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
+          \fp_compare:nT
+          {
+            \l__spath_split_first_tl > .01
+          }
+          {
+            \tl_set:Nx \l__spath_tmpa_tl {\fp_to_decimal:n {\l__spath_split_first_tl +  \l__spath_split_segment_int + 1}}
+            \seq_put_right:NV \l__spath_split_first_seq \l__spath_tmpa_tl
+          }
         }
-        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl
+      }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    }
+    % Increment the segment counter
+    \int_incr:N \l__spath_split_segment_int
+  }
 
-        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+  % Sort the sequence by reverse order along the path
+  \seq_sort:Nn \l__spath_split_first_seq
+  {
+    \fp_compare:nNnTF { ##1 } < { ##2 }
+    { \sort_return_swapped: }
+    { \sort_return_same: }
+  }
 
-      }
+  % Restore the original copy of the path
+  \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_final_tl
+
+  % Clear the token lists
+  \tl_clear:N \l__spath_split_path_b_start_tl
+  \tl_clear:N \l__spath_split_path_b_end_tl
+  \tl_clear:N \l__spath_split_path_b_final_tl
 
+  \tl_set:Nn \l__spath_split_prev_first_tl {-1}
+
+  \seq_map_inline:Nn \l__spath_split_first_seq
+  {
+    \tl_set:Nn \l__spath_split_first_tl {##1}
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_first_tl
+    \int_compare:nT
+    {
+      \fp_to_int:n {floor( \l__spath_split_first_tl ) }
+      =
+      \fp_to_int:n {floor( \l__spath_split_prev_first_tl) }
     }
     {
+      \tl_set:Nx \l__spath_split_first_tl
+      {
+        \fp_eval:n {
+          floor( \l__spath_split_first_tl )
+          +
+          ( \l__spath_split_first_tl - floor( \l__spath_split_first_tl) )
+          /
+          ( \l__spath_split_prev_first_tl - floor( \l__spath_split_prev_first_tl) )
+        }
+      }
+    }
+    \tl_set_eq:NN \l__spath_split_prev_first_tl \l__spath_tmpa_tl
 
-      \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpc_tl
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \spath_split_at:NNVV \l__spath_split_path_b_start_tl \l__spath_split_path_b_end_tl  \l__spath_split_path_b_tl \l__spath_split_first_tl
 
-      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
-      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
-      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_end_tl
+    \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_start_tl
 
-    }
+  }
 
-    #2 \l__spath_tmpc_tl \l__spath_tmpb_tl
-    \tl_clear:N \l__spath_tmpb_tl
+  \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
 
+  \tl_if_empty:NT \l__spath_split_path_b_final_tl
+  {
+    \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
   }
+
+  \spath_remove_empty_components:N \l__spath_split_path_b_final_tl
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_split_path_b_final_tl
+  \group_end:
 }
-\cs_generate_variant:Nn \spath_map_segment_function:NN {Nc}
-\NewDocumentCommand \MakeSPath { m m }
-{
-  \spath_clear_new:n {#1}
-  \spath_put:nno {#1} {path} {#2}
-}
-\NewDocumentCommand \MakeSPathList { m m }
+\cs_new_protected_nopar:Npn \spath_split_at_self_intersections:Nn #1#2
 {
-  \tl_gclear_new:c {l__spath_list_#1}
-  \int_zero:N \l__spath_tmpa_int
-  \spath_map_component:Nn #2 {
-    \spath_clear_new:n {#1 _ \int_use:N \l__spath_tmpa_int}
-    \spath_put:nnn  {#1 _ \int_use:N \l__spath_tmpa_int} {path} {##1}
-    \tl_gput_right:cx {l__spath_list_#1} {{#1 _ \int_use:N \l__spath_tmpa_int}}
-    \int_incr:N \l__spath_tmpa_int
-  }
+  \__spath_split_at_self_intersections:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \CloneSPath { m m }
+\cs_generate_variant:Nn \spath_split_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_split_at_self_intersections:N #1
 {
-  \spath_clone:nn {#1} {#2}
+  \spath_split_at_self_intersections:NV #1#1
 }
-\NewDocumentCommand \SPathInfo { m m }
+\cs_generate_variant:Nn \spath_split_at_self_intersections:N {c}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:Nn #1#2
 {
-  \spath_get:nn {#1} {#2}
+  \__spath_split_at_self_intersections:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathPrepare { m }
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:N #1
 {
-  \spath_generate_all:n {#1}
+  \spath_gsplit_at_self_intersections:NV #1#1
 }
-\NewDocumentCommand \SPathListPrepare { m }
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:N {c}
+\tl_new:N \l__spath_tmpj_tl
+\cs_new_protected_nopar:Npn \__spath_join_component:nn #1#2
 {
-  \tl_map_inline:cn {l__spath_list_#1}
+  \group_begin:
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \int_compare:nT
+  {
+    #2 == 1
+  }
+  {
+    \tl_clear:N \l__spath_tmpj_tl
+    \seq_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpj_tl
+
+    \prg_replicate:nn {3}
+    {
+      \tl_set:Nx \l__spath_tmpj_tl {\tl_tail:N \l__spath_tmpj_tl}
+    }
+
+    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpj_tl
+  }
+  \bool_if:nT
   {
-    \spath_generate_all:n {##1}
+    \int_compare_p:n
+    {
+      #2 > 1
+    }
+    &&
+    \int_compare_p:n
+    {
+      #2 <= \seq_count:N \l__spath_tmpa_seq
+    }
   }
+  {
+
+    \seq_clear:N \l__spath_tmpb_seq
+    \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+    {
+      \tl_set:Nn \l__spath_tmpj_tl {##2}
+      \int_compare:nT {##1 = #2}
+      {
+        \prg_replicate:nn {3}
+        {
+          \tl_set:Nx \l__spath_tmpj_tl {\tl_tail:N \l__spath_tmpj_tl}
+        }
+      }
+      \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpj_tl
+    }
+
+    \seq_set_eq:NN \l__spath_tmpa_seq \l__spath_tmpb_seq
+  }
+
+  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpa_seq {} }
+  \group_end:
 }
-\NewDocumentCommand \SPathInfoInto { m m m }
+\cs_new_protected_nopar:Npn \spath_join_component:Nnn #1#2#3
 {
-  \tl_clear_new:N #3
-  \spath_get:nnN {#1} {#2} #3
+  \__spath_join_component:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathShow { m }
+\cs_generate_variant:Nn \spath_join_component:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_join_component:Nn #1#2
 {
-  \spath_show:n {#1}
+  \spath_join_component:NVn #1#1{#2}
 }
-\NewDocumentCommand \SPathTranslate { m m m }
+\cs_generate_variant:Nn \spath_join_component:Nn {cn, NV, cV}
+\cs_new_protected_nopar:Npn \spath_gjoin_component:Nnn #1#2#3
 {
-  \spath_translate:nnn {#1} {#2} {#3}
+  \__spath_join_component:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathTranslateInto { m m m m }
+\cs_generate_variant:Nn \spath_gjoin_component:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gjoin_component:Nn #1#2
 {
-  \spath_clone:nn {#1} {#2}
-  \spath_translate:nnn {#2} {#3} {#4}
+  \spath_gjoin_component:NVn #1#1{#2}
 }
-\NewDocumentCommand \SPathScale { m m m }
+\cs_generate_variant:Nn \spath_gjoin_component:Nn {cn, NV, cV}
+\cs_new_protected_nopar:Npn \__spath_spot_weld_components:n #1
 {
-  \spath_scale:nnn {#1} {#2} {#3}
+  \group_begin:
+  \dim_zero:N \l__spath_move_x_dim
+  \dim_zero:N \l__spath_move_y_dim
+
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \seq_clear:N \l__spath_tmpb_seq
+  \dim_set:Nn \l__spath_move_x_dim {\tl_item:nn {#1} {2} + 10 pt}
+  \dim_set:Nn \l__spath_move_y_dim {\tl_item:nn {#1} {3} + 10 pt}
+
+  \int_set:Nn \l__spath_tmpa_int {\seq_count:N \l__spath_tmpa_seq}
+
+  \seq_map_inline:Nn \l__spath_tmpa_seq
+  {
+    \tl_set:Nn \l__spath_tmpa_tl {##1}
+    \bool_if:nT
+    {
+      \dim_compare_p:n
+      {
+        \dim_abs:n {\l__spath_move_x_dim - \tl_item:Nn \l__spath_tmpa_tl {2} } < 0.01pt
+      }
+      &&
+      \dim_compare_p:n
+      {
+        \dim_abs:n {\l__spath_move_y_dim - \tl_item:Nn \l__spath_tmpa_tl {3} } < 0.01pt
+      }
+    }
+    {
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      }
+      \int_decr:N \l__spath_tmpa_int
+    }
+    \tl_reverse:N \l__spath_tmpa_tl
+    \dim_set:Nn \l__spath_move_x_dim {\tl_item:Nn \l__spath_tmpa_tl {2}}
+    \dim_set:Nn \l__spath_move_y_dim {\tl_item:Nn \l__spath_tmpa_tl {1}}
+    \tl_reverse:N \l__spath_tmpa_tl
+    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+  }
+
+  \tl_set:Nx \l__spath_tmpa_tl {\seq_use:Nn \l__spath_tmpb_seq {} }
+  \spath_components_to_seq:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+
+  \spath_initialpoint:Nn \l__spath_tmpa_tl {#1}
+  \spath_finalpoint:Nn \l__spath_tmpb_tl {#1}
+
+  \bool_if:nT
+  {
+    \dim_compare_p:n
+    {
+      \dim_abs:n {\tl_item:Nn \l__spath_tmpa_tl {1} - \tl_item:Nn \l__spath_tmpb_tl {1} } < 0.01pt
+    }
+    &&
+    \dim_compare_p:n
+    {
+      \dim_abs:n {\tl_item:Nn \l__spath_tmpa_tl {2} - \tl_item:Nn \l__spath_tmpb_tl {2} } < 0.01pt
+    }
+  }
+  {
+    \int_compare:nTF
+    {
+      \seq_count:N \l__spath_tmpb_seq > 1
+    }
+    {
+      \seq_pop_left:NN \l__spath_tmpb_seq \l__spath_tmpb_tl
+
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+      }
+      \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpb_tl
+    }
+    {
+      \tl_set:NV \l__spath_tmpb_tl \c_spath_closepath_tl
+      \tl_put_right:Nx \l__spath_tmpb_tl
+      {
+        { \tl_item:Nn \l__spath_tmpa_tl {1} }
+        { \tl_item:Nn \l__spath_tmpa_tl {2} }
+      }
+      \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpb_tl
+    }
+  }
+
+  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpb_seq {}}
+  \group_end:
 }
-\NewDocumentCommand \SPathScaleInto { m m m m }
+\cs_new_protected_nopar:Npn \spath_spot_weld_components:Nn #1#2
 {
-  \spath_clone:nn {#1} {#2}
-  \spath_scale:nnn {#2} {#3} {#4}
+  \__spath_spot_weld_components:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\NewDocumentCommand \SPathWeld { m m }
+\cs_generate_variant:Nn \spath_spot_weld_components:Nn {NV, cV, cn}
+\cs_new_protected_nopar:Npn \spath_spot_weld_components:N #1
 {
-  \spath_weld:nn {#1} {#2}
+  \spath_spot_weld_components:NV #1#1
 }
-\NewDocumentCommand \SPathWeldInto { m m m }
+\cs_generate_variant:Nn \spath_spot_weld_components:N {c}
+\cs_new_protected_nopar:Npn \spath_spot_gweld_components:Nn #1#2
 {
-  \spath_clone:nn {#1} {#2}
-  \spath_weld:nn {#2} {#3}
+  \__spath_spot_weld_components:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
 }
-\tikzset{
-  save~spath/.code={
-    \tikz@addmode{
-      \spath_get_current_path:n {#1}
-    }
-  },
-  restore~spath/.code={
-    \spath_set_current_path:n {#1}
-  }
+\cs_generate_variant:Nn \spath_spot_gweld_components:Nn {NV, cV, cn}
+\cs_new_protected_nopar:Npn \spath_spot_gweld_components:N #1
+{
+  \spath_spot_gweld_components:NV #1#1
 }
-\cs_new_nopar:Npn \spath_split_curve:nnNN #1#2#3#4
+\cs_generate_variant:Nn \spath_spot_gweld_components:N {c}
+\cs_new_protected_nopar:Npn \__spath_convert_to_svg:n #1
 {
   \group_begin:
-  \tl_gclear:N \l__spath_smuggle_tl
-  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl {
-    {\tl_item:nn {#2} {2}}
-    {\tl_item:nn {#2} {3}}
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_put_right:Nn \l__spath_tmpa_tl
+  {
+    <?xml~ version="1.0"~ standalone="no"?>
+    \iow_newline:
+    <!DOCTYPE~ svg~ PUBLIC~ "-//W3C//DTD SVG 1.1//EN"~
+    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+    \iow_newline:
+    <svg~ xmlns="http://www.w3.org/2000/svg"~ version="1.1"~viewBox="
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
+
+  \spath_minbb:Nn \l__spath_tmpb_tl {#1}
+  \spath_maxbb:Nn \l__spath_tmpc_tl {#1}
   \tl_put_right:Nx \l__spath_tmpa_tl
   {
-    {\fp_to_dim:n
+    \dim_to_decimal:n
     {
-      (1 - #1) * \tl_item:nn {#2} {2} + (#1) * \tl_item:nn {#2} {5}
-    }}
-    {\fp_to_dim:n
+      \tl_item:Nn \l__spath_tmpb_tl {1} - 10pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
     {
-      (1 - #1) * \tl_item:nn {#2} {3} + (#1) * \tl_item:nn {#2} {6}
-    }}
-  }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
-  {
-    {\fp_to_dim:n
+      \tl_item:Nn \l__spath_tmpb_tl {2} - 10pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
     {
-      (1 - #1)^2 * \tl_item:nn {#2} {2} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {5} + (#1)^2 * \tl_item:nn {#2} {8}
-    }}
-    {\fp_to_dim:n
+      \tl_item:Nn \l__spath_tmpc_tl {1}
+      -
+      \tl_item:Nn \l__spath_tmpb_tl {1}
+      + 20pt
+    }
+    \exp_not:n {~}
+    \dim_to_decimal:n
     {
-      (1 - #1)^2 * \tl_item:nn {#2} {3} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {6} + (#1)^2 * \tl_item:nn {#2} {9}
-    }}
+      \tl_item:Nn \l__spath_tmpc_tl {2}
+      -
+      \tl_item:Nn \l__spath_tmpb_tl {2}
+      + 20pt
+    }
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+
+  \tl_put_right:Nn \l__spath_tmpa_tl
   {
-    {\fp_to_dim:n
-      {
-      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
-    }}
+    ">
+    \iow_newline:
+    <path~ d="
   }
-  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
-  \group_end:
-  \tl_set_eq:NN #3 \l__spath_smuggle_tl
-  \group_begin:
-  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+  \tl_set:Nn \l__spath_tmpc_tl {use:n}
+  \tl_map_inline:Nn #1
   {
-    {\fp_to_dim:n
+    \tl_set:Nn \l__spath_tmpb_tl {##1}
+    \tl_case:NnF \l__spath_tmpb_tl
+    {
+      \c_spath_moveto_tl
       {
-      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
+        \tl_put_right:Nn \l__spath_tmpa_tl {M~}
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_lineto_tl
+      {
+        \tl_put_right:Nn \l__spath_tmpa_tl {L~}
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_closepath_tl
+      {
+        \tl_put_right:Nn \l__spath_tmpa_tl {Z~}
+        \tl_set:Nn \l__spath_tmpc_tl {use_none:n}
+      }
+      \c_spath_curvetoa_tl
+      {
+        \tl_put_right:Nn \l__spath_tmpa_tl {C~}
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_curvetob_tl {
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+      \c_spath_curveto_tl {
+        \tl_set:Nn \l__spath_tmpc_tl {use:n}
+      }
+    }
     {
-      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
-    }}
+      \tl_put_right:Nx \l__spath_tmpa_tl {\use:c { \l__spath_tmpc_tl } {\dim_to_decimal:n {##1}} ~}
+    }
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+  \tl_put_right:Nn \l__spath_tmpa_tl
   {
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {5} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {8} + (#1)^2 * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1)^2 * \tl_item:nn {#2} {6} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {9} + (#1)^2 * \tl_item:nn {#2} {12}
-    }}
+    "~ fill="none"~ stroke="black"~ />
+    \iow_newline:
+    </svg>
+    \iow_newline:
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_convert_to_svg:Nn #1#2
+{
+  \__spath_convert_to_svg:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_new_protected_nopar:Npn \spath_gconvert_to_svg:Nn #1#2
+{
+  \__spath_convert_to_svg:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\iow_new:N \g__spath_stream
+\cs_new_protected_nopar:Npn \spath_export_to_svg:nn #1#2
+{
+  \spath_convert_path_to_svg:Nn \l__spath_iterp_tl {#2}
+  \iow_open:Nn \g__spath_stream {#1 .svg}
+  \iow_now:Nx \g__spath_stream
   {
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {8} + (#1) * \tl_item:nn {#2} {11}
-    }}
-    {\fp_to_dim:n
-    {
-      (1 - #1) * \tl_item:nn {#2} {9} + (#1) * \tl_item:nn {#2} {12}
-    }}
+    \tl_use:N \l__spath_iterp_tl
   }
-  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
-  \tl_put_right:Nx \l__spath_tmpa_tl {
-    {\tl_item:nn {#2} {11}}
-    {\tl_item:nn {#2} {12}}
+  \iow_close:N \g__spath_stream
+}
+\cs_new_protected_nopar:Npn \spath_show:n #1
+{
+  \int_step_inline:nnnn {1} {3} {\tl_count:n {#1}}
+  {
+    \iow_term:x {
+      \tl_item:Nn \l__spath_tmpa_tl {##1}
+      {\tl_item:Nn \l__spath_tmpa_tl {##1+1}}
+      {\tl_item:Nn \l__spath_tmpa_tl {##1+2}}
+    }
   }
-  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
-  \group_end:
-  \tl_set_eq:NN #4 \l__spath_smuggle_tl
 }
+\cs_generate_variant:Nn \spath_show:n {V, v}
 
-\cs_generate_variant:Nn \spath_split_curve:nnNN {nVNN, VVNN}
+\cs_new_protected_nopar:Npn \spath_get_current_path:N #1
+{
+  \pgfsyssoftpath@getcurrentpath #1
+}
+\cs_new_protected_nopar:Npn \spath_gget_current_path:N #1
+{
+  \pgfsyssoftpath@getcurrentpath #1
+  \tl_gset_eq:NN #1 #1
+}
+\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
+{
+  \spath_minbb:Nn \l__spath_tmpa_tl {#1}
+  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
+
+  \spath_maxbb:Nn \l__spath_tmpa_tl {#1}
+  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
+}
+\cs_generate_variant:Nn \spath_protocol_path:n {V}
+\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
+{
+  \spath_protocol_path:n {#1}
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \pgfsyssoftpath@setcurrentpath\l__spath_tmpa_tl
+}
+\cs_new_protected_nopar:Npn \spath_set_current_path:N #1
+{
+  \spath_protocol_path:V #1
+  \pgfsyssoftpath@setcurrentpath #1
+}
+\cs_generate_variant:Nn \spath_set_current_path:N {c}
+\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
+{
+  \spath_set_current_path:n {#1}
+  \pgfusepath{#2}
+}
+\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
+{
+  \path[#1] \pgfextra{
+    \spath_set_current_path:n {#2}
+    \tl_put_right:Nn \tikz@preactions {\def\tikz@actions@path{#2}}
+  };
+}
+\cs_generate_variant:Nn \spath_tikz_path:nn {Vn, VV, nv, Vv, nV}
+\cs_new_protected_nopar:Npn \spath_set_tikz_coords:n #1
+{
+  \spath_finalpoint:Nn \l__spath_tmpa_tl {#1}
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    \exp_not:c {tikz@lastx}=\tl_item:Nn \l__spath_tmpa_tl {1}
+    \exp_not:c {tikz@lasty}=\tl_item:Nn \l__spath_tmpa_tl {2}
+    \exp_not:c {tikz@lastxsaved}=\tl_item:Nn \l__spath_tmpa_tl {1}
+    \exp_not:c {tikz@lastysaved}=\tl_item:Nn \l__spath_tmpa_tl {2}
+  }
+  \tl_use:N \l__spath_tmpa_tl
+}
+\cs_generate_variant:Nn \spath_set_tikz_coords:n {V, v}
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -1500,13 +3130,16 @@ manipulating PGF soft paths}
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
index 9b0e082b144..e987539cb0b 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
@@ -4,10 +4,10 @@
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `calligraphy')
+%% spath3_code.dtx  (with options: `calligraphy')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
@@ -17,10 +17,24 @@
 
 \tl_new:N \l__cal_tmpa_tl
 \tl_new:N \l__cal_tmpb_tl
+\tl_new:N \l__cal_tmp_path_tl
+\tl_new:N \l__cal_tmp_rpath_tl
+\tl_new:N \l__cal_tmp_rpathb_tl
+\tl_new:N \l__cal_tmp_patha_tl
+
+\seq_new:N \l__cal_tmpa_seq
+
 \int_new:N \l__cal_tmpa_int
 \int_new:N \l__cal_tmpb_int
-\int_new:N \l__cal_path_component_int
-\int_new:N \l__cal_label_int
+\int_new:N \g__cal_path_component_int
+\int_new:N \g__cal_label_int
+
+\fp_new:N \l__cal_tmpa_fp
+\fp_new:N \l__cal_tmpb_fp
+\fp_new:N \l__cal_tmpc_fp
+\fp_new:N \l__cal_tmpd_fp
+\fp_new:N \l__cal_tmpe_fp
+
 \dim_new:N \l__cal_tmpa_dim
 \dim_new:N \l__cal_tmpb_dim
 \dim_new:N \l__cal_tmpc_dim
@@ -29,10 +43,12 @@
 \dim_new:N \l__cal_tmpf_dim
 \dim_new:N \l__cal_tmpg_dim
 \dim_new:N \l__cal_tmph_dim
+
 \bool_new:N \l__cal_annotate_bool
 \bool_new:N \l__cal_taper_start_bool
 \bool_new:N \l__cal_taper_end_bool
 \bool_new:N \l__cal_taperable_bool
+
 \dim_new:N \l__cal_taper_width_dim
 \dim_new:N \l__cal_line_width_dim
 
@@ -40,27 +56,35 @@
 \bool_set_true:N \l__cal_taper_end_bool
 
 \cs_generate_variant:Nn \tl_put_right:Nn {Nv}
+
+\msg_new:nnn { calligraphy } { undefined pen } { The~ pen~ "#1"~ is~ not~ defined. }
 \tikzset{
   define~pen/.code={
     \tikzset{pen~name=#1}
     \pgf@relevantforpicturesizefalse
     \tikz@addmode{
       \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
-      \MakeSPathList{calligraphy pen \pgfkeysvalueof{/tikz/pen~name}}{\l__cal_tmpa_tl}
-      \SPathListPrepare{calligraphy pen \pgfkeysvalueof{/tikz/pen~name}}
+      \spath_components_to_seq:NV \l__cal_tmpa_seq \l__cal_tmpa_tl
+      \seq_gclear_new:c {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      \seq_gset_eq:cN {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq} \l__cal_tmpa_seq
       \pgfusepath{discard}%
     }
   },
   define~pen/.default={default},
   use~pen/.code={
     \tikzset{pen~name=#1}
-    \int_gzero:N \l__cal_path_component_int
+    \int_gzero:N \g__cal_path_component_int
     \cs_set_eq:NN \pgfpathmoveto \cal_moveto:n
     \tikz@addmode{
       \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
-      \MakeSPathList{calligraphy path}{\l__cal_tmpa_tl}
-      \SPathListPrepare{calligraphy path}
-      \CalligraphyPathCreate{calligraphy path}{\pgfkeysvalueof{/tikz/pen~name}}
+      \spath_components_to_seq:NV \l__cal_tmpa_seq \l__cal_tmpa_tl
+      \tl_if_exist:cTF {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      {
+        \cal_path_create:Nc \l__cal_tmpa_seq {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq}
+      }
+      {
+        \msg_warning:nnx { calligraphy } { undefined pen } { \pgfkeysvalueof{/tikz/pen~name} }
+      }
     }
   },
   use~pen/.default={default},
@@ -132,8 +156,8 @@
     \tl_set:cn {l__cal_stroke_style_#1} {#2}
   },
   this~stroke~style/.code={
-    \tl_clear_new:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_path_component_int}
-    \tl_set:cn {l__cal_stroke_inline_style_ \int_use:N \l__cal_path_component_int} {#1}
+    \tl_clear_new:c {l__cal_stroke_inline_style_ \int_use:N \g__cal_path_component_int}
+    \tl_set:cn {l__cal_stroke_inline_style_ \int_use:N \g__cal_path_component_int} {#1}
   },
   annotate/.style={
     annotate~if,
@@ -151,12 +175,13 @@
     }
   },
   annotate~reset/.code={
-    \int_gzero:N \l__cal_label_int
+    \int_gzero:N \g__cal_label_int
   },
   annotation~style/.initial={draw,->},
   annotation~shift/.initial={(0,1ex)},
   every~annotation~node/.initial={anchor=south~west},
   annotation~node~style/.code~2~args={
+    \tl_clear_new:c {l__cal_annotation_style_ #1 _tl}
     \tl_set:cn {l__cal_annotation_style_ #1 _tl}{#2}
   },
   tl~use:N/.code={
@@ -179,7 +204,7 @@
     {
       \pgfkeyssetvalue{\pgfkeyscurrentpath}{#1}
     }
-  }
+  },
 }
 \NewDocumentCommand \pen { O{} }
 {
@@ -195,100 +220,99 @@
 {
   \path[use~ pen,every~ calligraphy/.try,#1]
 }
-\NewDocumentCommand \CalligraphyPathCreate { m m }
+\cs_new_protected_nopar:Npn \cal_path_create:NN #1#2
 {
   \int_zero:N \l__cal_tmpa_int
-  \tl_map_inline:cn {l__spath_list_#1}
+  \seq_map_inline:Nn #1
   {
-    \int_incr:N \l__cal_tmpa_int
-    \int_zero:N \l__cal_tmpb_int
-    \tl_map_inline:cn {l__spath_list_calligraphy pen #2}
+    \int_compare:nT {\tl_count:n {##1} > 3}
     {
-      \int_incr:N \l__cal_tmpb_int
-      \group_begin:
-      \pgfsys@beginscope
-
-      \cal_apply_style:c {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-      \cal_apply_style:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-      \cal_apply_style:c {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-
-      \spath_clone:nn {##1} {calligraphy temp path}
 
-      \__spath_get:nnN {####1} {initial point} \l__cal_tmpa_tl
-      \spath_translate:nV {calligraphy temp path} \l__cal_tmpa_tl
+      \int_incr:N \l__cal_tmpa_int
+      \int_zero:N \l__cal_tmpb_int
 
-      \__spath_get:nnN {####1} {length} \l__cal_tmpa_tl
+      \tl_set:Nn \l__cal_tmp_path_tl {##1}
+      \spath_open:N \l__cal_tmp_path_tl
+      \spath_reverse:NV \l__cal_tmp_rpath_tl \l__cal_tmp_path_tl
 
-      \int_compare:nTF {\l__cal_tmpa_tl = 1}
+      \seq_map_inline:Nn #2
       {
-        \cal_at_least_three:n {calligraphy temp path}
-
-        \spath_protocol_path:n {calligraphy temp path}
+        \int_incr:N \l__cal_tmpb_int
+        \group_begin:
+        \pgfsys@beginscope
+        \cal_apply_style:c {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
+        \cal_apply_style:c {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
+        \cal_apply_style:c {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
+
+        \spath_initialpoint:Nn \l__cal_tmpa_tl {####1}
+        \tl_set_eq:NN \l__cal_tmp_patha_tl \l__cal_tmp_path_tl
+        \spath_translate:NV \l__cal_tmp_patha_tl \l__cal_tmpa_tl
+
+        \int_compare:nTF {\tl_count:n {####1} == 3}
+        {
+          \cal_at_least_three:N \l__cal_tmp_patha_tl
+          \spath_protocol_path:V \l__cal_tmp_patha_tl
 
-        \__spath_get:nnN {calligraphy temp path} {path} \l__cal_tmpa_tl
+          \tikz@options
+          \dim_set:Nn \l__cal_line_width_dim {\pgflinewidth}
+          \cal_maybe_taper:N \l__cal_tmp_patha_tl
+        }
+        {
+          \spath_weld:Nn \l__cal_tmp_patha_tl {####1}
+          \spath_weld:NV \l__cal_tmp_patha_tl \l__cal_tmp_rpath_tl
+          \spath_reverse:Nn \l__cal_tmp_rpathb_tl {####1}
+          \spath_weld:NV \l__cal_tmp_patha_tl \l__cal_tmp_rpathb_tl
+
+          \tl_clear:N \l__cal_tmpa_tl
+          \tl_set:Nn \l__cal_tmpa_tl {fill=\pgfkeysvalueof{/tikz/pen~colour},draw=none}
+          \tl_if_exist:cT  {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
+          {
+            \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
+          }
+          \tl_if_exist:cT  {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
+          {
+            \tl_put_right:Nn \l__cal_tmpa_tl {,}
+            \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
+          }
+          \tl_if_exist:cT  {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
+          {
+            \tl_put_right:Nn \l__cal_tmpa_tl {,}
+            \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
+          }
+          \spath_tikz_path:VV \l__cal_tmpa_tl \l__cal_tmp_patha_tl
 
-        \tikz@options
-        \dim_set:Nn \l__cal_line_width_dim {\pgflinewidth}
-        \cal_maybe_taper:N \l__cal_tmpa_tl
+        }
+        \pgfsys@endscope
+        \group_end:
       }
+
+      \bool_if:NT \l__cal_annotate_bool
       {
+        \seq_get_right:NN #2 \l__cal_tmpa_tl
+        \spath_finalpoint:NV \l__cal_tmpa_tl \l__cal_tmpa_tl
+        \spath_translate:NV \l__cal_tmp_path_tl \l__cal_tmpa_tl
+        \tikz@scan@one@point\pgfutil@firstofone\pgfkeysvalueof{/tikz/annotation~shift}
 
-        \spath_weld:nn {calligraphy temp path} {####1}
-        \spath_reverse:n {##1}
-        \spath_reverse:n {####1}
-        \spath_weld:nn {calligraphy temp path} {##1}
-        \spath_weld:nn {calligraphy temp path} {####1}
-        \spath_reverse:n {##1}
-        \spath_reverse:n {####1}
-
-        \tl_clear:N \l__cal_tmpa_tl
-        \tl_set:Nn \l__cal_tmpa_tl {fill=\pgfkeysvalueof{/tikz/pen~colour},draw=none}
-        \tl_if_exist:cT  {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-        {
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_style_ \int_use:N \l__cal_tmpa_int}
-        }
-        \tl_if_exist:cT  {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-        {
-          \tl_put_right:Nn \l__cal_tmpa_tl {,}
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_stroke_inline_style_ \int_use:N \l__cal_tmpa_int}
-        }
-        \tl_if_exist:cT  {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-        {
-          \tl_put_right:Nn \l__cal_tmpa_tl {,}
-          \tl_put_right:Nv \l__cal_tmpa_tl {l__cal_nib_style_ \int_use:N \l__cal_tmpb_int}
-        }
-        \spath_tikz_path:Vn \l__cal_tmpa_tl {calligraphy temp path}
+        \spath_translate:Nnn \l__cal_tmp_path_tl {\pgf@x} {\pgf@y}
 
+        \pgfkeysgetvalue{/tikz/annotation~style}{\l__cal_tmpa_tl}
+        \spath_tikz_path:VV \l__cal_tmpa_tl \l__cal_tmp_path_tl
+
+        \spath_finalpoint:NV \l__cal_tmpa_tl \l__cal_tmp_path_tl
+
+        \exp_last_unbraced:NV \pgfqpoint \l__cal_tmpa_tl
+        \begin{scope}[reset~ cm]
+        \node[every~annotation~node/.try,tl~use:c =  {l__cal_annotation_style_ \int_use:N \l__cal_tmpa_int _tl}] at (\pgf@x,\pgf@y) {\int_use:N \l__cal_tmpa_int};
+        \end{scope}
       }
-      \pgfsys@endscope
-      \group_end:
-    }
-    \bool_if:NT \l__cal_annotate_bool
-    {
-      \spath_clone:nn {##1} {calligraphy temp path}
-      \tl_set_eq:Nc \l_tmpa_tl {l__spath_list_calligraphy pen #2}
-      \tl_reverse:N \l_tmpa_tl
-      \tl_set:Nx \l_tmpa_tl {\tl_head:N \l_tmpa_tl}
-      \spath_generate_finalpoint:V \l_tmpa_tl
-      \spath_get:VnN \l_tmpa_tl {final point} \l_tmpa_tl
-      \spath_translate:nV {calligraphy temp path} \l_tmpa_tl
-      \tikz@scan@one@point\pgfutil@firstofone\pgfkeysvalueof{/tikz/annotation~shift}
-      \spath_translate:nnn {calligraphy temp path} {\pgf@x} {\pgf@y}
-
-      \pgfkeysgetvalue{/tikz/annotation~style}{\l_tmpa_tl}
-      \spath_tikz_path:Vn \l_tmpa_tl {calligraphy temp path}
-      \spath_get:nnN {calligraphy temp path} {final point} \l_tmpa_tl
-      \exp_last_unbraced:NV \pgfqpoint \l_tmpa_tl
-      \begin{scope}[reset~ cm]
-      \node[every~annotation~node/.try,tl~use:c =  {l__cal_annotation_style_ \int_use:N \l__cal_tmpa_int _tl}] at (\pgf@x,\pgf@y) {\int_use:N \l__cal_tmpa_int};
-      \end{scope}
     }
   }
 }
+\cs_generate_variant:Nn \cal_path_create:NN {Nc}
 \cs_new_eq:NN \cal_orig_moveto:n \pgfpathmoveto
 \cs_new_nopar:Npn \cal_moveto:n #1
 {
-  \int_gincr:N \l__cal_path_component_int
+  \int_gincr:N \g__cal_path_component_int
   \cal_orig_moveto:n {#1}
 }
 \cs_new_nopar:Npn \cal_apply_style:N #1
@@ -298,154 +322,32 @@
   }
 }
 \cs_generate_variant:Nn \cal_apply_style:N {c}
-\cs_new_nopar:Npn \cal_at_least_three:n #1
+\cs_new_protected_nopar:Npn \cal_at_least_three:Nn #1#2
 {
-  \spath_get:nnN {#1} {real length} \l__cal_tmpa_tl
+  \spath_reallength:Nn \l__cal_tmpa_int {#2}
   \tl_clear:N \l__cal_tmpb_tl
-  \int_compare:nTF {\l__cal_tmpa_tl = 1}
+  \tl_set:Nn \l__cal_tmpb_tl {#2}
+  \int_compare:nTF {\l__cal_tmpa_int = 1}
   {
-    \spath_get:nnN {#1} {path} \l__cal_tmpa_tl
-    \spath_map_segment_inline:Nn \l__cal_tmpa_tl
-    {
-      \tl_case:NnF ##1 {
-        \g__spath_lineto_tl {
-          \cal_split_line_in_three:NN \l__cal_tmpb_tl ##2
-        }
-        \g__spath_curvetoa_tl {
-          \cal_split_curve_in_three:NN \l__cal_tmpb_tl ##2
-        }
-      }
-      {
-        \tl_put_right:NV \l__cal_tmpb_tl ##2
-      }
-    }
-    \spath_put:nnV {#1} {path} \l__cal_tmpb_tl
+    \spath_split_at:Nn \l__cal_tmpb_tl {2/3}
+    \spath_split_at:Nn \l__cal_tmpb_tl {1/2}
   }
   {
-    \int_compare:nT {\l__cal_tmpa_tl = 2}
+    \int_compare:nT {\l__cal_tmpa_int = 2}
     {
-      \spath_get:nnN {#1} {path} \l__cal_tmpa_tl
-      \spath_map_segment_inline:Nn \l__cal_tmpa_tl
-      {
-        \tl_case:NnF ##1 {
-          \g__spath_lineto_tl {
-            \cal_split_line_in_two:NN \l__cal_tmpb_tl ##2
-          }
-          \g__spath_curvetoa_tl {
-            \cal_split_curve_in_two:NN \l__cal_tmpb_tl ##2
-          }
-        }
-        {
-          \tl_put_right:NV \l__cal_tmpb_tl ##2
-        }
-      }
-      \spath_put:nnV {#1} {path} \l__cal_tmpb_tl
+      \spath_split_at:Nn \l__cal_tmpb_tl {1.5}
+      \spath_split_at:Nn \l__cal_tmpb_tl {.5}
     }
   }
+  \tl_set_eq:NN #1 \l__cal_tmpb_tl
 }
-\cs_new_nopar:Npn \cal_split_line_in_two:NN #1#2
+\cs_generate_variant:Nn \cal_at_least_three:Nn {NV}
+\cs_new_protected_nopar:Npn \cal_at_least_three:N #1
 {
-  \tl_set_eq:NN \l__cal_tmpc_tl #2
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpa_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpb_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpc_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-  \dim_set:Nn \l__cal_tmpd_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(\l__cal_tmpa_dim + \l__cal_tmpc_dim)/2}}
-    {\dim_eval:n {(\l__cal_tmpb_dim + \l__cal_tmpd_dim)/2}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-  \tl_put_right:Nx #1 {
-    {\dim_use:N \l__cal_tmpc_dim}
-    {\dim_use:N \l__cal_tmpd_dim}
-  }
+  \cal_at_least_three:NV #1#1
 }
-\cs_new_nopar:Npn \cal_split_line_in_three:NN #1#2
-{
-  \tl_set_eq:NN \l__cal_tmpc_tl #2
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpa_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpb_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \dim_set:Nn \l__cal_tmpc_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-  \dim_set:Nn \l__cal_tmpd_dim {\tl_head:N \l__cal_tmpc_tl}
-  \tl_set:Nx \l__cal_tmpc_tl {\tl_tail:N \l__cal_tmpc_tl}
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(2\l__cal_tmpa_dim + \l__cal_tmpc_dim)/3}}
-    {\dim_eval:n {(2\l__cal_tmpb_dim + \l__cal_tmpd_dim)/3}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-
-  \tl_put_right:Nx #1 {
-    {\dim_eval:n {(\l__cal_tmpa_dim + 2\l__cal_tmpc_dim)/3}}
-    {\dim_eval:n {(\l__cal_tmpb_dim + 2\l__cal_tmpd_dim)/3}}
-  }
-
-  \tl_put_right:NV #1 \g__spath_lineto_tl
-  \tl_put_right:Nx #1 {
-    {\dim_use:N \l__cal_tmpc_dim}
-    {\dim_use:N \l__cal_tmpd_dim}
-  }
-}
-\cs_new_nopar:Npn \cal_split_curve_in_two:NN #1#2
-{
-  \spath_split_curve:nVNN {.5} #2 \l_tmpa_tl \l_tmpb_tl
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-  \tl_put_right:NV #1 \l_tmpb_tl
-}
-\cs_new_nopar:Npn \cal_split_curve_in_three:NN #1#2
-{
-  \spath_split_curve:nVNN {1/3} #2 \l_tmpa_tl \l_tmpb_tl
-
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-
-  \spath_split_curve:nVNN {.5} \l_tmpb_tl \l_tmpa_tl \l_tmpb_tl
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-  \tl_put_right:NV #1 \l_tmpa_tl
-  \tl_put_right:NV #1 \l_tmpb_tl
-}
-\cs_new_nopar:Npn \cal_maybe_taper:N #1
+\cs_generate_variant:Nn \cal_at_least_three:N {c}
+\cs_new_protected_nopar:Npn \cal_maybe_taper:N #1
 {
   \tl_set_eq:NN \l__cal_tmpa_tl #1
 
@@ -458,7 +360,7 @@
 
     \tl_case:NnF \l__cal_tmpb_tl
     {
-      \g__spath_lineto_tl
+      \c_spath_lineto_tl
       {
 
         \bool_set_true:N \l__cal_taperable_bool
@@ -472,9 +374,9 @@
         {
           \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
         }
-        \tl_put_left:NV \l__cal_tmpa_tl \g__spath_moveto_tl
+        \tl_put_left:NV \l__cal_tmpa_tl \c_spath_moveto_tl
       }
-      \g__spath_curvetoa_tl
+      \c_spath_curvetoa_tl
       {
         \bool_set_true:N \l__cal_taperable_bool
         \dim_set:Nn \l__cal_tmpc_dim {\tl_item:Nn \l__cal_tmpa_tl {5}}
@@ -487,7 +389,7 @@
         {
           \tl_set:Nx \l__cal_tmpa_tl {\tl_tail:N \l__cal_tmpa_tl}
         }
-        \tl_put_left:NV \l__cal_tmpa_tl \g__spath_moveto_tl
+        \tl_put_left:NV \l__cal_tmpa_tl \c_spath_moveto_tl
       }
     }
     {
@@ -510,7 +412,7 @@
 
     \tl_case:NnF \l__cal_tmpb_tl
     {
-      \g__spath_lineto_tl
+      \c_spath_lineto_tl
       {
 
         \bool_set_true:N \l__cal_taperable_bool
@@ -527,7 +429,7 @@
         }
         \tl_reverse:N \l__cal_tmpa_tl
       }
-      \g__spath_curveto_tl
+      \c_spath_curveto_tl
       {
         \bool_set_true:N \l__cal_taperable_bool
         \dim_set:Nn \l__cal_tmpc_dim {\tl_item:Nn \l__cal_tmpa_tl {-5}}
@@ -560,10 +462,10 @@
   \pgfusepath{stroke}
 
 }
-\cs_new_nopar:Npn \__cal_taper_aux:
+\cs_new_protected_nopar:Npn \__cal_taper_aux:
 {
   \tl_clear:N \l__cal_tmpb_tl
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_moveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_moveto_tl
 
   \fp_set:Nn \l__cal_tmpa_fp
   {
@@ -603,7 +505,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp +             \l__cal_tmpb_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -611,7 +513,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpd_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -619,7 +521,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmpf_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -627,7 +529,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -635,7 +537,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32* \l__cal_tmpc_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -643,7 +545,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32 * \l__cal_tmpc_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -651,7 +553,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -659,7 +561,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmpf_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -667,7 +569,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpd_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -675,7 +577,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetoa_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -683,7 +585,7 @@
     {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32* \l__cal_tmpa_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curvetob_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -691,7 +593,7 @@
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32 * \l__cal_tmpa_fp}}}
   }
 
-  \tl_put_right:NV \l__cal_tmpb_tl \g__spath_curveto_tl
+  \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
@@ -704,8 +606,14 @@
   \pgfusepath{fill}
 }
 \tl_set:Nn \l__cal_tmpa_tl {\pgfsyssoftpath@movetotoken{0pt}{0pt}}
-\MakeSPathList{calligraphy pen copperplate}{\l__cal_tmpa_tl}
-\SPathListPrepare{calligraphy pen copperplate}
+\spath_components_to_seq:NV \l__cal_tmpa_seq \l__cal_tmpa_tl
+\seq_gclear_new:N \g__cal_pen_copperplate_seq
+\seq_gset_eq:NN \g__cal_pen_copperplate_seq \l__cal_tmpa_seq
+\DeclareDocumentCommand \CopperplatePath { m }
+{
+  \spath_components_to_seq:NV \l__cal_tmpa_seq #1
+  \cal_path_create:NN \l__cal_tmpa_seq \g__cal_pen_copperplate_seq
+}
 \ExplSyntaxOff
 \expandafter\ifx\csname pgfdeclaredecoration\endcsname\relax
 \else
@@ -745,9 +653,7 @@
       taper
     }%
     \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
+    \CopperplatePath{\cal@tmp@path}
   }
   \state{final}{}
 }
@@ -774,9 +680,7 @@
       taper
     }%
     \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
+    \CopperplatePath{\cal@tmp@path}
   }
   \state{final}{}%
 }
@@ -798,15 +702,13 @@
       taper
     }%
     \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \MakeSPathList{calligraphy path}{\cal@tmp@path}%
-    \SPathListPrepare{calligraphy path}%
-    \CalligraphyPathCreate{calligraphy path}{copperplate}%
+    \CopperplatePath{\cal@tmp@path}
   }
   \state{final}{}%
 }
 \fi
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -821,13 +723,16 @@
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
index 0322a679410..5872a71fdf3 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
@@ -4,17 +4,17 @@
 %%
 %% The original source files were:
 %%
-%% spath3.dtx  (with options: `knots')
+%% spath3_code.dtx  (with options: `knots')
 %% ----------------------------------------------------------------
 %% spath3 --- Functions for manipulating PGF soft paths
-%% E-mail: stacey@math.ntnu.no
+%% E-mail: loopspace@mathforge.org
 %% Released under the LaTeX Project Public License v1.3c or later
 %% See http://www.latex-project.org/lppl.txt
 %% ----------------------------------------------------------------
 %% 
 %%
 \RequirePackage{spath3}
-\usetikzlibrary{intersections}
+\usetikzlibrary{intersections,spath3}
 
 \ExplSyntaxOn
 
@@ -22,8 +22,6 @@
 \tl_new:N \l__knot_tmpb_tl
 \tl_new:N \l__knot_tmpc_tl
 \tl_new:N \l__knot_tmpd_tl
-\tl_new:N \l__knot_tmpe_tl
-\tl_new:N \l__knot_tmpf_tl
 \tl_new:N \l__knot_tmpg_tl
 \tl_new:N \l__knot_redraws_tl
 \tl_new:N \l__knot_clip_width_tl
@@ -31,16 +29,21 @@
 \tl_new:N \l__knot_node_tl
 \tl_new:N \l__knot_aux_tl
 \tl_new:N \l__knot_auxa_tl
+\tl_new:N \l__knot_prefix_tl
+
+\seq_new:N \l__knot_segments_seq
 
 \int_new:N \l__knot_tmpa_int
 \int_new:N \l__knot_strands_int
-\int_new:N \l__knot_intersections_int
-\int_new:N \l__knot_filaments_int
+\int_new:N \g__knot_intersections_int
+\int_new:N \g__knot_filaments_int
 \int_new:N \l__knot_component_start_int
 
+\fp_new:N \l__knot_tmpa_fp
+\fp_new:N \l__knot_tmpb_fp
+
 \dim_new:N \l__knot_tmpa_dim
 \dim_new:N \l__knot_tmpb_dim
-\dim_new:N \l__knot_tmpc_dim
 \dim_new:N \l__knot_tolerance_dim
 \dim_new:N \l__knot_clip_bg_radius_dim
 \dim_new:N \l__knot_clip_draw_radius_dim
@@ -56,10 +59,16 @@
 \bool_new:N \l__knot_skip_bool
 \bool_new:N \l__knot_save_bool
 
-\seq_new:N \l__knot_nodes_seq
+\seq_new:N \g__knot_nodes_seq
 
 \bool_set_true:N \l__knot_ignore_ends_bool
 \tikzset{
+  spath/prefix/knot/.style={
+    spath/set~ prefix=knot strand,
+  },
+  spath/suffix/knot/.style={
+    spath/set~ suffix={},
+  },
   knot/.code={
     \tl_if_eq:nnTF {#1} {none}
     {
@@ -218,7 +227,7 @@
   \int_incr:N \l__knot_strands_int
   \tl_clear_new:c {l__knot_options_strand \int_use:N \l__knot_strands_int}
   \tl_set:cn {l__knot_options_strand \int_use:N \l__knot_strands_int} {#1}
-  \path[#1,save~ spath=knot strand \int_use:N  \l__knot_strands_int]
+  \path[#1,spath/set~ name=knot,spath/save=\int_use:N \l__knot_strands_int]
 }
 \NewDocumentEnvironment{knot} { O{} }
 {
@@ -232,7 +241,7 @@
   \tikzset{knot~ diagram/.cd,every~ knot~ diagram/.try,#1}
   \int_zero:N \l__knot_strands_int
   \tl_clear:N \l__knot_redraws_tl
-  \seq_gclear:N \l__knot_nodes_seq
+  \seq_gclear:N \g__knot_nodes_seq
 }
 \cs_new_protected_nopar:Npn \knot_render:
 {
@@ -245,25 +254,23 @@
     \bool_if:NTF \l__knot_self_intersections_bool
     {
       \knot_split_strands:
-      \int_set_eq:NN \l__knot_tmpa_int \l__knot_filaments_int
+      \int_set_eq:NN \l__knot_tmpa_int \g__knot_filaments_int
       \tl_set:Nn \l__knot_prefix_tl {filament}
     }
     {
       \int_set_eq:NN \l__knot_tmpa_int \l__knot_strands_int
       \tl_set:Nn \l__knot_prefix_tl {strand}
     }
-    \int_gzero:N \l__knot_intersections_int
-    \bool_if:NTF \l__knot_draft_bool
+    \int_gzero:N \g__knot_intersections_int
+    \tl_clear:N \l__knot_node_tl
+    \bool_if:NT \l__knot_draft_bool
     {
       \tl_set:Nn \l__knot_node_tl {
         \exp_not:N \node[coordinate,
-          pin={[node~ contents={\int_use:N \l__knot_intersections_int},knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \l__knot_intersections_int \c_space_tl label/.try]
+          pin={[node~ contents={\int_use:N \g__knot_intersections_int},knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \g__knot_intersections_int \c_space_tl label/.try]
             }]
       }
     }
-    {
-      \tl_set:Nn \l__knot_node_tl {\exp_not:N \node[coordinate]}
-    }
     \int_step_variable:nnnNn {1} {1} {\l__knot_tmpa_int - 1} \l__knot_tmpa_tl
     {
       \int_step_variable:nnnNn {\tl_use:N \l__knot_tmpa_tl + 1} {1}     {\l__knot_tmpa_int} \l__knot_tmpb_tl
@@ -272,7 +279,7 @@
       }
     }
     \tl_use:N \l__knot_redraws_tl
-    \seq_use:Nn \l__knot_nodes_seq {}
+    \seq_use:Nn \g__knot_nodes_seq {}
   }
   \endpgfscope
 }
@@ -280,11 +287,11 @@
 {
   \pgfscope
   \group_begin:
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_strand #1}
-  \tl_put_right:Nn \l_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
-  \spath_bake_round:n {knot strand #1}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot strand #1}
+  \spath_bake_round:c {knot strand #1}
+  \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_strand #1}
+  \tl_put_right:Nn \l__knot_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \spath_tikz_path:Vv \l__knot_tmpa_tl {knot strand #1}
   \group_end:
   \endpgfscope
 }
@@ -293,11 +300,11 @@
 {
   \bool_if:NT \l__knot_draft_bool
   {
-    \spath_get:nnN {knot strand #1} {final point} \l__knot_tmpb_tl
+    \spath_finalpoint:Nv \l__knot_tmpb_tl {knot strand #1}
     \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}}
     \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}}
     \node[knot~ diagram/draft/strand~label] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
-    \spath_get:nnN {knot strand #1} {initial point} \l__knot_tmpb_tl
+    \spath_initialpoint:Nv \l__knot_tmpb_tl {knot strand #1}
     \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}}
     \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}}
     \node[knot~ diagram/draft/strand~label] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
@@ -309,84 +316,86 @@
   }
   {
     \tl_clear:N \l__knot_tmpa_tl
-    \spath_map_segment_function:nN {knot strand #1} \knot_split_self_intersects:NN
-    \spath_put:nnV {knot strand #1} {path} \l__knot_tmpa_tl
+    \spath_segments_to_seq:Nv \l__knot_segments_seq {knot strand #1}
+    \seq_map_function:NN \l__knot_segments_seq \knot_split_self_intersects:N
+    \tl_set_eq:cN {knot strand #1} \l__knot_tmpa_tl
   }
 }
-\cs_new_protected_nopar:Npn \knot_split_self_intersects:NN #1#2
+\cs_new_protected_nopar:Npn \knot_split_self_intersects:N #1
 {
-  \tl_case:NnF #1
+  \tl_set:Nx \l__knot_tmpc_tl {\tl_item:nn {#1} {4}}
+  \tl_case:NnF \l__knot_tmpc_tl
   {
-    \g__spath_curvetoa_tl
+    \c_spath_curvetoa_tl
     {
-      \fp_set:Nn \l_tmpa_fp
+      \fp_set:Nn \l__knot_tmpa_fp
       {
-        (\tl_item:Nn #2 {3} - 3 * \tl_item:Nn #2 {6} + 3 * \tl_item:Nn #2 {9} - \tl_item:Nn #2 {12})
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
         *
-        (3 * \tl_item:Nn #2 {8} - 3 * \tl_item:Nn #2 {11})
+        (3 * \tl_item:nn {#1} {8} - 3 * \tl_item:nn {#1} {11})
         -
-        (\tl_item:Nn #2 {2} - 3 * \tl_item:Nn #2 {5} + 3 * \tl_item:Nn #2 {8} - \tl_item:Nn #2 {11})
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
         *
-        (3 * \tl_item:Nn #2 {9} - 3 * \tl_item:Nn #2 {12})
+        (3 * \tl_item:nn {#1} {9} - 3 * \tl_item:nn {#1} {12})
       }
-      \fp_set:Nn \l_tmpb_fp
+      \fp_set:Nn \l__knot_tmpb_fp
       {
-        (\tl_item:Nn #2 {2} - 3 * \tl_item:Nn #2 {5} + 3 * \tl_item:Nn #2 {8} - \tl_item:Nn #2 {11})
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
         *
-        (3 * \tl_item:Nn #2 {6} - 6 * \tl_item:Nn #2 {9} + 3 * \tl_item:Nn #2 {12})
+        (3 * \tl_item:nn {#1} {6} - 6 * \tl_item:nn {#1} {9} + 3 * \tl_item:nn {#1} {12})
         -
-        (\tl_item:Nn #2 {3} - 3 * \tl_item:Nn #2 {6} + 3 * \tl_item:Nn #2 {9} - \tl_item:Nn #2 {12})
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
         *
-        (3 * \tl_item:Nn #2 {5} - 6 * \tl_item:Nn #2 {8} + 3 * \tl_item:Nn #2 {11})
+        (3 * \tl_item:nn {#1} {5} - 6 * \tl_item:nn {#1} {8} + 3 * \tl_item:nn {#1} {11})
       }
       \fp_compare:nTF
       {
-        \l_tmpb_fp != 0
+        \l__knot_tmpb_fp != 0
       }
       {
-        \fp_set:Nn \l_tmpa_fp {.5 * \l_tmpa_fp / \l_tmpb_fp}
+        \fp_set:Nn \l__knot_tmpa_fp {.5 * \l__knot_tmpa_fp / \l__knot_tmpb_fp}
         \fp_compare:nTF
         {
-          0 < \l_tmpa_fp && \l_tmpa_fp < 1
+          0 < \l__knot_tmpa_fp && \l__knot_tmpa_fp < 1
         }
         {
-          \spath_split_curve:VVNN \l_tmpa_fp #2 \l_tmpa_tl \l_tmpb_tl
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_set:Nx \l_tmpb_tl {\tl_tail:N \l_tmpb_tl}
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpb_tl
+          \spath_split_curve:NNnV \l__knot_tmpc_tl \l__knot_tmpd_tl {#1} \l__knot_tmpa_fp
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl}
+          \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl}
+          \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl}
+          \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
+          \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpd_tl
         }
         {
-          \tl_set_eq:NN \l_tmpa_tl #2
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-          \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
+          \tl_set:Nn \l__knot_tmpc_tl {#1}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+          \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
         }
       }
       {
-        \tl_set_eq:NN \l_tmpa_tl #2
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-        \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
+        \tl_set:Nn \l__knot_tmpc_tl {#1}
+        \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+        \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+        \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+        \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
       }
     }
-    \g__spath_lineto_tl
+    \c_spath_lineto_tl
     {
-      \tl_set_eq:NN \l_tmpa_tl #2
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_set:Nx \l_tmpa_tl {\tl_tail:N \l_tmpa_tl}
-      \tl_put_right:NV \l__knot_tmpa_tl \l_tmpa_tl
+      \tl_set:Nn \l__knot_tmpc_tl {#1}
+      \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+      \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+      \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl}
+      \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl
     }
   }
   {
-    \tl_put_right:NV \l__knot_tmpa_tl #2
+    \tl_put_right:Nn \l__knot_tmpa_tl {#1}
   }
 }
 \cs_new_protected_nopar:Npn \knot_intersections:nn #1#2
@@ -396,8 +405,8 @@
   \tl_put_right:Nn \l__knot_tmpa_tl {#1}
   \tl_set_eq:NN \l__knot_tmpb_tl \l__knot_prefix_tl
   \tl_put_right:Nn \l__knot_tmpb_tl {#2}
-  \spath_get:nnN {knot \tl_use:N \l__knot_tmpa_tl} {path} \l__knot_tmpc_tl
-  \spath_get:nnN {knot \tl_use:N \l__knot_tmpb_tl} {path} \l__knot_tmpd_tl
+  \tl_set_eq:Nc \l__knot_tmpc_tl {knot \tl_use:N \l__knot_tmpa_tl}
+  \tl_set_eq:Nc \l__knot_tmpd_tl {knot \tl_use:N \l__knot_tmpb_tl}
 
   \bool_if:nTF {
     \l__knot_save_bool
@@ -411,10 +420,12 @@
 \pgfintersectionofpaths{\pgfsetpath\l__knot_tmpc_tl}{\pgfsetpath\l__knot_tmpd_tl}
 
   }
+
   \int_compare:nT {\pgfintersectionsolutions > 0}
   {
     \int_step_function:nnnN {1} {1} {\pgfintersectionsolutions} \knot_do_intersection:n
   }
+
   \knot_save_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
   \group_end:
 }
@@ -464,10 +475,10 @@
   \bool_set_false:N \l__knot_skip_bool
   \bool_if:NT \l__knot_self_intersections_bool
   {
-    \tl_set:Nn \l_tmpa_tl {knot previous}
-    \tl_put_right:NV \l_tmpa_tl \l__knot_tmpa_tl
-    \tl_set:Nv \l_tmpa_tl \l_tmpa_tl
-    \tl_if_eq:NNT \l_tmpa_tl \l__knot_tmpb_tl
+    \tl_set:Nn \l__knot_tmpc_tl {knot previous}
+    \tl_put_right:NV \l__knot_tmpc_tl \l__knot_tmpa_tl
+    \tl_set:Nv \l__knot_tmpc_tl \l__knot_tmpc_tl
+    \tl_if_eq:NNT \l__knot_tmpc_tl \l__knot_tmpb_tl
     {
       \knot_test_endpoint:VnT \l__knot_tmpb_tl {final point}
       {
@@ -475,10 +486,10 @@
       }
     }
 
-    \tl_set:Nn \l_tmpa_tl {knot previous}
-    \tl_put_right:NV \l_tmpa_tl \l__knot_tmpb_tl
-    \tl_set:Nv \l_tmpa_tl \l_tmpa_tl
-    \tl_if_eq:NNT \l_tmpa_tl \l__knot_tmpa_tl
+    \tl_set:Nn \l__knot_tmpc_tl {knot previous}
+    \tl_put_right:NV \l__knot_tmpc_tl \l__knot_tmpb_tl
+    \tl_set:Nv \l__knot_tmpc_tl \l__knot_tmpc_tl
+    \tl_if_eq:NNT \l__knot_tmpc_tl \l__knot_tmpa_tl
     {
       \knot_test_endpoint:VnT \l__knot_tmpa_tl {final point}
       {
@@ -508,23 +519,23 @@
   \bool_if:NF \l__knot_skip_bool
   {
 
-    \int_gincr:N \l__knot_intersections_int
+    \int_gincr:N \g__knot_intersections_int
     \bool_if:nF
     {
       \tl_if_exist_p:c {l__knot_ignore_crossing_ \int_use:N
-        \l__knot_intersections_int}
+        \g__knot_intersections_int}
       &&
       ! \tl_if_empty_p:c {l__knot_ignore_crossing_ \int_use:N
-        \l__knot_intersections_int}
+        \g__knot_intersections_int}
     }
     {
       \bool_if:nTF
       {
         \tl_if_exist_p:c {l__knot_crossing_ \int_use:N
-          \l__knot_intersections_int}
+          \g__knot_intersections_int}
         &&
         ! \tl_if_empty_p:c {l__knot_crossing_ \int_use:N
-          \l__knot_intersections_int}
+          \g__knot_intersections_int}
       }
       {
         \tl_set_eq:NN \l__knot_tmpg_tl \l__knot_tmpb_tl
@@ -553,9 +564,10 @@
           \l__knot_prepend_prev_bool || \l__knot_append_next_bool
         }
         {
-          \spath_clone:nn {knot \tl_use:N \l__knot_tmpg_tl}
-          {knot \tl_use:N \l__knot_prefix_tl -1}
+          \tl_clear_new:c {knot \tl_use:N \l__knot_prefix_tl -1}
+          \tl_set_eq:cc {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:N \l__knot_tmpg_tl}
 
+          \tl_clear_new:c {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1}
           \tl_set_eq:cc {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1} {l__knot_options_ \tl_use:N \l__knot_tmpg_tl}
 
           \bool_if:nT
@@ -567,7 +579,7 @@
             !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
           }
           {
-            \spath_prepend_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}
+            \spath_prepend_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}
             \bool_if:nT
             {
               \l__knot_splits_bool
@@ -579,10 +591,9 @@
             {
               \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {initial point}
               {
-                \spath_get:nnN {knot \tl_use:N \l__knot_prefix_tl -1} {path} \l_tmpa_tl
-                \spath_prepend_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}}
-                \spath_get:nnN {knot \tl_use:N \l__knot_prefix_tl -1} {path} \l_tmpa_tl
 
+                \spath_prepend_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}}}
+                \tl_set_eq:Nc \l__knot_tmpa_tl {knot \tl_use:N \l__knot_prefix_tl -1}
               }
             }
           }
@@ -595,7 +606,7 @@
             !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
           }
           {
-            \spath_append_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}
+            \spath_append_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}
             \bool_if:nT
             {
               \l__knot_splits_bool
@@ -608,7 +619,7 @@
             {
               \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {final point}
               {
-                \spath_append_no_move:nn {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}}
+                \spath_append_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}}}
 
               }
             }
@@ -619,13 +630,16 @@
       }
       \pgfscope
       \group_begin:
-      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \l__knot_intersections_int/.try}
-      \knot_draw_crossing:nVV {\tl_use:N \l__knot_tmpg_tl} \l__knot_tmpa_dim \l__knot_tmpb_dim
+      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \g__knot_intersections_int/.try}
+      \knot_draw_crossing:VVV \l__knot_tmpg_tl \l__knot_tmpa_dim \l__knot_tmpb_dim
+      \coordinate (\l__knot_name_tl \c_space_tl \int_use:N \g__knot_intersections_int) at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim);
       \group_end:
       \endpgfscope
     }
-    \seq_gpush:Nx \l__knot_nodes_seq { \l__knot_node_tl (\l__knot_name_tl \c_space_tl \int_use:N \l__knot_intersections_int) at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim) {};}
-
+    \tl_if_empty:NF \l__knot_node_tl
+    {
+      \seq_gpush:Nx \g__knot_nodes_seq { \l__knot_node_tl at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim) {};}
+    }
   }
 }
 
@@ -649,7 +663,7 @@
 }
 \prg_new_protected_conditional:Npnn \knot_test_endpoint:nn #1#2 {T,F,TF}
 {
-  \spath_get:nnN {knot #1} {#2} \l__knot_tmpd_tl
+  \use:c {spath_#2:Nv} \l__knot_tmpd_tl {knot #1}
   \knot_test_endpoint:NTF \l__knot_tmpd_tl
   {
     \prg_return_true:
@@ -662,49 +676,49 @@
 \cs_generate_variant:Nn \knot_test_endpoint:nnT {VnT,vnT}
 \cs_generate_variant:Nn \knot_test_endpoint:nnF {VnF,vnF}
 \cs_generate_variant:Nn \knot_test_endpoint:nnTF {VnTF,vnTF}
-\cs_new_nopar:Npn \knot_draw_crossing:nnn #1#2#3
+\cs_new_protected_nopar:Npn \knot_draw_crossing:nnn #1#2#3
 {
   \group_begin:
   \pgfscope
   \path[knot~ diagram/background~ clip] (#2, #3) circle[radius=\l__knot_clip_bg_radius_dim];
 
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,}
   \tl_if_exist:cT {l__knot_options_ #1}
   {
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_ #1}
+  \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_ #1}
   }
-  \tl_put_right:Nn \l_tmpa_tl {,knotbg,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot #1}
+  \tl_put_right:Nn \l__knot_tmpa_tl {,knotbg,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth}
+  \spath_tikz_path:Vv \l__knot_tmpa_tl {knot #1}
 
   \endpgfscope
 
   \pgfscope
   \path[knot~ diagram/clip] (#2, #3) circle[radius=\l__knot_clip_draw_radius_dim];
 
-  \tl_set:Nn \l_tmpa_tl {knot~ diagram/every~ strand/.try,}
+  \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,}
   \tl_if_exist:cT {l__knot_options_ #1}
   {
-  \tl_put_right:Nv \l_tmpa_tl {l__knot_options_ #1}
+  \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_ #1}
   }
-  \tl_put_right:Nn \l_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
-  \spath_tikz_path:Vn \l_tmpa_tl {knot #1}
+  \tl_put_right:Nn \l__knot_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \spath_tikz_path:Vv \l__knot_tmpa_tl {knot #1}
 
   \endpgfscope
   \group_end:
 }
 
-\cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV}
+\cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV, VVV}
 
-\cs_new_nopar:Npn \knot_draw_crossing:nn #1#2
+\cs_new_protected_nopar:Npn \knot_draw_crossing:nn #1#2
 {
   \tikz@scan@one@point\pgfutil@firstofone #2 \relax
   \knot_draw_crossing:nVV {#1} \pgf@x \pgf@y
 }
 \cs_new_protected_nopar:Npn \knot_split_strands:
 {
-  \int_gzero:N \l__knot_filaments_int
+  \int_gzero:N \g__knot_filaments_int
   \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_split_strand:n
-  \int_step_function:nnnN {1} {1} {\l__knot_filaments_int} \knot_compute_nexts:n
+  \int_step_function:nnnN {1} {1} {\g__knot_filaments_int} \knot_compute_nexts:n
 }
 \cs_new_protected_nopar:Npn \knot_compute_nexts:n #1
 {
@@ -713,66 +727,70 @@
 }
 \cs_new_protected_nopar:Npn \knot_split_strand:n #1
 {
-  \int_set_eq:NN \l__knot_component_start_int \l__knot_filaments_int
+  \int_set_eq:NN \l__knot_component_start_int \g__knot_filaments_int
   \int_incr:N \l__knot_component_start_int
   \tl_set_eq:Nc \l__knot_tmpa_tl {l__knot_options_strand #1}
-  \spath_map_segment_function:nN {knot strand #1} \knot_save_filament:NN
+  \spath_segments_to_seq:Nv \l__knot_segments_seq {knot strand #1}
+  \seq_map_function:NN \l__knot_segments_seq \knot_save_filament:N
 }
-\cs_new_protected_nopar:Npn \knot_save_filament:NN #1#2
+\cs_new_protected_nopar:Npn \knot_save_filament:N #1
 {
-  \tl_case:NnF #1
+  \tl_set:Nx \l__knot_tmpb_tl {\tl_item:nn {#1} {4}}
+  \tl_case:NnF \l__knot_tmpb_tl
   {
-    \g__spath_moveto_tl
+    \c_spath_moveto_tl
     {
-      \int_compare:nT {\l__knot_component_start_int < \l__knot_filaments_int}
+      \int_compare:nT {\l__knot_component_start_int < \g__knot_filaments_int}
       {
-        \int_set_eq:NN \l__knot_component_start_int \l__knot_filaments_int
+        \int_set_eq:NN \l__knot_component_start_int \g__knot_filaments_int
       }
     }
-    \g__spath_lineto_tl
+    \c_spath_lineto_tl
     {
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} #2
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
+      \int_gincr:N \g__knot_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int}
+      \tl_set:cn {knot filament \int_use:N \g__knot_filaments_int} {#1}
+
+      \tl_clear_new:c {l__knot_options_filament \int_use:N \g__knot_filaments_int}
+      \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
 
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
+      \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int}
+      \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int}
       {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
+        \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}}
       }
     }
-    \g__spath_curvetoa_tl
+    \c_spath_curvetoa_tl
     {
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} #2
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
+      \int_gincr:N \g__knot_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int}
+      \tl_set:cn {knot filament \int_use:N \g__knot_filaments_int} {#1}
+      \tl_clear_new:c {l__knot_options_filament \int_use:N \g__knot_filaments_int}
+      \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
 
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
+      \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int}
+      \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int}
       {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
+        \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}}
       }
     }
-    \g__spath_closepath_tl
+    \c_spath_closepath_tl
     {
-      \tl_show:N #2
-      \int_gincr:N \l__knot_filaments_int
-      \spath_clear_new:n {knot filament \int_use:N \l__knot_filaments_int}
-      \tl_clear:N \l_tmpa_tl
-      \tl_put_right:Nx {\tl_item:Nn #2 {1}\tl_item:Nn #2 {2}\tl_item:Nn #2 {3}}
-      \tl_put_right:NV \l_tmpa_tl \g__spath_lineto_tl
-      \tl_put_right:Nx {\tl_item:Nn #2 {5}\tl_item:Nn #2 {6}}
-      \tl_show:N \l_tmpa_tl
-      \spath_put:nnV {knot filament \int_use:N \l__knot_filaments_int} {path} \l_tmpa_tl
-      \tl_set_eq:cN {l__knot_options_filament \int_use:N \l__knot_filaments_int} \l__knot_tmpa_tl
-      \tl_clear_new:c {knot previous filament \int_use:N \l__knot_filaments_int}
-      \int_compare:nF {\l__knot_component_start_int == \l__knot_filaments_int}
+      \int_gincr:N \g__knot_filaments_int
+      \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int}
+      \tl_clear:N \l__knot_tmpa_tl
+      \tl_put_right:Nx {\tl_item:nn {#1} {1}\tl_item:nn {#1} {2}\tl_item:nn {#1} {3}}
+      \tl_put_right:NV \l__knot_tmpa_tl \c_spath_lineto_tl
+      \tl_put_right:Nx {\tl_item:nn {#1} {5}\tl_item:nn {#1} {6}}
+
+      \tl_set:cV {knot filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
+      \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl
+      \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int}
+      \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int}
       {
-        \tl_set:cx {knot previous filament \int_use:N \l__knot_filaments_int} {filament \int_eval:n {\l__knot_filaments_int - 1}}
+        \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}}
       }
-      \tl_set:cx {knot previous filament \int_use:N \l__knot_component_start_int} {filament \int_use:N \l__knot_filaments_int}
+      \tl_set:cx {knot previous filament \int_use:N \l__knot_component_start_int} {filament \int_use:N \g__knot_filaments_int}
     }
   }
   {
@@ -990,7 +1008,7 @@
  }
 }
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <stacey@math.ntnu.no>
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
 %% 
 %% This work may be distributed and/or modified under the
 %% conditions of the LaTeX Project Public License (LPPL), either
@@ -1005,13 +1023,16 @@
 %% This work consists of the files  spath3.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
+%%                                  spath3.tex
 %% and the derived files            spath3.ins,
 %%                                  spath3_code.pdf,
 %%                                  spath3.sty,
 %%                                  tikzlibrarycalligraphy.code.tex
 %%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
 %%                                  calligraphy.pdf
 %%                                  knots.pdf
+%%                                  spath3.pdf
 %%                                  README
 %% 
 %%
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
new file mode 100644
index 00000000000..32d0d9fea08
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
@@ -0,0 +1,595 @@
+%%
+%% This is file `tikzlibraryspath3.code.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% spath3_code.dtx  (with options: `tikzspath3')
+%% ----------------------------------------------------------------
+%% spath3 --- Functions for manipulating PGF soft paths
+%% E-mail: loopspace@mathforge.org
+%% Released under the LaTeX Project Public License v1.3c or later
+%% See http://www.latex-project.org/lppl.txt
+%% ----------------------------------------------------------------
+%% 
+\RequirePackage{spath3}
+\RequirePackage{expl3}
+\ExplSyntaxOn
+
+\tl_new:N \l__spath_current_tl
+\tl_new:N \l__spath_reverse_tl
+\tl_new:N \l__spath_prefix_tl
+\tl_new:N \l__spath_suffix_tl
+\tl_new:N \g__spath_smuggle_tl
+\seq_new:N \g__spath_tmpa_seq
+\seq_new:N \g__spath_tmpb_seq
+\bool_new:N \l__spath_draft_bool
+\tl_set:Nn \l__spath_prefix_tl {tikz@intersect@path@name@}
+\tl_set:Nn \l__spath_suffix_tl {}
+\tl_new:N \g__spath_tikzfinish_tl
+\cs_new_protected_nopar:Npn \spath_at_end_of_path:
+{
+  \tl_use:N \g__spath_tikzfinish_tl
+  \tl_gclear:N \g__spath_tikzfinish_tl
+}
+\tl_put_right:Nn \tikz@finish {\spath_at_end_of_path:}
+
+\cs_new_protected_nopar:Npn \spath_save_path:Nn #1#2
+{
+  \tl_gput_right:Nn \g__spath_tikzfinish_tl
+  {
+    \tl_clear_new:N #1
+    \tl_set:Nn #1 {#2}
+  }
+}
+\cs_generate_variant:Nn \spath_save_path:Nn {cn, NV, cV}
+
+\cs_new_protected_nopar:Npn \spath_gsave_path:Nn #1#2
+{
+  \tl_gput_right:Nn \g__spath_tikzfinish_tl
+  {
+    \tl_gclear_new:N #1
+    \tl_gset:Nn #1 {#2}
+  }
+}
+\cs_generate_variant:Nn \spath_gsave_path:Nn {cn, NV, cV}
+\tikzset{
+  spath/.is~family,
+  spath/.cd,
+  set~ prefix/.store~ in=\l__spath_prefix_tl,
+  prefix/.is~choice,
+  prefix/default/.style={
+    /tikz/spath/set~ prefix=tikz@intersect@path@name@
+  },
+  set~ suffix/.store~ in=\l__spath_suffix_tl,
+  suffix/.is~choice,
+  suffix/default/.style={
+    /tikz/spath/set~ suffix={}
+  },
+  set~ name/.style={
+    /tikz/spath/prefix=#1,
+    /tikz/spath/suffix=#1
+  },
+  save/.code={
+    \tikz@addmode{
+      \spath_get_current_path:N \l__spath_tmpa_tl
+      \spath_bake_round:NV \l__spath_tmpa_tl \l__spath_tmpa_tl
+      \spath_save_path:cV {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} \l__spath_tmpa_tl
+    }
+  },
+  clone/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_clear_new:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \tl_set_eq:cc
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  clone~ global/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_gclear_new:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \tl_gset_eq:cc
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  save~ global/.code={
+    \tikz@addmode{
+      \spath_get_current_path:N \l__spath_tmpa_tl
+      \spath_bake_round:NV \l__spath_tmpa_tl \l__spath_tmpa_tl
+      \spath_gsave_path:cV
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \l__spath_tmpa_tl
+    }
+  },
+  save~ to~ aux/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_save_to_aux:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  restore/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_set_current_path:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_set_tikz_coords:v
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  show~current~path/.code={
+    \tikz@addmode{
+      \pgfsyssoftpath@getcurrentpath\l__spath_tmpa_tl
+      \iow_term:n {---~ current~ soft~ path~ ---}
+      \spath_show:V \l__spath_tmpa_tl
+    }
+  },
+  show/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \iow_term:n {---~ soft~ path~ #1~ ---}
+      \spath_show:v {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  append/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_weld:Nv
+      \l__spath_current_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  join~ with/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_append:cv
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+  },
+  spot~ weld/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_spot_weld_components:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_reverse:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  append~ reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_reverse:Nv
+      \l__spath_reverse_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_weld:NV \l__spath_current_tl \l__spath_reverse_tl
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  insert/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_append:Nv
+      \l__spath_current_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  insert~ reverse/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_reverse:Nv
+      \l__spath_reverse_tl
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_get_current_path:N \l__spath_current_tl
+      \spath_append:NV \l__spath_current_tl \l__spath_reverse_tl
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_coords:V \l__spath_current_tl
+    }
+  },
+  shorten~ at~ end/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_shorten_at_end:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+  },
+  shorten~ at~ start/.code~ 2~ args ={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_shorten_at_start:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+  },
+  shorten~ at~ both~ ends/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_shorten_at_end:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+      \spath_shorten_at_start:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+  },
+  translate/.code~ n~ args={3}{
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_translate:cnn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{#2}{#3}
+    }
+  },
+  export~ to~ svg/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_export_to_svg:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  transform/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \pgftransformreset
+      \tikzset{#2}
+      \pgfgettransform \l__spath_tmpa_tl
+      \tl_gset:Nn \g__spath_smuggle_tl
+      {
+        \spath_transform:cnnnnnn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+      \tl_gput_right:NV \g__spath_smuggle_tl \l__spath_tmpa_tl
+      \group_end:
+      \tl_use:N \g__spath_smuggle_tl
+    }
+  },
+  transform~global/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \pgftransformreset
+      \tikzset{#2}
+      \pgfgettransform \l__spath_tmpa_tl
+      \tl_gset:Nn \g__spath_smuggle_tl
+      {
+        \spath_gtransform:cnnnnnn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+      \tl_gput_right:NV \g__spath_smuggle_tl \l__spath_tmpa_tl
+      \group_end:
+      \tl_use:N \g__spath_smuggle_tl
+    }
+  },
+  split~ at~ intersections/.code~ n~ args={2}{
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_split_at_intersections:cc
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+  },
+  split~ at~ self~ intersections/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_split_at_self_intersections:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  get~ components~ of/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \clist_clear_new:N #2
+      \spath_components_to_seq:Nv
+      \l__spath_tmpa_seq
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \seq_map_inline:Nn \l__spath_tmpa_seq
+      {
+        \tl_new:c
+        {\tl_use:N \l__spath_prefix_tl anonymous_\int_use:N \g__spath_anon_int \tl_use:N \l__spath_suffix_tl}
+        \tl_set:cn
+        {\tl_use:N \l__spath_prefix_tl anonymous_\int_use:N \g__spath_anon_int \tl_use:N \l__spath_suffix_tl} {##1}
+        \clist_put_right:Nx #2 {anonymous_\int_use:N \g__spath_anon_int}
+        \int_gincr:N \g__spath_anon_int
+      }
+    }
+  },
+  render~ components/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \spath_components_to_seq:Nv
+      \l__spath_tmpa_seq
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+      {
+        \spath_tikz_path:nn
+        {
+          every~ spath~ component/.try,
+          spath ~component~ ##1/.try,
+          spath ~component/.try={##1},
+          every~ #1~ component/.try,
+          #1 ~component~ ##1/.try,
+          #1 ~component/.try={##1},
+        }
+        {
+          ##2
+        }
+      }
+      \group_end:
+    }
+  },
+  insert~ gaps~ after~ components/.code~ n~ args={3}{
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \group_begin:
+      \seq_gclear:N \g__spath_tmpa_seq
+      \seq_gclear:N \g__spath_tmpb_seq
+      \foreach \l__spath_tmpa_tl in {#3}
+      {
+        \seq_gput_right:NV \g__spath_tmpa_seq \l__spath_tmpa_tl
+        \seq_gput_right:Nx \g__spath_tmpb_seq {\int_eval:n { \l__spath_tmpa_tl + 1 }}
+      }
+      \spath_components_to_seq:Nv
+      \l__spath_tmpa_seq
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \seq_clear:N \l__spath_tmpb_seq
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+      {
+        \tl_set:Nn \l__spath_tmpa_tl {##2}
+        \seq_if_in:NnT \g__spath_tmpa_seq {##1}
+        {
+          \spath_shorten_at_end:Nn \l__spath_tmpa_tl {#2/2}
+        }
+        \seq_if_in:NnT \g__spath_tmpb_seq {##1}
+        {
+          \spath_shorten_at_start:Nn \l__spath_tmpa_tl {#2/2}
+        }
+        \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+      }
+      \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpb_seq {} }
+      \group_end:
+      \tl_set_eq:cN
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \g__spath_output_tl
+      \tl_gclear:N \g__spath_output_tl
+    }
+  },
+  join~ components/.code~ 2~ args={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \seq_gclear:N \g__spath_tmpa_seq
+      \foreach \l__spath_tmpa_tl in {#2}
+      {
+        \seq_gput_right:NV \g__spath_tmpa_seq \l__spath_tmpa_tl
+      }
+      \seq_gsort:Nn \g__spath_tmpa_seq
+      {
+        \int_compare:nNnTF {##1} > {##2}
+        { \sort_return_same: }
+        { \sort_return_swapped: }
+      }
+      \seq_map_inline:Nn \g__spath_tmpa_seq
+      {
+        \spath_join_component:cn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{##1}
+      }
+    }
+  },
+  remove~ empty~ components/.code={
+    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_remove_empty_components:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+  },
+  draft~ mode/.is~ choice,
+  draft~ mode/true/.code={
+    \bool_set_true:N \l__spath_draft_bool
+  },
+  draft~ mode/false/.code={
+    \bool_set_false:N \l__spath_draft_bool
+  },
+  maybe~ spot~ weld/.code={
+    \bool_if:NF \l__spath_draft_bool
+    {
+      \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_spot_weld_components:c
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+  },
+  transform~ to/.code~ 2~ args={
+    \group_begin:
+    \tl_if_exist:cTF
+    {
+      \tl_use:N \l__spath_prefix_tl
+      #1
+      \tl_use:N \l__spath_suffix_tl
+    }
+    {
+      \spath_reallength:Nv
+      \l__spath_tmpa_int
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+
+      \tl_set:Nx \l__spath_tmpb_tl
+      {\fp_to_decimal:n {(#2) * (\l__spath_tmpa_int)}}
+      \spath_transformation_at:NvV \l__spath_tmpc_tl
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+      \l__spath_tmpb_tl
+      \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpc_tl
+    }
+    {
+      \tl_gset_eq:NN \g__spath_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
+    }
+    \group_end:
+    \exp_last_unbraced:NV \pgfsettransformentries \g__spath_smuggle_tl
+    \tl_gclear:N \g__spath_smuggle_tl
+  },
+  upright~ transform~ to/.code~ 2~ args={
+    \group_begin:
+    \tl_if_exist:cTF
+    {
+      \tl_use:N \l__spath_prefix_tl
+      #1
+      \tl_use:N \l__spath_suffix_tl
+    }
+    {
+      \spath_reallength:Nv
+      \l__spath_tmpa_int
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+
+      \tl_set:Nx \l__spath_tmpb_tl
+      {\fp_to_decimal:n {(#2) * (\l__spath_tmpa_int)}}
+      \spath_transformation_at:NvV \l__spath_tmpc_tl
+      {
+        \tl_use:N \l__spath_prefix_tl
+        #1
+        \tl_use:N \l__spath_suffix_tl
+      }
+      \l__spath_tmpb_tl
+      \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpc_tl
+    }
+    {
+      \tl_gset_eq:NN \g__spath_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
+    }
+    \fp_compare:nT { \tl_item:Nn \g__spath_smuggle_tl {4} < 0}
+    {
+      \tl_gset:Nx \g__spath_smuggle_tl
+      {
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {1})} }
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {2})} }
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {3})} }
+        { \fp_eval:n { - (\tl_item:Nn \g__spath_smuggle_tl {4})} }
+        { \tl_item:Nn \g__spath_smuggle_tl {5} }
+        { \tl_item:Nn \g__spath_smuggle_tl {6} }
+      }
+    }
+    \group_end:
+    \exp_last_unbraced:NV \pgfsettransformentries \g__spath_smuggle_tl
+    \tl_gclear:N \g__spath_smuggle_tl
+  },
+  knot/.style~ n~ args={3}{
+    spath/.cd,
+    split~ at~ self~ intersections=#1,
+    insert~ gaps~ after~ components={#1}{#2}{#3},
+    maybe~ spot~ weld=#1,
+    render~ components=#1
+  },
+}
+\tikzdeclarecoordinatesystem{spath}{%
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_trim_spaces:N \l__spath_tmpa_tl
+
+  \seq_set_split:NnV \l__spath_tmpa_seq {~} \l__spath_tmpa_tl
+  \seq_pop_right:NN \l__spath_tmpa_seq \l__spath_tmpb_tl
+
+  \tl_set:Nx \l__spath_tmpa_tl { \seq_use:Nn \l__spath_tmpa_seq {~} }
+  \tl_if_exist:cTF
+  {
+    \tl_use:N \l__spath_prefix_tl
+    \tl_use:N \l__spath_tmpa_tl
+    \tl_use:N \l__spath_suffix_tl
+  }
+  {
+
+    \tl_set_eq:Nc
+    \l__spath_tmpa_tl
+    {
+      \tl_use:N \l__spath_prefix_tl
+      \tl_use:N \l__spath_tmpa_tl
+      \tl_use:N \l__spath_suffix_tl
+    }
+
+    \tl_if_empty:NTF \l__spath_tmpa_tl
+    {
+      \tl_gset_eq:NN \g__spath_smuggle_tl \pgfpointorigin
+    }
+    {
+      \spath_reallength:NV \l__spath_tmpa_int \l__spath_tmpa_tl
+      \tl_set:Nx \l__spath_tmpb_tl
+      {\fp_to_decimal:n {(\l__spath_tmpb_tl) * (\l__spath_tmpa_int)}}
+      \spath_point_at:NVV \l__spath_tmpc_tl \l__spath_tmpa_tl \l__spath_tmpb_tl
+
+      \tl_clear:N \l__spath_tmpd_tl
+      \tl_put_right:Nn \l__spath_tmpd_tl {\pgf@x=}
+      \tl_put_right:Nx \l__spath_tmpd_tl {\tl_item:Nn \l__spath_tmpc_tl {1}}
+      \tl_put_right:Nn \l__spath_tmpd_tl {\relax}
+      \tl_put_right:Nn \l__spath_tmpd_tl {\pgf@y=}
+      \tl_put_right:Nx \l__spath_tmpd_tl {\tl_item:Nn \l__spath_tmpc_tl {2}}
+      \tl_put_right:Nn \l__spath_tmpd_tl {\relax}
+      \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpd_tl
+    }
+  }
+  {
+    \tl_gset_eq:NN \g__spath_smuggle_tl \pgfpointorigin
+  }
+    \group_end:
+    \tl_use:N \g__spath_smuggle_tl
+}
+
+\ExplSyntaxOff
+%% 
+%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License (LPPL), either
+%% version 1.3c of this license or (at your option) any later
+%% version.  The latest version of this license is in the file:
+%% 
+%% http://www.latex-project.org/lppl.txt
+%% 
+%% This work is "maintained" (as per LPPL maintenance status) by
+%% Andrew Stacey.
+%% 
+%% This work consists of the files  spath3.dtx
+%%                                  calligraphy_doc.tex
+%%                                  knots_doc.tex
+%%                                  spath3.tex
+%% and the derived files            spath3.ins,
+%%                                  spath3_code.pdf,
+%%                                  spath3.sty,
+%%                                  tikzlibrarycalligraphy.code.tex
+%%                                  tikzlibraryknots.code.tex
+%%                                  tikzlibraryspath3.code.tex
+%%                                  calligraphy.pdf
+%%                                  knots.pdf
+%%                                  spath3.pdf
+%%                                  README
+%% 
+%%
+%% End of file `tikzlibraryspath3.code.tex'.