spath3 (6feb21)

git-svn-id: svn://tug.org/texlive/trunk@57639 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 2857 insertions, 880 deletions

diff --git a/Master/texmf-dist/tex/latex/spath3/spath3.sty b/Master/texmf-dist/tex/latex/spath3/spath3.sty
index 155441947b0..868e648f570 100644
--- a/Master/texmf-dist/tex/latex/spath3/spath3.sty
+++ b/Master/texmf-dist/tex/latex/spath3/spath3.sty
@@ -15,7 +15,7 @@
 \NeedsTeXFormat{LaTeX2e}
 \RequirePackage{expl3}
 \RequirePackage{pgf}
-\ProvidesExplPackage {spath3} {2021/01/19} {2.0} {Functions for
+\ProvidesExplPackage {spath3} {2021/02/05} {2.2} {Functions for
 manipulating PGF soft paths}
 \RequirePackage{xparse}
 \cs_new_protected:Nn \__spath_tl_put_right_braced:Nn
@@ -40,29 +40,40 @@ manipulating PGF soft paths}
   \tl_gput_left:Nn #1 { { #2 } }
 }
 \cs_generate_variant:Nn \__spath_tl_gput_left_braced:Nn { NV, cV, cv, Nx, cx }
+\tl_new:N \g__spath_output_tl
+\int_new:N \g__spath_output_int
+\seq_new:N \g__spath_output_seq
+\bool_new:N \g__spath_output_bool
 \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_tmpe_tl
+\tl_new:N \l__spath_tmpf_tl
+\tl_new:N \l__spath_tmpg_tl
+\tl_new:N \l__spath_tmph_tl
+\tl_new:N \l__spath_tmpi_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
+\seq_new:N \l__spath_tmpc_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
+\fp_new:N \l__spath_tmpc_fp
+
 \int_new:N \l__spath_tmpa_int
+\int_new:N \l__spath_tmpb_int
 
-\bool_new:N \g__spath_output_bool
+\bool_new:N \l__spath_tmpa_bool
+\dim_new:N \l__spath_move_x_dim
+\dim_new:N \l__spath_move_y_dim
 \bool_new:N \l__spath_closed_bool
+\tl_new:N \l__spath_intersecta_tl
+\tl_new:N \l__spath_intersectb_tl
 \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}
@@ -71,143 +82,136 @@ manipulating PGF soft paths}
 \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.}
+\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
 {
   \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
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \seq_clear:N \l__spath_tmpa_seq
+  \dim_zero:N \l__spath_tmpa_dim
+  \dim_zero:N \l__spath_tmpb_dim
 
   \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_itera_tl
+    \tl_if_empty_p:N \l__spath_tmpa_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
+    \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
     {
       \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_set_eq:NN \l__spath_tmpb_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_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-        \tl_put_right:Nx \l__spath_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_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_iterd_tl {\tl_head:N \l__spath_itera_tl}
-        \tl_if_eq:NNF \l__spath_iterd_tl \c_spath_moveto_tl
+        \tl_set:Nx \l__spath_tmpd_tl {\tl_head:N \l__spath_tmpa_tl}
+        \tl_if_eq:NNF \l__spath_tmpd_tl \c_spath_moveto_tl
         {
-          \tl_clear:N \l__spath_iterb_tl
+          \tl_clear:N \l__spath_tmpb_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
+        \tl_set_eq:NN \l__spath_tmpb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_tmpb_tl
         {
-          {\dim_use:N \l__spath_itera_dim}
-          {\dim_use:N \l__spath_iterb_dim}
+          {\dim_use:N \l__spath_tmpa_dim}
+          {\dim_use:N \l__spath_tmpb_dim}
         }
-        \tl_put_right:NV \l__spath_iterb_tl \c_spath_lineto_tl
+        \tl_put_right:NV \l__spath_tmpb_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_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-        \tl_put_right:Nx \l__spath_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_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}
 
       }
 
       \c_spath_curvetoa_tl
       {
-        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
-        \tl_put_right:Nx \l__spath_iterb_tl
+        \tl_set_eq:NN \l__spath_tmpb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_tmpb_tl
         {
-          {\dim_use:N \l__spath_itera_dim}
-          {\dim_use:N \l__spath_iterb_dim}
+          {\dim_use:N \l__spath_tmpa_dim}
+          {\dim_use:N \l__spath_tmpb_dim}
         }
-        \tl_put_right:NV \l__spath_iterb_tl \c_spath_curvetoa_tl
+        \tl_put_right:NV \l__spath_tmpb_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_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+          \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
+          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
         }
 
-        \tl_put_right:Nx \l__spath_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_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-        \tl_put_right:Nx \l__spath_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_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}
 
       }
 
       \c_spath_closepath_tl
       {
-        \tl_set_eq:NN \l__spath_iterb_tl \c_spath_moveto_tl
-        \tl_put_right:Nx \l__spath_iterb_tl
+        \tl_set_eq:NN \l__spath_tmpb_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_tmpb_tl
         {
-          {\dim_use:N \l__spath_itera_dim}
-          {\dim_use:N \l__spath_iterb_dim}
+          {\dim_use:N \l__spath_tmpa_dim}
+          {\dim_use:N \l__spath_tmpb_dim}
         }
-        \tl_put_right:NV \l__spath_iterb_tl \c_spath_lineto_tl
+        \tl_put_right:NV \l__spath_tmpb_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_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-        \tl_put_right:Nx \l__spath_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_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
       }
 
     }
     {
 
-      \tl_set_eq:NN \l__spath_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_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpc_tl
+      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
 
-      \tl_put_right:Nx \l__spath_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_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_iterb_tl
+    \tl_if_empty:NF \l__spath_tmpb_tl
     {
-      \seq_put_right:NV \l__spath_iter_seq \l__spath_iterb_tl
+      \seq_put_right:NV \l__spath_tmpa_seq \l__spath_tmpb_tl
     }
-    \tl_clear:N \l__spath_iterb_tl
+    \tl_clear:N \l__spath_tmpb_tl
   }
 
   \seq_gclear:N \g__spath_output_seq
-  \seq_gset_eq:NN \g__spath_output_seq \l__spath_iter_seq
+  \seq_gset_eq:NN \g__spath_output_seq \l__spath_tmpa_seq
   \group_end:
 }
 \cs_new_protected_nopar:Npn \spath_segments_to_seq:Nn #1#2
@@ -229,33 +233,33 @@ manipulating PGF soft paths}
 \cs_new_protected_nopar:Npn \__spath_components_to_seq:n #1
 {
   \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
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \seq_clear:N \l__spath_tmpa_seq
+  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+  \tl_put_right:NV \l__spath_tmpa_tl \c_spath_moveto_tl
+  \tl_set_eq:NN \l__spath_tmpb_tl \c_spath_moveto_tl
   \bool_do_until:nn {
-    \tl_if_empty_p:N \l__spath_itera_tl
+    \tl_if_empty_p:N \l__spath_tmpa_tl
   }
   {
-    \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
+    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
+    \tl_if_eq:NNT \l__spath_tmpc_tl \c_spath_moveto_tl
     {
-      \seq_put_right:NV \l__spath_iter_seq \l__spath_iterb_tl
-      \tl_clear:N \l__spath_iterb_tl
+      \seq_put_right:NV \l__spath_tmpa_seq \l__spath_tmpb_tl
+      \tl_clear:N \l__spath_tmpb_tl
     }
-    \tl_if_single:NTF \l__spath_iterc_tl
+    \tl_if_single:NTF \l__spath_tmpc_tl
     {
-      \tl_put_right:NV \l__spath_iterb_tl \l__spath_iterc_tl
+      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
     }
     {
-      \tl_put_right:Nx \l__spath_iterb_tl {{\l__spath_iterc_tl}}
+      \tl_put_right:Nx \l__spath_tmpb_tl {{\l__spath_tmpc_tl}}
     }
-    \tl_set:Nx \l__spath_itera_tl {\tl_tail:N \l__spath_itera_tl}
+    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   }
 
   \seq_gclear:N \g__spath_output_seq
-  \seq_gset_eq:NN \g__spath_output_seq \l__spath_iter_seq
+  \seq_gset_eq:NN \g__spath_output_seq \l__spath_tmpa_seq
   \group_end:
 }
 \cs_new_protected_nopar:Npn \spath_components_to_seq:Nn #1#2
@@ -300,8 +304,8 @@ manipulating PGF soft paths}
   \group_begin:
   \int_set:Nn \l__spath_tmpa_int {0}
   \tl_map_inline:nn {#1} {
-    \tl_set:Nn \l__spath_tmpc_tl {##1}
-    \tl_case:NnT \l__spath_tmpc_tl
+    \tl_set:Nn \l__spath_tmpa_tl {##1}
+    \tl_case:NnT \l__spath_tmpa_tl
     {
       \c_spath_lineto_tl {}
       \c_spath_curveto_tl {}
@@ -353,24 +357,24 @@ manipulating PGF soft paths}
   \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_generate_variant:Nn \spath_numberofcomponents:Nn {NV, cn, cV, Nv}
 \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_generate_variant:Nn \spath_gnumberofcomponents:Nn {NV, cn, cV}
+\cs_generate_variant:Nn \spath_gnumberofcomponents:Nn {NV, cn, cV, Nv}
 \cs_new_protected_nopar:Npn \__spath_initialpoint:n #1
 {
   \group_begin:
-  \tl_clear:N \l__spath_tmpb_tl
-  \tl_set:Nx \l__spath_tmpb_tl
+  \tl_clear:N \l__spath_tmpa_tl
+  \tl_set:Nx \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
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
   \group_end:
 }
 \cs_new_protected_nopar:Npn \spath_initialpoint:Nn #1#2
@@ -415,6 +419,50 @@ manipulating PGF soft paths}
   \tl_gclear:N \g__spath_output_tl
 }
 \cs_generate_variant:Nn \spath_gfinalpoint:Nn {NV, cn, cV, Nv}
+\cs_new_protected_nopar:Npn \__spath_finalmovepoint:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpc_tl { {0pt} {0pt} }
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \bool_do_until:nn
+  {
+    \tl_if_empty_p:N \l__spath_tmpa_tl
+  }
+  {
+    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_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} }
+        }
+      }
+    }
+    \prg_replicate:nn {3}
+    {
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+    }
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpc_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_finalmovepoint:Nn #1#2
+{
+  \__spath_finalmovepoint:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_finalmovepoint:Nn {NV, cn, cV}
+\cs_new_protected_nopar:Npn \spath_gfinalmovepoint:Nn #1#2
+{
+  \__spath_finalmovepoint:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gfinalmovepoint:Nn {NV, cn, cV}
 \cs_new_protected_nopar:Npn \__spath_reverse:n #1
 {
   \group_begin:
@@ -495,7 +543,10 @@ manipulating PGF soft paths}
         \bool_set_true:N \l__spath_closed_bool
       }
       {
-        \msg_warning:nnx { spath3 } { unknown path construction } {\l__spath_tmpc_tl }
+        \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}
@@ -629,9 +680,11 @@ manipulating PGF soft paths}
   }
   {
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
+    \dim_set:Nn \l__spath_tmpa_dim
+    {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
+    \dim_set:Nn \l__spath_tmpb_dim
+    {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   }
   \tl_clear:N \l__spath_tmpb_tl
@@ -671,9 +724,11 @@ manipulating PGF soft paths}
   }
   {
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
+    \dim_set:Nn \l__spath_tmpa_dim
+    {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
-    \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
+    \dim_set:Nn \l__spath_tmpb_dim
+    {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
     \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
   }
   \tl_clear:N \l__spath_tmpb_tl
@@ -752,6 +807,7 @@ manipulating PGF soft paths}
   \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
   \group_end:
 }
+\cs_generate_variant:Nn \__spath_translate:nnn {nVV}
 \cs_new_protected_nopar:Npn \spath_translate:Nnnn #1#2#3#4
 {
   \__spath_translate:nnn {#2}{#3}{#4}
@@ -786,6 +842,61 @@ manipulating PGF soft paths}
   \spath_gtranslate:Nnn #1 #2
 }
 \cs_generate_variant:Nn \spath_gtranslate:Nn {NV}
+\cs_new_protected_nopar:Npn \__spath_translate_to:nnn #1#2#3
+{
+  \group_begin:
+  \spath_initialpoint:Nn \l__spath_tmpa_tl {#1}
+
+  \dim_set:Nn \l__spath_tmpa_dim
+  {
+    #2
+    -
+    \tl_item:Nn \l__spath_tmpa_tl {1}
+  }
+  \dim_set:Nn \l__spath_tmpb_dim
+  {
+    #3
+    -
+    \tl_item:Nn \l__spath_tmpa_tl {2}
+  }
+
+  \__spath_translate:nVV {#1} \l__spath_tmpa_dim \l__spath_tmpb_dim
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_translate_to:Nnnn #1#2#3#4
+{
+  \__spath_translate_to: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_to:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_translate_to:Nnn #1#2#3
+{
+  \spath_translate_to:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_translate_to:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_gtranslate_to:Nnnn #1#2#3#4
+{
+  \__spath_translate_to: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_to:Nnnn {NVxx, NVVV, NVnn}
+\cs_new_protected_nopar:Npn \spath_gtranslate_to:Nnn #1#2#3
+{
+  \spath_gtranslate_to:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gtranslate_to:Nnn {NVV, cnn, cVV}
+\cs_new_protected_nopar:Npn \spath_translate_to:Nn #1#2
+{
+  \spath_translate_to:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_translate_to:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gtranslate_to:Nn #1#2
+{
+  \spath_gtranslate_to:Nnn #1 #2
+}
+\cs_generate_variant:Nn \spath_gtranslate_to:Nn {NV}
 \cs_new_protected_nopar:Npn \__spath_scale:nnn #1#2#3
 {
   \group_begin:
@@ -865,8 +976,10 @@ manipulating PGF soft paths}
     \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}
 
-    \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}
+    \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}
@@ -883,7 +996,8 @@ manipulating PGF soft paths}
   \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_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}
@@ -922,39 +1036,276 @@ manipulating PGF soft paths}
   \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
+\cs_new_protected_nopar:Npn \__spath_span:nnn #1#2#3
 {
   \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
+  \spath_initialpoint:Nn \l__spath_tmpa_tl {#1}
+  \spath_finalpoint:Nn \l__spath_tmpb_tl {#1}
 
-  \dim_set:Nn \l__spath_tmpa_dim
+  \fp_set:Nn \l__spath_tmpa_fp
   {
-    \tl_item:Nn \l__spath_tmpc_tl {1}
-    -
-    \tl_item:Nn \l__spath_tmpd_tl {1}
+    (\tl_item:Nn \l__spath_tmpb_tl {1}) -
+    (\tl_item:Nn \l__spath_tmpa_tl {1})
   }
-  \dim_set:Nn \l__spath_tmpb_dim
+  \fp_set:Nn \l__spath_tmpb_fp
   {
-    \tl_item:Nn \l__spath_tmpc_tl {2}
-    -
-    \tl_item:Nn \l__spath_tmpd_tl {2}
+    (\tl_item:Nn \l__spath_tmpb_tl {2}) -
+    (\tl_item:Nn \l__spath_tmpa_tl {2})
+  }
+  \fp_set:Nn \l__spath_tmpc_fp
+  {
+    (\l__spath_tmpa_fp) * (\l__spath_tmpa_fp)
+    +
+    (\l__spath_tmpb_fp * \l__spath_tmpb_fp)
   }
 
-  \spath_translate:NVV \l__spath_tmpb_tl \l__spath_tmpa_dim \l__spath_tmpb_dim
-
-  \prg_replicate:nn {3}
+  \fp_compare:nTF
+  {
+    \l__spath_tmpc_fp < 0.001
+  }
   {
-    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
+    \spath_translate_to:Nnnn \l__spath_tmpd_tl {#1} #2
   }
+  {
+    \fp_set:Nn \l__spath_tmpa_fp
+    {
+      (
+      ((\tl_item:nn {#3} {1})
+      -
+      (\tl_item:nn {#2} {1}))
+      *
+      ((\tl_item:Nn \l__spath_tmpb_tl {1})
+      -
+      (\tl_item:Nn \l__spath_tmpa_tl {1}))
+      +
+      ((\tl_item:nn {#3} {2})
+      -
+      (\tl_item:nn {#2} {2}))
+      *
+      ((\tl_item:Nn \l__spath_tmpb_tl {2})
+      -
+      (\tl_item:Nn \l__spath_tmpa_tl {2}))
+      )
+      /
+      \l__spath_tmpc_fp
+    }
+    \fp_set:Nn \l__spath_tmpb_fp
+    {
+      (
+      ((\tl_item:nn {#3} {2})
+      -
+      (\tl_item:nn {#2} {2}))
+      *
+      ((\tl_item:Nn \l__spath_tmpb_tl {1})
+      -
+      (\tl_item:Nn \l__spath_tmpa_tl {1}))
+      -
+      ((\tl_item:nn {#3} {1})
+      -
+      (\tl_item:nn {#2} {1}))
+      *
+      ((\tl_item:Nn \l__spath_tmpb_tl {2})
+      -
+      (\tl_item:Nn \l__spath_tmpa_tl {2}))
+      )
+      /
+      \l__spath_tmpc_fp
+    }
 
-  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+    \tl_set:Nx \l__spath_tmpc_tl
+    {
+      {
+        \fp_to_decimal:N \l__spath_tmpa_fp
+      }
+      {
+        \fp_to_decimal:N \l__spath_tmpb_fp
+      }
+      {
+        \fp_eval:n { - \l__spath_tmpb_fp }
+      }
+      {
+        \fp_to_decimal:N \l__spath_tmpa_fp
+      }
+      {
+        \fp_to_dim:n
+        {
+          \tl_item:nn {#2} {1}
+          -
+          \l__spath_tmpa_fp * (\tl_item:Nn \l__spath_tmpa_tl {1})
+          +
+          \l__spath_tmpb_fp * (\tl_item:Nn \l__spath_tmpa_tl {2})
+        }
+      }
+      {
+        \fp_to_dim:n
+        {
+          \tl_item:nn {#2} {2}
+          -
+          \l__spath_tmpb_fp * (\tl_item:Nn \l__spath_tmpa_tl {1})
+          -
+          \l__spath_tmpa_fp * (\tl_item:Nn \l__spath_tmpa_tl {2})
+        }
+      }
+    }
+    \spath_transform:NnV \l__spath_tmpd_tl {#1} \l__spath_tmpc_tl
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpd_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_span:Nnnn #1#2#3#4
+{
+  \__spath_span: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_span:Nnnn {NVnn, NVVV, NnVV}
+\cs_new_protected_nopar:Npn \spath_span:Nnn #1#2#3
+{
+  \spath_span:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_span:Nnn {NVV, cnn, cvv, cVV}
+\cs_new_protected_nopar:Npn \spath_gspan:Nnnn #1#2#3#4
+{
+  \__spath_span: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_gspan:Nnnn {NVnn, NVVV}
+\cs_new_protected_nopar:Npn \spath_gspan:Nnn #1#2#3
+{
+  \spath_gspan:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gspan:Nnn {NVV, cnn, cvv, cVV}
+\cs_new_protected_nopar:Npn \__spath_normalise:n #1
+{
+  \__spath_span:nnn {#1}{{0pt}{0pt}}{{1pt}{0pt}}
+}
+\cs_new_protected_nopar:Npn \spath_normalise:Nn #1#2
+{
+  \__spath_normalise:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_normalise:Nn {cn,NV, cV, cv}
+\cs_new_protected_nopar:Npn \spath_normalise:N #1
+{
+  \spath_normalise:NV #1#1
+}
+\cs_generate_variant:Nn \spath_normalise:N {c}
+\cs_new_protected_nopar:Npn \spath_gnormalise:Nn #1#2
+{
+  \__spath_normalise:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gnormalise:Nn {cn,NV, cV, cv}
+\cs_new_protected_nopar:Npn \spath_gnormalise:N #1
+{
+  \spath_gnormalise:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gnormalise:N {c}
+\cs_new_protected_nopar:Npn \__spath_splice_between:nnn #1#2#3
+{
+  \group_begin:
+  \spath_finalpoint:NV \l__spath_tmpd_tl {#1}
+  \spath_initialpoint:NV \l__spath_tmpe_tl {#3}
+  \spath_span:NnVV \l__spath_tmpb_tl {#2} \l__spath_tmpd_tl \l__spath_tmpe_tl
+  \spath_append_no_move:NnV \l__spath_tmpa_tl {#1} \l__spath_tmpb_tl
+  \spath_append_no_move:Nn \l__spath_tmpa_tl {#3}
   \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
   \group_end:
 }
+\cs_new_protected_nopar:Npn \spath_splice_between:Nnnn #1#2#3#4
+{
+  \__spath_splice_between: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_splice_between:Nnnn {NVnn, NVVV}
+\cs_new_protected_nopar:Npn \spath_splice_between:Nnn #1#2#3
+{
+  \spath_splice_between:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_splice_between:Nnn {NVV, cnn, cvv, Nvn}
+\cs_new_protected_nopar:Npn \spath_gsplice_between:Nnnn #1#2#3#4
+{
+  \__spath_splice_between: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_gsplice_between:Nnnn {NVnn, NVVV}
+\cs_new_protected_nopar:Npn \spath_gsplice_between:Nnn #1#2#3
+{
+  \spath_gsplice_between:NVnn #1#1{#2}{#3}
+}
+\cs_generate_variant:Nn \spath_gsplice_between:Nnn {NVV, cnn, cvv}
+\cs_new_protected_nopar:Npn \__spath_close_with:nn #1#2
+{
+  \group_begin:
+  \spath_finalmovepoint:Nn \l__spath_tmpa_tl {#1}
+  \spath_finalpoint:Nn \l__spath_tmpb_tl {#1}
+  \dim_compare:nTF
+  {
+    \dim_abs:n
+    {
+      \tl_item:Nn \l__spath_tmpa_tl {1}
+      -
+      \tl_item:Nn \l__spath_tmpb_tl {1}
+    }
+    +
+    \dim_abs:n
+    {
+      \tl_item:Nn \l__spath_tmpa_tl {2}
+      -
+      \tl_item:Nn \l__spath_tmpb_tl {2}
+    }
+    < 0.01pt
+  }
+  {
+    \__spath_close:n {#1}
+  }
+  {
+    \spath_span:NnVV \l__spath_tmpc_tl {#2} \l__spath_tmpb_tl \l__spath_tmpa_tl
+    \spath_append_no_move:NnV \l__spath_tmpd_tl {#1} \l__spath_tmpc_tl
+    \__spath_close:V \l__spath_tmpd_tl
+  }
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_close_with:Nnn #1#2#3
+{
+  \__spath_close_with:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_close_with:Nnn {cnn, cVV, cvv, NVn}
+\cs_new_protected_nopar:Npn \spath_close_with:Nn #1#2
+{
+  \spath_close_with:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_close_with:Nn {cn, cV, cv, NV}
+\cs_new_protected_nopar:Npn \spath_gclose_with:Nnn #1#2#3
+{
+  \__spath_close_with:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gclose_with:Nnn {cnn, cVV, cvv, NVn}
+\cs_new_protected_nopar:Npn \spath_gclose_with:Nn #1#2
+{
+  \spath_gclose_with:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gclose_with:Nn {cn, cV, 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:Nn \l__spath_tmpc_tl {#1}
+  \spath_translate_to:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
+
+  \__spath_append_no_move:VV \l__spath_tmpa_tl \l__spath_tmpb_tl
+  \group_end:
+}
 \cs_new_protected_nopar:Npn \spath_weld:Nnn #1#2#3
 {
   \__spath_weld:nn {#2}{#3}
@@ -992,18 +1343,19 @@ manipulating PGF soft paths}
   \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
   \group_end:
 }
+\cs_generate_variant:Nn \__spath_append_no_move:nn {VV}
 \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_generate_variant:Nn \spath_append_no_move:Nnn {NVV, NVn, NnV}
 \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_generate_variant:Nn \spath_append_no_move:Nn {NV, cv, Nv}
 \cs_new_protected_nopar:Npn \spath_gappend_no_move:Nnn #1#2#3
 {
   \__spath_append_no_move:nn {#2}{#3}
@@ -1015,7 +1367,7 @@ manipulating PGF soft paths}
 {
   \spath_gappend_no_move:NVn #1#1{#2}
 }
-\cs_generate_variant:Nn \spath_gappend_no_move:Nn {NV, cv}
+\cs_generate_variant:Nn \spath_gappend_no_move:Nn {NV, cv, Nv}
 \cs_new_protected_nopar:Npn \spath_append:Nnn #1#2#3
 {
   \tl_set:Nn #1 {#2}
@@ -1026,7 +1378,7 @@ manipulating PGF soft paths}
 {
   \spath_append:NVn #1#1{#2}
 }
-\cs_generate_variant:Nn \spath_append:Nn {NV, Nv}
+\cs_generate_variant:Nn \spath_append:Nn {NV, Nv, cv}
 \cs_new_protected_nopar:Npn \spath_gappend:Nnn #1#2#3
 {
   \tl_gset:Nn #1 {#2}
@@ -1037,7 +1389,7 @@ manipulating PGF soft paths}
 {
   \spath_gappend:NVn #1#1{#2}
 }
-\cs_generate_variant:Nn \spath_gappend:Nn {NV, Nv}
+\cs_generate_variant:Nn \spath_gappend:Nn {NV, Nv, cv}
 \cs_new_protected_nopar:Npn \spath_prepend_no_move:Nnn #1#2#3
 {
   \spath_append_no_move:Nnn #1{#3}{#2}
@@ -1114,12 +1466,13 @@ manipulating PGF soft paths}
 {
   \group_begin:
   \tl_set:Nn \l__spath_tmpa_tl {#1}
-  \spath_initialpoint:NV \l__spath_tmpb_tl \l__spath_tmpa_tl
+  \spath_finalmovepoint: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_generate_variant:Nn \__spath_close:n {V}
 \cs_new_protected_nopar:Npn \spath_close:Nn #1#2
 {
   \__spath_close:n {#2}
@@ -1291,7 +1644,10 @@ manipulating PGF soft paths}
   \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}
+  \int_compare:nNnTF
+  {\tl_count:N \l__spath_tmpa_tl}
+  =
+  {\tl_count:N \l__spath_tmpb_tl}
   {
     \int_step_inline:nnnn {1} {3} {\tl_count:N \l__spath_tmpa_tl}
     {
@@ -1303,13 +1659,27 @@ manipulating PGF soft paths}
       }
       \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 }
+      \dim_compare:nF
+      {
+        \dim_abs:n
+        {
+          \l__spath_tmpa_dim - \l__spath_tmpb_dim
+        }
+        < 0.001pt
+      }
       {
         \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 }
+      \dim_compare:nF
+      {
+        \dim_abs:n
+        {
+          \l__spath_tmpa_dim - \l__spath_tmpb_dim
+        }
+        < 0.001pt
+      }
       {
         \bool_gset_false:N \g__spath_tmpa_bool
       }
@@ -1354,11 +1724,15 @@ manipulating PGF soft paths}
   {
     {\fp_to_dim:n
     {
-      (1 - #2)^2 * \tl_item:nn {#1} {2} + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {5} + (#2)^2 * \tl_item:nn {#1} {8}
+      (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}
+      (1 - #2)^2 * \tl_item:nn {#1} {3}
+      + 2 * (1 - #2) * (#2) * \tl_item:nn {#1} {6}
+      + (#2)^2 * \tl_item:nn {#1} {9}
     }}
   }
 
@@ -1367,11 +1741,17 @@ manipulating PGF soft paths}
   {
     {\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}
+        (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}
+      (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}
     }}
   }
 
@@ -1384,11 +1764,17 @@ manipulating PGF soft paths}
   {
     {\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}
+        (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}
+      (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}
     }}
   }
 
@@ -1397,11 +1783,15 @@ manipulating PGF soft paths}
   {
     {\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}
+      (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}
+      (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
@@ -1425,6 +1815,7 @@ manipulating PGF soft paths}
   \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpa_tl
   \group_end:
 }
+\cs_generate_variant:Nn \__spath_split_curve:nn {nv, nV}
 \cs_new_protected_nopar:Npn \spath_split_curve:NNnn #1#2#3#4
 {
   \__spath_split_curve:nn {#3}{#4}
@@ -1441,6 +1832,201 @@ manipulating PGF soft paths}
   \tl_gclear:N \g__spath_output_tl
 }
 \cs_generate_variant:Nn \spath_gsplit_curve:NNnn {NNnV, NNVn, NNVV}
+\cs_new_protected_nopar:Npn \__spath_maybe_split_curve:n #1
+{
+  \group_begin:
+  \fp_set:Nn \l__spath_tmpa_fp
+  {
+    (
+    \tl_item:nn {#1} {3}
+    - 3 * \tl_item:nn {#1} {6}
+    + 3 * \tl_item:nn {#1} {9}
+    - \tl_item:nn {#1} {12}
+    )
+    *
+    (3 * \tl_item:nn {#1} {8} - 3 * \tl_item:nn {#1} {11})
+    -
+    (
+    \tl_item:nn {#1} {2}
+    - 3 * \tl_item:nn {#1} {5}
+    + 3 * \tl_item:nn {#1} {8}
+    - \tl_item:nn {#1} {11}
+    )
+    *
+    (3 * \tl_item:nn {#1} {9} - 3 * \tl_item:nn {#1} {12})
+  }
+  \fp_set:Nn \l__spath_tmpb_fp
+  {
+    (
+    \tl_item:nn {#1} {2}
+    - 3 * \tl_item:nn {#1} {5}
+    + 3 * \tl_item:nn {#1} {8}
+    - \tl_item:nn {#1} {11}
+    )
+    *
+    (
+    3 * \tl_item:nn {#1} {6}
+    - 6 * \tl_item:nn {#1} {9}
+    + 3 * \tl_item:nn {#1} {12}
+    )
+    -
+    (
+    \tl_item:nn {#1} {3}
+    - 3 * \tl_item:nn {#1} {6}
+    + 3 * \tl_item:nn {#1} {9}
+    - \tl_item:nn {#1} {12}
+    )
+    *
+    (
+    3 * \tl_item:nn {#1} {5}
+    - 6 * \tl_item:nn {#1} {8}
+    + 3 * \tl_item:nn {#1} {11}
+    )
+  }
+  \fp_compare:nTF
+  {
+    \l__spath_tmpb_fp != 0
+  }
+  {
+    \fp_set:Nn \l__spath_tmpa_fp {.5 * \l__spath_tmpa_fp / \l__spath_tmpb_fp}
+    \fp_compare:nTF
+    {
+      0 < \l__spath_tmpa_fp && \l__spath_tmpa_fp < 1
+    }
+    {
+      \__spath_split_curve:nV {#1} \l__spath_tmpa_fp
+    }
+    {
+      \tl_gset:Nn \g__spath_output_tl { {#1} {} }
+    }
+  }
+  {
+    \tl_gset:Nn \g__spath_output_tl { {#1} {} }
+  }
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_maybe_split_curve:NNn #1#2#3
+{
+  \__spath_maybe_split_curve:n {#3}
+  \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_maybe_split_curve:NNn {NNn, NNV }
+\cs_new_protected_nopar:Npn \spath_maybe_gsplit_curve:NNn #1#2#3
+{
+  \__spath_maybe_split_curve:n {#3}
+  \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_maybe_gsplit_curve:NNn {NNn, NNV}
+\cs_new_protected_nopar:Npn \__spath_split_curves:n #1
+{
+  \group_begin:
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
+  \tl_clear:N \l__spath_tmpb_tl
+  \tl_clear:N \l__spath_tmpc_tl
+  \bool_do_until: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_case:NnF \l__spath_tmpc_tl
+    {
+      \c_spath_curvetoa_tl
+      {
+        \tl_clear:N \l__spath_tmpd_tl
+        \tl_set_eq:NN \l__spath_tmpd_tl \c_spath_moveto_tl
+        \tl_put_right:Nx \l__spath_tmpd_tl
+        {
+          { \dim_use:N \l__spath_tmpa_dim }
+          { \dim_use:N \l__spath_tmpb_dim }
+        }
+        \dim_set:Nn \l__spath_tmpa_dim
+        {
+          \tl_item:Nn \l__spath_tmpa_tl {8}
+        }
+        \dim_set:Nn \l__spath_tmpb_dim
+        {
+          \tl_item:Nn \l__spath_tmpa_tl {9}
+        }
+        \prg_replicate:nn {3}
+        {
+          \tl_put_right:Nx \l__spath_tmpd_tl
+          {
+            \tl_item:Nn \l__spath_tmpa_tl {1}
+            {\tl_item:Nn \l__spath_tmpa_tl {2}}
+            {\tl_item:Nn \l__spath_tmpa_tl {3}}
+          }
+          \prg_replicate:nn {3}
+          {
+            \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+          }
+        }
+
+        \spath_maybe_split_curve:NNV
+        \l__spath_tmpd_tl
+        \l__spath_tmpe_tl
+        \l__spath_tmpd_tl
+        \prg_replicate:nn {3}
+        {
+          \tl_set:Nx \l__spath_tmpd_tl {\tl_tail:N \l__spath_tmpd_tl}
+          \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_tl}
+        }
+        \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
+        \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpe_tl
+      }
+    }
+    {
+      \dim_set:Nn \l__spath_tmpa_dim
+      {
+        \tl_item:Nn \l__spath_tmpa_tl {2}
+      }
+      \dim_set:Nn \l__spath_tmpb_dim
+      {
+        \tl_item:Nn \l__spath_tmpa_tl {3}
+      }
+      \tl_put_right:Nx \l__spath_tmpb_tl
+      {
+        \tl_item:Nn \l__spath_tmpa_tl {1}
+        {\tl_item:Nn \l__spath_tmpa_tl {2}}
+        {\tl_item:Nn \l__spath_tmpa_tl {3}}
+      }
+      \prg_replicate:nn {3}
+      {
+        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      }
+    }
+  }
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_curves:Nn #1#2
+{
+  \__spath_split_curves:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_curves:Nn {NV, cV, cn, cv }
+\cs_new_protected_nopar:Npn \spath_split_curves:N #1
+{
+  \spath_split_curves:NV #1#1
+}
+\cs_generate_variant:Nn \spath_split_curves:N {c}
+\cs_new_protected_nopar:Npn \spath_gsplit_curves:Nn #1#2
+{
+  \__spath_split_curves:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_curves:Nn {NV, cV, cn, cv }
+\cs_new_protected_nopar:Npn \spath_gsplit_curves:N #1
+{
+  \spath_gsplit_curves:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gsplit_curves:N {c}
 \cs_new_protected_nopar:Npn \__spath_split_line:nn #1#2
 {
   \group_begin:
@@ -1502,179 +2088,168 @@ manipulating PGF soft paths}
   \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)}
+  \int_set:Nn \l__spath_tmpa_int {\fp_to_int:n {floor(#2) + 1}}
+  \fp_set:Nn \l__spath_tmpa_fp {#2 - floor(#2)}
 
   % Is split point near one end or other of a component?
   \fp_compare:nT
   {
-    \l__spath_split_fp < 0.01
+    \l__spath_tmpa_fp < 0.01
   }
   {
     % Near the start, so we'll place it at the start
-    \fp_set:Nn \l__spath_split_fp {0}
+    \fp_set:Nn \l__spath_tmpa_fp {0}
   }
   \fp_compare:nT
   {
-    \l__spath_split_fp > 0.99
+    \l__spath_tmpa_fp > 0.99
   }
   {
     % 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
+    \fp_set:Nn \l__spath_tmpa_fp {0}
+    \int_incr:N \l__spath_tmpa_int
   }
 
-  \int_zero:N \l__spath_split_int
-  \bool_set_true:N \l__spath_split_bool
+  \int_zero:N \l__spath_tmpb_int
+  \bool_set_true:N \l__spath_tmpa_bool
 
-  \tl_set:Nn \l__spath_split_path_tl {#1}
-  \tl_clear:N \l__spath_split_patha_tl
+  \tl_set:Nn \l__spath_tmpe_tl {#1}
+  \tl_clear:N \l__spath_tmpc_tl
 
-  \dim_zero:N \l__spath_splitx_dim
-  \dim_zero:N \l__spath_splity_dim
+  \dim_zero:N \l__spath_tmpa_dim
+  \dim_zero:N \l__spath_tmpb_dim
 
   \bool_until_do:nn {
-    \tl_if_empty_p:N \l__spath_split_path_tl
+    \tl_if_empty_p:N \l__spath_tmpe_tl
     ||
-    \int_compare_p:n { \l__spath_splitat_int == \l__spath_split_int  }
+    \int_compare_p:n { \l__spath_tmpa_int == \l__spath_tmpb_int  }
   }
   {
-    \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
+    \tl_set:Nx \l__spath_tmpf_tl {\tl_head:N \l__spath_tmpe_tl}
+    \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_tl }
+    \tl_case:Nn \l__spath_tmpf_tl
     {
       \c_spath_lineto_tl
       {
-        \int_incr:N \l__spath_split_int
+        \int_incr:N \l__spath_tmpb_int
       }
       \c_spath_curvetoa_tl
       {
-        \int_incr:N \l__spath_split_int
+        \int_incr:N \l__spath_tmpb_int
       }
     }
-    \int_compare:nT { \l__spath_split_int < \l__spath_splitat_int  }
+    \int_compare:nT { \l__spath_tmpb_int < \l__spath_tmpa_int  }
     {
-      \tl_put_right:NV \l__spath_split_patha_tl \l__spath_tmpc_tl
+      \tl_put_right:NV \l__spath_tmpc_tl \l__spath_tmpf_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_tmpc_tl
+      {{ \tl_head:N \l__spath_tmpe_tl }}
+      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpe_tl}
+      \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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 }
+      \tl_put_right:Nx \l__spath_tmpc_tl
+      {{ \tl_head:N \l__spath_tmpe_tl }}
+      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpe_tl}
+      \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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
+  \tl_clear:N \l__spath_tmpd_tl
+  \tl_put_right:NV \l__spath_tmpd_tl \c_spath_moveto_tl
+  \tl_put_right:Nx \l__spath_tmpd_tl
   {
-    {\dim_use:N \l__spath_splitx_dim}
-    {\dim_use:N \l__spath_splity_dim}
+    {\dim_use:N \l__spath_tmpa_dim}
+    {\dim_use:N \l__spath_tmpb_dim}
   }
 
   \fp_compare:nTF
   {
-    \l__spath_split_fp == 0
+    \l__spath_tmpa_fp == 0
   }
   {
-    \tl_set_eq:NN \l__spath_split_intob_tl \l__spath_split_pathb_tl
-    \tl_if_empty:NF \l__spath_split_path_tl
+    \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpd_tl
+    \tl_if_empty:NF \l__spath_tmpe_tl
     {
-      \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
+      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpf_tl
+      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpe_tl
     }
   }
   {
 
-    \tl_case:Nn \l__spath_tmpc_tl
+    \tl_case:Nn \l__spath_tmpf_tl
     {
       \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:NV \l__spath_tmpd_tl \l__spath_tmpf_tl
+        \tl_put_right:Nx \l__spath_tmpd_tl
+        {{ \tl_head:N \l__spath_tmpe_tl }}
+        \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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_tmpd_tl
+        {{ \tl_head:N \l__spath_tmpe_tl }}
+        \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_tl }
 
         \spath_split_line:NNVV
-        \l__spath_split_intoa_tl
-        \l__spath_split_intob_tl
-        \l__spath_split_pathb_tl
-        \l__spath_split_fp
+        \l__spath_tmpa_tl
+        \l__spath_tmpb_tl
+        \l__spath_tmpd_tl
+        \l__spath_tmpa_fp
 
         \prg_replicate:nn {3} {
-          \tl_set:Nx \l__spath_split_intoa_tl {\tl_tail:N \l__spath_split_intoa_tl}
+          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_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_put_right:NV \l__spath_tmpc_tl \l__spath_tmpa_tl
+        \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpe_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:NV \l__spath_tmpd_tl \l__spath_tmpf_tl
+        \tl_put_right:Nx \l__spath_tmpd_tl
+        {{ \tl_head:N \l__spath_tmpe_tl }}
+        \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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_tmpd_tl
+        {{ \tl_head:N \l__spath_tmpe_tl }}
+        \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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_tmpd_tl
+          { \tl_head:N \l__spath_tmpe_tl }
+          \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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_tmpd_tl
+          {{ \tl_head:N \l__spath_tmpe_tl }}
+          \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_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_tmpd_tl
+          {{ \tl_head:N \l__spath_tmpe_tl }}
+          \tl_set:Nx \l__spath_tmpe_tl {\tl_tail:N \l__spath_tmpe_tl }
         }
 
         \spath_split_curve:NNVV
-        \l__spath_split_intoa_tl
-        \l__spath_split_intob_tl
-        \l__spath_split_pathb_tl \l__spath_split_fp
+        \l__spath_tmpa_tl
+        \l__spath_tmpb_tl
+        \l__spath_tmpd_tl \l__spath_tmpa_fp
 
         \prg_replicate:nn {3} {
-          \tl_set:Nx \l__spath_split_intoa_tl {\tl_tail:N \l__spath_split_intoa_tl}
+          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_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_put_right:NV \l__spath_tmpc_tl \l__spath_tmpa_tl
+        \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpe_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
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpc_tl
+  \__spath_tl_gput_right_braced:NV \g__spath_output_tl \l__spath_tmpb_tl
   \group_end:
 }
 \cs_new_protected_nopar:Npn \spath_split_at:NNnn #1#2#3#4
@@ -1696,7 +2271,11 @@ manipulating PGF soft paths}
 \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_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}
@@ -1707,7 +2286,11 @@ manipulating PGF soft paths}
 \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_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}
@@ -1715,15 +2298,6 @@ manipulating PGF soft paths}
 {
   \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
@@ -1732,121 +2306,121 @@ manipulating PGF soft paths}
   }
   {
     \group_begin:
-    \tl_set:Nn \l__spath_shorten_path_tl {#1}
-    \tl_reverse:N \l__spath_shorten_path_tl
+    \tl_set:Nn \l__spath_tmpa_tl {#1}
+    \tl_reverse:N \l__spath_tmpa_tl
 
-    \tl_set:Nx \l__spath_shorten_fa_tl {\tl_item:Nn \l__spath_shorten_path_tl {3}}
+    \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {3}}
 
-    \tl_clear:N \l__spath_shorten_last_tl
-    \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curveto_tl
+    \tl_clear:N \l__spath_tmpe_tl
+    \tl_if_eq:NNTF \l__spath_tmpb_tl \c_spath_curveto_tl
     {
-      \int_set:Nn \l__spath_shorten_int {3}
+      \int_set:Nn \l__spath_tmpa_int {3}
     }
     {
-      \int_set:Nn \l__spath_shorten_int {1}
+      \int_set:Nn \l__spath_tmpa_int {1}
     }
 
-    \prg_replicate:nn { \l__spath_shorten_int }
+    \prg_replicate:nn { \l__spath_tmpa_int }
     {
-      \tl_put_right:Nx \l__spath_shorten_last_tl
+      \tl_put_right:Nx \l__spath_tmpe_tl
       {
-        {\tl_head:N \l__spath_shorten_path_tl}
+        {\tl_head:N \l__spath_tmpa_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_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \tl_put_right:Nx \l__spath_tmpe_tl
       {
-        {\tl_head:N \l__spath_shorten_path_tl}
+        {\tl_head:N \l__spath_tmpa_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_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+      \tl_put_right:Nx \l__spath_tmpe_tl
       {
-        \tl_head:N \l__spath_shorten_path_tl
+        \tl_head:N \l__spath_tmpa_tl
       }
-      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
     }
 
-    \tl_put_right:Nx \l__spath_shorten_last_tl
+    \tl_put_right:Nx \l__spath_tmpe_tl
     {
-      {\tl_item:Nn \l__spath_shorten_path_tl {1}}
-      {\tl_item:Nn \l__spath_shorten_path_tl {2}}
+      {\tl_item:Nn \l__spath_tmpa_tl {1}}
+      {\tl_item:Nn \l__spath_tmpa_tl {2}}
     }
-    \tl_put_right:NV \l__spath_shorten_last_tl \c_spath_moveto_tl
+    \tl_put_right:NV \l__spath_tmpe_tl \c_spath_moveto_tl
 
-    \tl_reverse:N \l__spath_shorten_path_tl
+    \tl_reverse:N \l__spath_tmpa_tl
 
-    \fp_set:Nn \l__spath_shorten_x_fp
+    \fp_set:Nn \l__spath_tmpa_fp
     {
-      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {4}}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {4}}
       -
-      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {1}}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {1}}
     }
 
-    \fp_set:Nn \l__spath_shorten_y_fp
+    \fp_set:Nn \l__spath_tmpb_fp
     {
-      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {5}}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {5}}
       -
-      \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {2}}
+      \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {2}}
     }
 
-    \fp_set:Nn \l__spath_shorten_len_fp
+    \fp_set:Nn \l__spath_tmpc_fp
     {
-      sqrt( \l__spath_shorten_x_fp * \l__spath_shorten_x_fp +  \l__spath_shorten_y_fp *  \l__spath_shorten_y_fp )
+      sqrt(
+      \l__spath_tmpa_fp * \l__spath_tmpa_fp
+      +
+      \l__spath_tmpb_fp *  \l__spath_tmpb_fp
+      ) * \l__spath_tmpa_int
     }
 
     \fp_compare:nTF
     {
-      \l__spath_shorten_len_fp > #2
+      \l__spath_tmpc_fp > #2
     }
     {
 
-      \fp_set:Nn \l__spath_shorten_len_fp
+      \fp_set:Nn \l__spath_tmpc_fp
       {
-        (\l__spath_shorten_len_fp - #2)/ \l__spath_shorten_len_fp
+        (\l__spath_tmpc_fp - #2)/ \l__spath_tmpc_fp
       }
 
-      \tl_reverse:N \l__spath_shorten_last_tl
+      \tl_reverse:N \l__spath_tmpe_tl
 
-      \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curveto_tl
+      \tl_if_eq:NNTF \l__spath_tmpb_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
+        \l__spath_tmpc_tl
+        \l__spath_tmpd_tl
+        \l__spath_tmpe_tl
+        \l__spath_tmpc_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
+        \l__spath_tmpc_tl
+        \l__spath_tmpd_tl
+        \l__spath_tmpe_tl
+        \l__spath_tmpc_fp
       }
 
       \prg_replicate:nn {3}
       {
-        \tl_set:Nx \l__spath_shorten_lasta_tl {\tl_tail:N \l__spath_shorten_lasta_tl}
+        \tl_set:Nx \l__spath_tmpc_tl {\tl_tail:N \l__spath_tmpc_tl}
       }
 
-      \tl_put_right:NV \l__spath_shorten_path_tl \l__spath_shorten_lasta_tl
+      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpc_tl
 
     }
     {
 
       \int_compare:nT
       {
-        \tl_count:N \l__spath_shorten_path_tl > 3
+        \tl_count:N \l__spath_tmpa_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
+        \dim_set:Nn \l__spath_tmpa_dim {\fp_to_dim:n {#2 - \l__spath_tmpc_fp } }
+        \spath_shorten_at_end:NV \l__spath_tmpa_tl \l__spath_tmpa_dim
       }
     }
 
-    \tl_gset_eq:NN \g__spath_output_tl \l__spath_shorten_path_tl
+    \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
     \group_end:
   }
   {
@@ -1885,110 +2459,120 @@ manipulating PGF soft paths}
   }
   {
   \group_begin:
-  \tl_set:Nn \l__spath_shorten_path_tl {#1}
+  \tl_set:Nn \l__spath_tmpa_tl {#1}
 
-  \tl_set:Nx \l__spath_shorten_fa_tl {\tl_item:Nn \l__spath_shorten_path_tl {4}}
+  \tl_set:Nx \l__spath_tmpb_tl {\tl_item:Nn \l__spath_tmpa_tl {4}}
 
-    \tl_clear:N \l__spath_shorten_last_tl
+    \tl_clear:N \l__spath_tmpe_tl
 
-  \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curvetoa_tl
+  \tl_if_eq:NNTF \l__spath_tmpb_tl \c_spath_curvetoa_tl
   {
-    \int_set:Nn \l__spath_shorten_int {3}
+    \int_set:Nn \l__spath_tmpa_int {3}
   }
   {
-    \int_set:Nn \l__spath_shorten_int {1}
+    \int_set:Nn \l__spath_tmpa_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 }
+  \tl_set_eq:NN \l__spath_tmpe_tl \c_spath_moveto_tl
+  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl }
 
-  \prg_replicate:nn { \l__spath_shorten_int }
+  \prg_replicate:nn { \l__spath_tmpa_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}}
+    \__spath_tl_put_right_braced:Nx
+    \l__spath_tmpe_tl
+    {\tl_item:Nn \l__spath_tmpa_tl {1}}
+    \__spath_tl_put_right_braced:Nx
+    \l__spath_tmpe_tl
+    {\tl_item:Nn \l__spath_tmpa_tl {2}}
+    \tl_put_right:Nx \l__spath_tmpe_tl {\tl_item:Nn \l__spath_tmpa_tl {3}}
 
     \prg_replicate:nn {3}
     {
-      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl }
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_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}}
+  \__spath_tl_put_right_braced:Nx
+  \l__spath_tmpe_tl
+  {\tl_item:Nn \l__spath_tmpa_tl {1}}
+  \__spath_tl_put_right_braced:Nx
+  \l__spath_tmpe_tl
+  {\tl_item:Nn \l__spath_tmpa_tl {2}}
 
-  \fp_set:Nn \l__spath_shorten_x_fp
+  \fp_set:Nn \l__spath_tmpa_fp
   {
-    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {5}}
+    \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {5}}
     -
-    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {2}}
+    \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {2}}
   }
 
-  \fp_set:Nn \l__spath_shorten_y_fp
+  \fp_set:Nn \l__spath_tmpb_fp
   {
-    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {6}}
+    \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {6}}
     -
-    \dim_to_fp:n {\tl_item:Nn \l__spath_shorten_last_tl {3}}
+    \dim_to_fp:n {\tl_item:Nn \l__spath_tmpe_tl {3}}
   }
 
-  \fp_set:Nn \l__spath_shorten_len_fp
+  \fp_set:Nn \l__spath_tmpc_fp
   {
-    sqrt( \l__spath_shorten_x_fp * \l__spath_shorten_x_fp +  \l__spath_shorten_y_fp *  \l__spath_shorten_y_fp )
+    sqrt(
+    \l__spath_tmpa_fp * \l__spath_tmpa_fp
+    +
+    \l__spath_tmpb_fp *  \l__spath_tmpb_fp
+    )
+    *
+    \l__spath_tmpa_int
   }
 
   \fp_compare:nTF
   {
-    \l__spath_shorten_len_fp > #2
+    \l__spath_tmpc_fp > #2
   }
   {
 
-    \fp_set:Nn \l__spath_shorten_len_fp
+    \fp_set:Nn \l__spath_tmpc_fp
     {
-      #2/ \l__spath_shorten_len_fp
+      #2/ \l__spath_tmpc_fp
     }
 
-    \tl_if_eq:NNTF \l__spath_shorten_fa_tl \c_spath_curvetoa_tl
+    \tl_if_eq:NNTF \l__spath_tmpb_tl \c_spath_curvetoa_tl
     {
-      \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
+      \l__spath_tmpc_tl
+      \l__spath_tmpd_tl
+      \l__spath_tmpe_tl
+      \l__spath_tmpc_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
+      \l__spath_tmpc_tl
+      \l__spath_tmpd_tl
+      \l__spath_tmpe_tl
+      \l__spath_tmpc_fp
     }
 
     \prg_replicate:nn {2}
     {
-      \tl_set:Nx \l__spath_shorten_path_tl {\tl_tail:N \l__spath_shorten_path_tl}
+      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
     }
 
-    \tl_put_left:NV \l__spath_shorten_path_tl \l__spath_shorten_lastb_tl
+    \tl_put_left:NV \l__spath_tmpa_tl \l__spath_tmpd_tl
 
   }
   {
 
-    \tl_put_left:NV \l__spath_shorten_path_tl \c_spath_moveto_tl
+    \tl_put_left:NV \l__spath_tmpa_tl \c_spath_moveto_tl
 
     \int_compare:nT
     {
-      \tl_count:N \l__spath_shorten_path_tl > 3
+      \tl_count:N \l__spath_tmpa_tl > 3
     }
     {
-      \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
+      \dim_set:Nn \l__spath_tmpa_dim {\fp_to_dim:n {#2 - \l__spath_tmpc_fp } }
+      \spath_shorten_at_start:NV \l__spath_tmpa_tl \l__spath_tmpa_dim
     }
   }
 
-  \tl_gset_eq:NN \g__spath_output_tl \l__spath_shorten_path_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
   \group_end:
   }
   {
@@ -2044,7 +2628,9 @@ manipulating PGF soft paths}
     }
     {
 
-      \tl_set:Nx \l__spath_tmpa_tl {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
+      \tl_set:Nx
+      \l__spath_tmpa_tl
+      {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
 
       \int_compare:nTF
       {
@@ -2122,11 +2708,21 @@ manipulating PGF soft paths}
           {
             {\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}
+                (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}
+                (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}
             }}
           }
         }
@@ -2177,7 +2773,9 @@ manipulating PGF soft paths}
     }
     {
 
-      \tl_set:Nx \l__spath_tmpa_tl {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
+      \tl_set:Nx
+      \l__spath_tmpa_tl
+      {\seq_item:Nn \l__spath_tmpa_seq { \l__spath_tmpa_int} }
 
       \int_compare:nTF
       {
@@ -2255,16 +2853,24 @@ manipulating PGF soft paths}
           {
             {\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})
+                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})
+                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})
             }}
           }
         }
@@ -2296,15 +2902,24 @@ manipulating PGF soft paths}
   \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_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}
   {
     \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 }
+    \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
   {
@@ -2332,22 +2947,6 @@ manipulating PGF soft paths}
   \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%
@@ -2357,152 +2956,199 @@ manipulating PGF soft paths}
     \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
+\cs_new_protected_nopar:Npn \__spath_split_component_at_intersections:nn #1#2
 {
   \group_begin:
+  \tl_clear:N \l__spath_tmpe_tl
+  \seq_clear:N \l__spath_tmpb_seq
 
-  % 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
+  \tl_set:Nn \l__spath_tmpb_tl {#1}
+  \tl_set:Nn \l__spath_tmpc_tl {#2}
 
-  \spath_intersect:NN \l__spath_split_path_a_tl \l__spath_split_path_b_tl
+  \spath_reallength:Nn \l__spath_tmpa_int {#1}
 
-  % If we get intersections
-  \int_compare:nT {\pgfintersectionsolutions > 0}
+  % Remember if the component is closed
+  \spath_finalaction:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+
+  \bool_set:Nn \l__spath_closed_bool
   {
-    % 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}
-      \seq_put_left:NV \l__spath_split_first_seq \l__spath_split_first_tl
-    }
+    \tl_if_eq_p:NN \l__spath_tmpa_tl \c_spath_closepath_tl
   }
 
-  \spath_intersect:NN \l__spath_split_path_b_tl \l__spath_split_path_a_tl
+  % Open it
+  \spath_open:N \l__spath_tmpb_tl
+
+  % Sort intersections along the component
+  \pgfintersectionsortbyfirstpath
+  \spath_intersect:NN \l__spath_tmpb_tl \l__spath_tmpc_tl
 
   % If we get intersections
   \int_compare:nT {\pgfintersectionsolutions > 0}
   {
-    % Find the times of the intersections on each path
+    % Find the times of the intersections on the component
     \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
     {
-    \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
+      \pgfintersectiongetsolutiontimes{##1}{\l__spath_tmph_tl}{\l__spath_tmpi_tl}
+      \seq_put_left:NV \l__spath_tmpb_seq \l__spath_tmph_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
+    \seq_get_left:NN \l__spath_tmpb_seq \l__spath_tmpa_tl
+    \fp_compare:nT
     {
-      \fp_to_int:n {floor( \l__spath_split_first_tl) }
-      =
-      \fp_to_int:n {floor( \l__spath_split_prev_first_tl) }
+      \l__spath_tmpa_tl > \l__spath_tmpa_int - .01
     }
     {
-      \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) )
-        }
-      }
+      \bool_set_false:N \l__spath_closed_bool
     }
-    \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
+    \seq_get_right:NN \l__spath_tmpb_seq \l__spath_tmpa_tl
+    \fp_compare:nT
     {
-      \fp_to_int:n {floor( \l__spath_split_second_tl) }
-      =
-      \fp_to_int:n {floor( \l__spath_split_prev_second_tl) }
+      \l__spath_tmpa_tl < .01
     }
     {
-      \tl_set:Nx \l__spath_split_second_tl
+      \bool_set_false:N \l__spath_closed_bool
+    }
+
+    \tl_set:Nn \l__spath_tmpg_tl {-1}
+
+    \seq_map_inline:Nn \l__spath_tmpb_seq
+    {
+      \tl_set:Nn \l__spath_tmph_tl {##1}
+
+      \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_tmph_tl
+      \int_compare:nT
       {
-        \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) )
+        \fp_to_int:n {floor( \l__spath_tmph_tl) }
+        =
+        \fp_to_int:n {floor( \l__spath_tmpg_tl) }
+      }
+      {
+        \tl_set:Nx \l__spath_tmph_tl
+        {
+          \fp_eval:n {
+            floor( \l__spath_tmph_tl )
+            +
+            ( \l__spath_tmph_tl - floor( \l__spath_tmph_tl) )
+            /
+            ( \l__spath_tmpg_tl - floor( \l__spath_tmpg_tl) )
+          }
         }
       }
+      \tl_set_eq:NN \l__spath_tmpg_tl \l__spath_tmpa_tl
+
+      \spath_split_at:NNVV
+      \l__spath_tmpd_tl
+      \l__spath_tmpf_tl
+      \l__spath_tmpb_tl
+      \l__spath_tmph_tl
+
+      \tl_put_left:NV \l__spath_tmpe_tl \l__spath_tmpf_tl
+      \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpd_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_tmpe_tl \l__spath_tmpb_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
+    \spath_remove_empty_components:N \l__spath_tmpe_tl
 
+    \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpe_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
+  \bool_if:NT \l__spath_closed_bool
   {
-    \tl_set_eq:NN \l__spath_split_path_a_final_tl \l__spath_split_path_a_tl
+    \spath_join_component:Nn \l__spath_tmpb_tl {1}
   }
-  \tl_if_empty:NT \l__spath_split_path_b_final_tl
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpb_tl
+
+  \group_end:
+}
+\cs_new_protected_nopar:Npn \spath_split_component_at_intersections:Nnn #1#2#3
+{
+  \__spath_split_component_at_intersections:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_component_at_intersections:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_split_component_at_intersections:Nn #1#2
+{
+  \spath_split_component_at_intersections:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_split_component_at_intersections:Nn {cn, cv}
+\cs_new_protected_nopar:Npn \spath_gsplit_component_at_intersections:Nnn #1#2#3
+{
+  \__spath_split_component_at_intersections:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_component_at_intersections:Nnn {NVn, NVV}
+\cs_new_protected_nopar:Npn \spath_gsplit_component_at_intersections:Nn #1#2
+{
+  \spath_gsplit_component_at_intersections:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gsplit_component_at_intersections:Nn {cn, cv}
+\cs_new_protected_nopar:Npn \__spath_split_path_at_intersections:nn #1#2
+{
+  \group_begin:
+
+  \seq_clear:N \l__spath_tmpa_seq
+  \seq_clear:N \l__spath_tmpb_seq
+
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \seq_map_inline:Nn \l__spath_tmpa_seq
   {
-    \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+    \spath_split_component_at_intersections:Nnn \l__spath_tmpa_tl {##1} {#2}
+    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_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
+  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpb_seq {} }
   \group_end:
 }
+\cs_new_protected_nopar:Npn \spath_split_path_at_intersections:Nnn #1#2#3
+{
+  \__spath_split_path_at_intersections:nn {#2}{#3}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_path_at_intersections:Nnn
+{NVn, NVV, cVn, cVV, cvn, cvv}
+\cs_new_protected_nopar:Npn \spath_split_path_at_intersections:Nn #1#2
+{
+  \spath_split_path_at_intersections:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_split_path_at_intersections:Nn {cv, NV}
+\cs_new_protected_nopar:Npn \spath_gsplit_path_at_intersections:Nnn #1#2#3
+{
+  \__spath_split_path_at_intersections:nn {#2}{#3}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_path_at_intersections:Nnn
+{NVn, NVV, cVn, cVV, cvn, cvv}
+\cs_new_protected_nopar:Npn \spath_gsplit_path_at_intersections:Nn #1#2
+{
+  \spath_gsplit_path_at_intersections:NVn #1#1{#2}
+}
+\cs_generate_variant:Nn \spath_gsplit_path_at_intersections:Nn {cv, NV}
 \cs_new_protected_nopar:Npn \spath_split_at_intersections:NNnn #1#2#3#4
 {
-  \__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}}
+  \__spath_split_path_at_intersections:nn {#3}{#4}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \__spath_split_path_at_intersections:nn {#4}{#3}
+  \tl_set_eq:NN #2 \g__spath_output_tl
   \tl_gclear:N \g__spath_output_tl
 }
-\cs_generate_variant:Nn \spath_split_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_generate_variant:Nn \spath_split_at_intersections:NNnn
+{NNVn, NNVV, ccVn, ccVV, ccvn, ccvv}
 \cs_new_protected_nopar:Npn \spath_split_at_intersections:NN #1#2
 {
   \spath_split_at_intersections:NNVV #1#2#1#2
@@ -2510,213 +3156,283 @@ manipulating PGF soft paths}
 \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_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}}
+  \__spath_split_path_at_intersections:nn {#3}{#4}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \__spath_split_path_at_intersections:nn {#4}{#3}
+  \tl_gset_eq:NN #2 \g__spath_output_tl
   \tl_gclear:N \g__spath_output_tl
 }
-\cs_generate_variant:Nn \spath_gsplit_at_intersections:NNnn {NNVV, ccVV, ccvv}
+\cs_generate_variant:Nn \spath_gsplit_at_intersections:NNnn
+{NNVn, NNVV, ccVn, ccVV, ccvn, ccvv}
 \cs_new_protected_nopar:Npn \spath_gsplit_at_intersections:NN #1#2
 {
   \spath_gsplit_at_intersections:NNVV #1#2#1#2
 }
 \cs_generate_variant:Nn \spath_gsplit_at_intersections:NN {cc}
-\cs_new_protected_nopar:Npn \__spath_split_at_self_intersections:n #1
+\cs_new_protected_nopar:Npn \__spath_split_component_at_self_intersections:n #1
 {
   \group_begin:
+  \tl_set:Nn \l__spath_tmpe_tl {#1}
+
+  % Remember if the component is closed
+  \spath_finalaction:NV \l__spath_tmpa_tl \l__spath_tmpe_tl
+
+  \bool_set:Nn \l__spath_closed_bool
+  {
+    \tl_if_eq_p:NN \l__spath_tmpa_tl \c_spath_closepath_tl
+  }
 
   % Copy the path
-  \tl_set:Nn \l__spath_split_path_b_tl {#1}
+  \tl_set:Nn \l__spath_tmpe_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
+  \spath_open:N \l__spath_tmpe_tl
+  % Ensure beziers don't self-intersect
+  \spath_split_curves:N \l__spath_tmpe_tl
+
   % Make a copy for later
-  \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+  \tl_set_eq:NN \l__spath_tmpg_tl \l__spath_tmpe_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
+  \tl_clear:N \l__spath_tmpd_tl
+  \seq_clear:N \l__spath_tmpb_seq
+  \int_zero:N \l__spath_tmpa_int
 
   \pgfintersectionsortbyfirstpath
 
-  \bool_do_until:nn
-  {
-    \int_compare_p:n
-    {
-      \tl_count:N \l__spath_split_path_b_tl < 4
-    }
-  }
-  {
-    \tl_clear:N \l__spath_split_path_a_tl
-    \tl_put_right:Nx \l__spath_split_path_a_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}}
-    }
+  % Split the path into a sequence of segments
+  \spath_segments_to_seq:NV \l__spath_tmpa_seq \l__spath_tmpe_tl
 
-    \tl_set:Nx \l__spath_tmpa_tl { \tl_item:Nn \l__spath_split_path_b_tl {4} }
-
-    \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
+  \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+  {
+    \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
     {
-      \c_spath_moveto_tl
+      % Don't intersect a segment with itself
+      \int_compare:nF
       {
-        \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}
+        ##1 == ####1
       }
-      \c_spath_lineto_tl
-      {
-        \int_set:Nn \l__spath_tmpa_int {1}
-      }
-      \c_spath_curvetoa_tl
       {
-        \int_set:Nn \l__spath_tmpa_int {3}
-      }
-    }
-
-    \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_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_set:Nx \l__spath_split_path_b_tl {\tl_tail:N \l__spath_split_path_b_tl}
-    }
+        \spath_intersect:nn {##2} {####2}
 
-    \tl_put_left:NV \l__spath_split_path_b_tl \c_spath_moveto_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}
+        \int_compare:nT {\pgfintersectionsolutions > 0}
         {
-          \pgfintersectiongetsolutiontimes{##1}{\l__spath_split_first_tl}{\l__spath_split_second_tl}
-          \fp_compare:nT
-          {
-            \l__spath_split_first_tl < .99
-          }
+          % Find the times of the intersections on each path
+          \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions}
           {
-            \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
-          }
-        }
-      }
+            \pgfintersectiongetsolutiontimes
+            {########1}{\l__spath_tmpb_tl}{\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}
-        {
-          \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
+            \bool_if:nT
+            {
+              !(
+              \fp_compare_p:n { \l__spath_tmpb_tl > .99 }
+              &&
+              \int_compare_p:n {##1 + 1 == ####1}
+              )
+              &&
+              !(
+              \fp_compare_p:n { \l__spath_tmpb_tl < .01 }
+              &&
+              \int_compare_p:n {##1 - 1 == ####1}
+              )
+              &&
+              !(
+              \l__spath_closed_bool
+              &&
+              \fp_compare_p:n { \l__spath_tmpb_tl < .01 }
+              &&
+              \int_compare_p:n {##1 == 1}
+              &&
+              \int_compare_p:n {\seq_count:N \l__spath_tmpa_seq == ####1}
+              )
+              &&
+              !(
+              \l__spath_closed_bool
+              &&
+              \fp_compare_p:n { \l__spath_tmpb_tl > .99 }
+              &&
+              \int_compare_p:n {####1 == 1}
+              &&
+              \int_compare_p:n {\seq_count:N \l__spath_tmpa_seq == ##1}
+              )
+            }
+            {
+              \tl_set:Nx \l__spath_tmpa_tl
+              {\fp_to_decimal:n {\l__spath_tmpb_tl +  ##1 - 1}}
+              \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_tl
+            }
           }
         }
       }
-
     }
-    % Increment the segment counter
-    \int_incr:N \l__spath_split_segment_int
   }
 
   % Sort the sequence by reverse order along the path
-  \seq_sort:Nn \l__spath_split_first_seq
+  \seq_sort:Nn \l__spath_tmpb_seq
   {
     \fp_compare:nNnTF { ##1 } < { ##2 }
     { \sort_return_swapped: }
     { \sort_return_same: }
   }
 
+  \seq_get_left:NN \l__spath_tmpb_seq \l__spath_tmpa_tl
+  \fp_compare:nT
+  {
+    \l__spath_tmpa_tl > \seq_count:N \l__spath_tmpa_seq - .01
+  }
+  {
+    \bool_set_false:N \l__spath_closed_bool
+  }
+  \seq_get_right:NN \l__spath_tmpb_seq \l__spath_tmpa_tl
+  \fp_compare:nT
+  {
+    \l__spath_tmpa_tl < .01
+  }
+  {
+    \bool_set_false:N \l__spath_closed_bool
+  }
+
   % Restore the original copy of the path
-  \tl_set_eq:NN \l__spath_split_path_b_tl \l__spath_split_path_b_final_tl
+  \tl_set_eq:NN \l__spath_tmpe_tl \l__spath_tmpg_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_clear:N \l__spath_tmpf_tl
+  \tl_clear:N \l__spath_tmph_tl
+  \tl_clear:N \l__spath_tmpg_tl
 
-  \tl_set:Nn \l__spath_split_prev_first_tl {-1}
+  \tl_set:Nn \l__spath_tmpi_tl {-1}
 
-  \seq_map_inline:Nn \l__spath_split_first_seq
+  \seq_map_inline:Nn \l__spath_tmpb_seq
   {
-    \tl_set:Nn \l__spath_split_first_tl {##1}
-    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_split_first_tl
+    \tl_set:Nn \l__spath_tmpb_tl {##1}
+    \tl_set_eq:NN \l__spath_tmpa_tl \l__spath_tmpb_tl
     \int_compare:nT
     {
-      \fp_to_int:n {floor( \l__spath_split_first_tl ) }
+      \fp_to_int:n {floor( \l__spath_tmpb_tl ) }
       =
-      \fp_to_int:n {floor( \l__spath_split_prev_first_tl) }
+      \fp_to_int:n {floor( \l__spath_tmpi_tl) }
     }
     {
-      \tl_set:Nx \l__spath_split_first_tl
+      \tl_set:Nx \l__spath_tmpb_tl
       {
         \fp_eval:n {
-          floor( \l__spath_split_first_tl )
+          floor( \l__spath_tmpb_tl )
           +
-          ( \l__spath_split_first_tl - floor( \l__spath_split_first_tl) )
+          ( \l__spath_tmpb_tl - floor( \l__spath_tmpb_tl) )
           /
-          ( \l__spath_split_prev_first_tl - floor( \l__spath_split_prev_first_tl) )
+          ( \l__spath_tmpi_tl - floor( \l__spath_tmpi_tl) )
         }
       }
     }
-    \tl_set_eq:NN \l__spath_split_prev_first_tl \l__spath_tmpa_tl
+    \tl_set_eq:NN \l__spath_tmpi_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_first_tl
+    \spath_split_at:NNVV
+    \l__spath_tmpf_tl
+    \l__spath_tmph_tl
+    \l__spath_tmpe_tl
+    \l__spath_tmpb_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_tmpg_tl \l__spath_tmph_tl
+    \tl_set_eq:NN \l__spath_tmpe_tl \l__spath_tmpf_tl
 
   }
 
-  \tl_put_left:NV \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+  \tl_put_left:NV \l__spath_tmpg_tl \l__spath_tmpe_tl
 
-  \tl_if_empty:NT \l__spath_split_path_b_final_tl
+  \tl_if_empty:NT \l__spath_tmpg_tl
   {
-    \tl_set_eq:NN \l__spath_split_path_b_final_tl \l__spath_split_path_b_tl
+    \tl_set_eq:NN \l__spath_tmpg_tl \l__spath_tmpe_tl
   }
 
-  \spath_remove_empty_components:N \l__spath_split_path_b_final_tl
+  \spath_remove_empty_components:N \l__spath_tmpg_tl
+
+  % Do something with closed
+  \bool_if:NT \l__spath_closed_bool
+  {
+    \spath_join_component:Nn \l__spath_tmpg_tl {1}
+  }
 
   \tl_gclear:N \g__spath_output_tl
-  \tl_gset_eq:NN \g__spath_output_tl \l__spath_split_path_b_final_tl
+  \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpg_tl
   \group_end:
 }
+\cs_new_protected_nopar:Npn \spath_split_component_at_self_intersections:Nn #1#2
+{
+  \__spath_split_component_at_self_intersections:n {#2}
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_split_component_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_split_component_at_self_intersections:N #1
+{
+  \spath_split_component_at_self_intersections:NV #1#1
+}
+\cs_generate_variant:Nn \spath_split_component_at_self_intersections:N {c}
+\cs_new_protected_nopar:Npn \spath_gsplit_component_at_self_intersections:Nn #1#2
+{
+  \__spath_split_component_at_self_intersections:n {#2}
+  \tl_gset_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_generate_variant:Nn \spath_gsplit_component_at_self_intersections:Nn {NV}
+\cs_new_protected_nopar:Npn \spath_gsplit_component_at_self_intersections:N #1
+{
+  \spath_gsplit_component_at_self_intersections:NV #1#1
+}
+\cs_generate_variant:Nn \spath_gsplit_component_at_self_intersections:N {c}
+\cs_new_protected_nopar:Npn \__spath_split_at_self_intersections:n #1
+{
+  \group_begin:
+  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+  \seq_clear:N \l__spath_tmpb_seq
+  \seq_clear:N \l__spath_tmpc_seq
+
+  % Iterate over the components of the original path.
+  \bool_do_until:nn
+  {
+    \seq_if_empty_p:N \l__spath_tmpa_seq
+  }
+  {
+    % Get the next component
+    \seq_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpa_tl
+    % Copy for later
+    \tl_set_eq:NN \l__spath_tmpc_tl \l__spath_tmpa_tl
+    \int_compare:nT
+    {
+      \tl_count:N \l__spath_tmpa_tl > 3
+    }
+    {
+
+      % Split against itself
+      \spath_split_component_at_self_intersections:N \l__spath_tmpa_tl
+      % Grab the rest of the path
+      \tl_set:Nx \l__spath_tmpb_tl
+      {
+        \seq_use:Nn \l__spath_tmpb_seq {}
+        \seq_use:Nn \l__spath_tmpa_seq {}
+      }
+      % Split against the rest of the path
+      \spath_split_path_at_intersections:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
+    }
+    % Save the split path
+    \seq_put_right:NV \l__spath_tmpc_seq \l__spath_tmpa_tl
+    % Add the original copy to the sequence of processed components
+    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpc_tl
+  }
+
+  \tl_gclear:N \g__spath_output_tl
+  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpc_seq {} }
+  \group_end:
+}
+\cs_generate_variant:Nn \__spath_split_at_self_intersections:n {V, v}
 \cs_new_protected_nopar:Npn \spath_split_at_self_intersections:Nn #1#2
 {
   \__spath_split_at_self_intersections:n {#2}
   \tl_set_eq:NN #1 \g__spath_output_tl
   \tl_gclear:N \g__spath_output_tl
 }
-\cs_generate_variant:Nn \spath_split_at_self_intersections:Nn {NV}
+\cs_generate_variant:Nn \spath_split_at_self_intersections:Nn {NV, cn, cV, cv}
 \cs_new_protected_nopar:Npn \spath_split_at_self_intersections:N #1
 {
   \spath_split_at_self_intersections:NV #1#1
@@ -2728,64 +3444,82 @@ manipulating PGF soft paths}
   \tl_gset_eq:NN #1 \g__spath_output_tl
   \tl_gclear:N \g__spath_output_tl
 }
-\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:Nn {NV}
+\cs_generate_variant:Nn \spath_gsplit_at_self_intersections:Nn {NV, cn, cV, cv}
 \cs_new_protected_nopar:Npn \spath_gsplit_at_self_intersections:N #1
 {
   \spath_gsplit_at_self_intersections:NV #1#1
 }
 \cs_generate_variant:Nn \spath_gsplit_at_self_intersections:N {c}
-\tl_new:N \l__spath_tmpj_tl
 \cs_new_protected_nopar:Npn \__spath_join_component:nn #1#2
 {
   \group_begin:
-  \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
-  \int_compare:nT
+  \spath_numberofcomponents:Nn \l__spath_tmpa_int {#1}
+
+  \bool_if:nTF
   {
-    #2 == 1
+    \int_compare_p:n { #2 >= 1 }
+    &&
+    \int_compare_p:n { #2 <= \l__spath_tmpa_int }
   }
   {
-    \tl_clear:N \l__spath_tmpj_tl
-    \seq_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpj_tl
-
-    \prg_replicate:nn {3}
+    \int_compare:nTF
     {
-      \tl_set:Nx \l__spath_tmpj_tl {\tl_tail:N \l__spath_tmpj_tl}
+      #2 == 1
     }
-
-    \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpj_tl
-  }
-  \bool_if:nT
-  {
-    \int_compare_p:n
     {
-      #2 > 1
+      \int_compare:nTF
+      {
+        \l__spath_tmpa_int == 1
+      }
+      {
+        \tl_set:Nn \l__spath_tmpa_tl {#1}
+        \spath_initialpoint:Nn \l__spath_tmpb_tl {#1}
+        \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_gclear:N \g__spath_output_tl
+        \tl_gset_eq:NN \g__spath_output_tl \l__spath_tmpa_tl
+      }
+      {
+        \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
+        \seq_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpa_tl
+
+        \prg_replicate:nn {3}
+        {
+          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+        }
+
+        \seq_put_right:NV \l__spath_tmpa_seq \l__spath_tmpa_tl
+
+        \tl_gclear:N \g__spath_output_tl
+        \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpa_seq {}}
+      }
     }
-    &&
-    \int_compare_p:n
     {
-      #2 <= \seq_count:N \l__spath_tmpa_seq
-    }
-  }
-  {
+      \spath_components_to_seq:Nn \l__spath_tmpa_seq {#1}
 
-    \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}
+      \seq_clear:N \l__spath_tmpb_seq
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
       {
-        \prg_replicate:nn {3}
+        \tl_set:Nn \l__spath_tmpa_tl {##2}
+        \int_compare:nT {##1 = #2}
         {
-          \tl_set:Nx \l__spath_tmpj_tl {\tl_tail:N \l__spath_tmpj_tl}
+          \prg_replicate:nn {3}
+          {
+            \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
+          }
         }
+        \seq_put_right:NV \l__spath_tmpb_seq \l__spath_tmpa_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_gclear:N \g__spath_output_tl
+      \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpb_seq {}}
+    }
+  }
+  {
+    \tl_gclear:N \g__spath_output_tl
+    \tl_gset:Nn \g__spath_output_tl {#1}
   }
 
-  \tl_gset:Nx \g__spath_output_tl {\seq_use:Nn \l__spath_tmpa_seq {} }
   \group_end:
 }
 \cs_new_protected_nopar:Npn \spath_join_component:Nnn #1#2#3
@@ -2832,12 +3566,16 @@ manipulating PGF soft paths}
     {
       \dim_compare_p:n
       {
-        \dim_abs:n {\l__spath_move_x_dim - \tl_item:Nn \l__spath_tmpa_tl {2} } < 0.01pt
+        \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
+        \dim_abs:n
+        {\l__spath_move_y_dim - \tl_item:Nn \l__spath_tmpa_tl {3} }
+        < 0.01pt
       }
     }
     {
@@ -2864,12 +3602,22 @@ manipulating PGF soft paths}
   {
     \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_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
+      \dim_abs:n
+      {
+        \tl_item:Nn \l__spath_tmpa_tl {2} - \tl_item:Nn \l__spath_tmpb_tl {2}
+      }
+      <
+      0.01pt
     }
   }
   {
@@ -2976,7 +3724,7 @@ manipulating PGF soft paths}
     <path~ d="
   }
   \tl_set:Nn \l__spath_tmpc_tl {use:n}
-  \tl_map_inline:Nn #1
+  \tl_map_inline:nn {#1}
   {
     \tl_set:Nn \l__spath_tmpb_tl {##1}
     \tl_case:NnF \l__spath_tmpb_tl
@@ -3009,7 +3757,9 @@ manipulating PGF soft paths}
       }
     }
     {
-      \tl_put_right:Nx \l__spath_tmpa_tl {\use:c { \l__spath_tmpc_tl } {\dim_to_decimal:n {##1}} ~}
+      \tl_put_right:Nx
+      \l__spath_tmpa_tl
+      {\use:c { \l__spath_tmpc_tl } {\dim_to_decimal:n {##1}} ~}
     }
   }
   \tl_put_right:Nn \l__spath_tmpa_tl
@@ -3037,22 +3787,25 @@ manipulating PGF soft paths}
 \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}
+  \group_begin:
+  \spath_convert_to_svg:Nn \l__spath_tmpa_tl {#2}
   \iow_open:Nn \g__spath_stream {#1 .svg}
   \iow_now:Nx \g__spath_stream
   {
-    \tl_use:N \l__spath_iterp_tl
+    \tl_use:N \l__spath_tmpa_tl
   }
   \iow_close:N \g__spath_stream
+  \group_end:
 }
+\cs_generate_variant:Nn \spath_export_to_svg:nn {nv, nV}
 \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_item:nn {#1} {##1}
+      {\tl_item:nn {#1} {##1+1}}
+      {\tl_item:nn {#1} {##1+2}}
     }
   }
 }
@@ -3101,21 +3854,98 @@ manipulating PGF soft paths}
   };
 }
 \cs_generate_variant:Nn \spath_tikz_path:nn {Vn, VV, nv, Vv, nV}
-\cs_new_protected_nopar:Npn \spath_set_tikz_coords:n #1
+\cs_new_protected_nopar:Npn \spath_set_tikz_data: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}
+    \exp_not:c {pgf@x}=\tl_item:Nn \l__spath_tmpa_tl {1}
+    \exp_not:c {pgf@y}=\tl_item:Nn \l__spath_tmpa_tl {2}
+  }
+  \use:c {pgf@process}{%
+    \tl_use:N \l__spath_tmpa_tl
+    \pgftransforminvert
+    \use:c {pgf@pos@transform@glob}
+  }
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    \exp_not:c {tikz@lastx}=\exp_not:c {pgf@x}
+    \exp_not:c {tikz@lasty}=\exp_not:c {pgf@y}
+    \exp_not:c {tikz@lastxsaved}=\exp_not:c {pgf@x}
+    \exp_not:c {tikz@lastysaved}=\exp_not:c {pgf@y}
   }
   \tl_use:N \l__spath_tmpa_tl
+  \spath_finalmovepoint:Nn \l__spath_tmpa_tl {#1}
+  \ifpgfsyssoftpathmovetorelevant%
+  \tl_gset_eq:cN {pgfsyssoftpath@lastmoveto} \l__spath_tmpa_tl
+  \fi
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    \exp_not:c {pgf@x}=\tl_item:Nn \l__spath_tmpa_tl {1}
+    \exp_not:c {pgf@y}=\tl_item:Nn \l__spath_tmpa_tl {2}
+  }
+  \use:c {pgf@process}{%
+    \tl_use:N \l__spath_tmpa_tl
+    \pgftransforminvert
+    \use:c {pgf@pos@transform@glob}
+  }
+  \tl_set:Nx \l__spath_tmpa_tl
+  {
+    \exp_not:c {tikz@lastmovetox}=\exp_not:c {pgf@x}
+    \exp_not:c {tikz@lastmovetoy}=\exp_not:c {pgf@y}
+  }
+  \tl_use:N \l__spath_tmpa_tl
+  \tl_clear_new:c {tikz@timer}
+  \tl_set:cn {tikz@timer}
+  {
+    \spath_reallength:Nn \l__spath_tmpa_int {#1}
+    \tl_set_eq:Nc \l__spath_tmpb_tl {tikz@time}
+    \tl_set:Nx \l__spath_tmpb_tl
+    {\fp_to_decimal:n {(\l__spath_tmpb_tl) * (\l__spath_tmpa_int)}}
+    \spath_transformation_at:NnV \l__spath_tmpc_tl {#1} \l__spath_tmpb_tl
+
+    \tl_set:Nx \l__spath_tmpa_tl
+    {
+      \exp_not:N \pgfpoint
+      { \tl_item:Nn \l__spath_tmpc_tl {5} }
+      { \tl_item:Nn \l__spath_tmpc_tl {6} }
+    }
+    \exp_args:NV \pgftransformshift \l__spath_tmpa_tl
+
+    \ifpgfresetnontranslationattime
+    \pgftransformresetnontranslations
+    \fi
+
+    \ifpgfslopedattime
+
+    \tl_set:Nx \l__spath_tmpa_tl
+    {
+      { \tl_item:Nn \l__spath_tmpc_tl {1} }
+      { \tl_item:Nn \l__spath_tmpc_tl {2} }
+      { \tl_item:Nn \l__spath_tmpc_tl {3} }
+      { \tl_item:Nn \l__spath_tmpc_tl {4} }
+    }
+    \ifpgfallowupsidedownattime
+    \else
+    \fp_compare:nT { \tl_item:Nn \l__spath_tmpc_tl {4} < 0}
+    {
+      \tl_set:Nx \l__spath_tmpa_tl
+      {
+        { \fp_eval:n { - (\tl_item:Nn \l__spath_tmpc_tl {1})} }
+        { \fp_eval:n { - (\tl_item:Nn \l__spath_tmpc_tl {2})} }
+        { \fp_eval:n { - (\tl_item:Nn \l__spath_tmpc_tl {3})} }
+        { \fp_eval:n { - (\tl_item:Nn \l__spath_tmpc_tl {4})} }
+      }
+    }
+    \fi
+    \tl_put_right:Nn \l__spath_tmpa_tl {{\pgfpointorigin}}
+    \exp_last_unbraced:NV \pgftransformcm \l__spath_tmpa_tl
+    \fi
+  }
 }
-\cs_generate_variant:Nn \spath_set_tikz_coords:n {V, v}
+\cs_generate_variant:Nn \spath_set_tikz_data:n {V, v}
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+%% Copyright (C) 2011-2021 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
@@ -3127,7 +3957,7 @@ manipulating PGF soft paths}
 %% This work is "maintained" (as per LPPL maintenance status) by
 %% Andrew Stacey.
 %% 
-%% This work consists of the files  spath3.dtx
+%% This work consists of the files  spath3_code.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
 %%                                  spath3.tex
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
index e987539cb0b..35dd9f51c35 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex
@@ -66,7 +66,8 @@
       \pgfsyssoftpath@getcurrentpath\l__cal_tmpa_tl
       \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
+      \seq_gset_eq:cN
+      {g__cal_pen_\pgfkeysvalueof{/tikz/pen~name}_seq} \l__cal_tmpa_seq
       \pgfusepath{discard}%
     }
   },
@@ -80,10 +81,12 @@
       \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}
+        \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} }
+        \msg_warning:nnx { calligraphy } { undefined pen }
+        { \pgfkeysvalueof{/tikz/pen~name} }
       }
     }
   },
@@ -156,8 +159,10 @@
     \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 \g__cal_path_component_int}
-    \tl_set:cn {l__cal_stroke_inline_style_ \int_use:N \g__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,
@@ -264,23 +269,29 @@
           \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_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_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_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}
+            \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
-
         }
         \pgfsys@endscope
         \group_end:
@@ -291,7 +302,9 @@
         \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}
+        \tikz@scan@one@point
+        \pgfutil@firstofone
+        \pgfkeysvalueof{/tikz/annotation~shift}
 
         \spath_translate:Nnn \l__cal_tmp_path_tl {\pgf@x} {\pgf@y}
 
@@ -302,7 +315,10 @@
 
         \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};
+        \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}
       }
     }
@@ -480,8 +496,18 @@
     (\l__cal_tmpa_fp^2 + \l__cal_tmpb_fp^2)^.5
   }
 
-  \fp_set:Nn \l__cal_tmpa_fp {.5*\l__cal_taper_width_dim *     \l__cal_tmpa_fp / \l__cal_tmpe_fp}
-  \fp_set:Nn \l__cal_tmpb_fp {.5*\l__cal_taper_width_dim *     \l__cal_tmpb_fp / \l__cal_tmpe_fp}
+  \fp_set:Nn \l__cal_tmpa_fp
+  {
+    .5*\l__cal_taper_width_dim
+    *
+    \l__cal_tmpa_fp / \l__cal_tmpe_fp
+  }
+  \fp_set:Nn \l__cal_tmpb_fp
+  {
+    .5*\l__cal_taper_width_dim
+    *
+    \l__cal_tmpb_fp / \l__cal_tmpe_fp
+  }
 
   \fp_set:Nn \l__cal_tmpc_fp
   {
@@ -496,13 +522,23 @@
     (\l__cal_tmpc_fp^2 + \l__cal_tmpd_fp^2)^.5
   }
 
-  \fp_set:Nn \l__cal_tmpc_fp {.5*\l__cal_line_width_dim * \l__cal_tmpc_fp / \l__cal_tmpe_fp}
-  \fp_set:Nn \l__cal_tmpd_fp {.5*\l__cal_line_width_dim * \l__cal_tmpd_fp / \l__cal_tmpe_fp}
+  \fp_set:Nn \l__cal_tmpc_fp
+  {
+    .5*\l__cal_line_width_dim
+    *
+    \l__cal_tmpc_fp / \l__cal_tmpe_fp
+  }
+  \fp_set:Nn \l__cal_tmpd_fp
+  {
+    .5*\l__cal_line_width_dim
+    *
+    \l__cal_tmpd_fp / \l__cal_tmpe_fp
+  }
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp +             \l__cal_tmpb_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim}}
   }
 
   \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetoa_tl
@@ -533,16 +569,44 @@
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim - \fp_to_dim:n{ 1.32 * \l__cal_tmpd_fp}}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32* \l__cal_tmpc_fp}}}
+    {
+      \dim_eval:n
+      {
+        \fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim
+        - \fp_to_dim:n{ 1.32 * \l__cal_tmpd_fp
+        }
+      }
+    }
+    {
+      \dim_eval:n
+      {
+        \fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim
+        + \fp_to_dim:n {1.32* \l__cal_tmpc_fp
+        }
+      }
+    }
   }
 
   \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim - \fp_to_dim:n {1.32 * \l__cal_tmpd_fp}}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim + \fp_to_dim:n {1.32 * \l__cal_tmpc_fp}}}
+    {
+      \dim_eval:n
+      {
+        -\fp_to_dim:N \l__cal_tmpc_fp + \l__cal_tmpg_dim
+        - \fp_to_dim:n {1.32 * \l__cal_tmpd_fp
+        }
+      }
+    }
+    {
+      \dim_eval:n
+      {
+        -\fp_to_dim:N \l__cal_tmpd_fp + \l__cal_tmph_dim
+        + \fp_to_dim:n {1.32 * \l__cal_tmpc_fp
+        }
+      }
+    }
   }
 
   \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
@@ -581,16 +645,40 @@
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim + \fp_to_dim:n{ 1.32 * \l__cal_tmpb_fp}}}
-    {\dim_eval:n { -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32* \l__cal_tmpa_fp}}}
+    {
+      \dim_eval:n
+      {
+        -\fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim
+        + \fp_to_dim:n{ 1.32 * \l__cal_tmpb_fp}
+      }
+    }
+    {
+      \dim_eval:n
+      {
+        -\fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim
+        - \fp_to_dim:n {1.32* \l__cal_tmpa_fp}
+      }
+    }
   }
 
   \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curvetob_tl
 
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim + \fp_to_dim:n {1.32 * \l__cal_tmpb_fp}}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim - \fp_to_dim:n {1.32 * \l__cal_tmpa_fp}}}
+    {
+      \dim_eval:n
+      {
+        \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim
+        + \fp_to_dim:n {1.32 * \l__cal_tmpb_fp}
+      }
+    }
+    {
+      \dim_eval:n
+      {
+        \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim
+        - \fp_to_dim:n {1.32 * \l__cal_tmpa_fp}
+      }
+    }
   }
 
   \tl_put_right:NV \l__cal_tmpb_tl \c_spath_curveto_tl
@@ -598,7 +686,7 @@
   \tl_put_right:Nx \l__cal_tmpb_tl
   {
     {\dim_eval:n { \fp_to_dim:N \l__cal_tmpa_fp + \l__cal_tmpa_dim}}
-    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp +             \l__cal_tmpb_dim}}
+    {\dim_eval:n { \fp_to_dim:N \l__cal_tmpb_fp + \l__cal_tmpb_dim}}
   }
 
   \pgfsyssoftpath@setcurrentpath\l__cal_tmpb_tl
@@ -617,98 +705,187 @@
 \ExplSyntaxOff
 \expandafter\ifx\csname pgfdeclaredecoration\endcsname\relax
 \else
-\pgfdeclaredecoration{calligraphic brace}{brace}
-{
-  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
-  {
-    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
-    \pgfpathmoveto{\pgfpointorigin}
-    \pgfpathcurveto
-    {\pgfqpoint{.15\pgfdecorationsegmentamplitude}{.3\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-    {
-      \pgftransformxshift{+\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance}
-      \pgfpathlineto{\pgfqpoint{-\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{-.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{-.15\pgfdecorationsegmentamplitude}{.7\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{0\pgfdecorationsegmentamplitude}{1\pgfdecorationsegmentamplitude}}
-      \pgfpathmoveto{\pgfqpoint{0\pgfdecorationsegmentamplitude}{1\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{.15\pgfdecorationsegmentamplitude}{.7\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-    }
-    {
-      \pgftransformxshift{+\pgfdecoratedremainingdistance}
-      \pgfpathlineto{\pgfqpoint{-\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
+\pgfdeclaredecoration{calligraphic brace}{brace}%
+{%
+  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]%
+  {%
+    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}%
+    \pgfpathmoveto{\pgfpointorigin}%
+    \pgfpathcurveto%
+    {%
+      \pgfqpoint%
+      {.15\pgfdecorationsegmentamplitude}%
+      {.3\pgfdecorationsegmentamplitude}%
+    }%
+    {%
+      \pgfqpoint%
+      {.5\pgfdecorationsegmentamplitude}%
+      {.5\pgfdecorationsegmentamplitude}%
+    }%
+    {%
+      \pgfqpoint%
+      {\pgfdecorationsegmentamplitude}%
+      {.5\pgfdecorationsegmentamplitude}%
+    }%
+    {%
+      \pgftransformxshift%
+      {+\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance}%
+      \pgfpathlineto%
+      {%
+        \pgfqpoint%
+        {-\pgfdecorationsegmentamplitude}%
+        {.5\pgfdecorationsegmentamplitude}%
+      }%
       \pgfpathcurveto
-      {\pgfqpoint{-.5\pgfdecorationsegmentamplitude}{.5\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{-.15\pgfdecorationsegmentamplitude}{.3\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{0pt}{0pt}}
-    }
-    \tikzset{
-      taper width=.5\pgflinewidth,
-      taper
+      {%
+        \pgfqpoint%
+        {-.5\pgfdecorationsegmentamplitude}%
+        {.5\pgfdecorationsegmentamplitude}%
+      }%
+      {%
+        \pgfqpoint%
+        {-.15\pgfdecorationsegmentamplitude}%
+        {.7\pgfdecorationsegmentamplitude}%
+      }%
+      {%
+        \pgfqpoint%
+        {0\pgfdecorationsegmentamplitude}%
+        {1\pgfdecorationsegmentamplitude}%
+      }%
+      \pgfpathmoveto%
+      {%
+        \pgfqpoint%
+        {0\pgfdecorationsegmentamplitude}%
+        {1\pgfdecorationsegmentamplitude}%
+      }%
+      \pgfpathcurveto%
+      {%
+        \pgfqpoint%
+        {.15\pgfdecorationsegmentamplitude}%
+        {.7\pgfdecorationsegmentamplitude}%
+      }%
+      {%
+        \pgfqpoint%
+        {.5\pgfdecorationsegmentamplitude}%
+        {.5\pgfdecorationsegmentamplitude}%
+      }%
+      {%
+        \pgfqpoint%
+        {\pgfdecorationsegmentamplitude}%
+        {.5\pgfdecorationsegmentamplitude}%
+      }%
     }%
-    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \CopperplatePath{\cal@tmp@path}
-  }
-  \state{final}{}
-}
+    {%
+      \pgftransformxshift{+\pgfdecoratedremainingdistance}%
+      \pgfpathlineto%
+      {%
+        \pgfqpoint%
+        {-\pgfdecorationsegmentamplitude}%
+        {.5\pgfdecorationsegmentamplitude}%
+      }%
+      \pgfpathcurveto%
+      {%
+        \pgfqpoint%
+        {-.5\pgfdecorationsegmentamplitude}%
+        {.5\pgfdecorationsegmentamplitude}%
+      }%
+      {%
+        \pgfqpoint%
+        {-.15\pgfdecorationsegmentamplitude}%
+        {.3\pgfdecorationsegmentamplitude}%
+      }%
+      {\pgfqpoint{0pt}{0pt}}%
+    }%
+    \tikzset{%
+      taper width=.5\pgflinewidth,%
+      taper%
+    }%%
+    \pgfsyssoftpath@getcurrentpath\cal@tmp@path%
+    \CopperplatePath{\cal@tmp@path}%
+  }%
+  \state{final}{}%
+}%
 \pgfdeclaredecoration{calligraphic straight parenthesis}{brace}
 {
-  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
-  {
-    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
-    \pgfpathmoveto{\pgfpointorigin}
-    \pgfpathcurveto
-    {\pgfqpoint{.76604\pgfdecorationsegmentamplitude}{.64279\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{2.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{3.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-    {
-      \pgftransformxshift{+\pgfdecoratedremainingdistance}
-      \pgfpathlineto{\pgfqpoint{-3.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-      \pgfpathcurveto
-      {\pgfqpoint{-2.3333\pgfdecorationsegmentamplitude}{\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{-.76604\pgfdecorationsegmentamplitude}{.64279\pgfdecorationsegmentamplitude}}
-      {\pgfqpoint{0pt}{0pt}}
-    }
-    \tikzset{
-      taper width=.5\pgflinewidth,
-      taper
+  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]%
+  {%
+    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}%
+    \pgfpathmoveto{\pgfpointorigin}%
+    \pgfpathcurveto%
+    {%
+      \pgfqpoint%
+      {.76604\pgfdecorationsegmentamplitude}%
+      {.64279\pgfdecorationsegmentamplitude}%
     }%
-    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \CopperplatePath{\cal@tmp@path}
-  }
+    {%
+      \pgfqpoint%
+      {2.3333\pgfdecorationsegmentamplitude}%
+      {\pgfdecorationsegmentamplitude}%
+    }%
+    {%
+      \pgfqpoint%
+      {3.3333\pgfdecorationsegmentamplitude}%
+      {\pgfdecorationsegmentamplitude}%
+    }%
+    {%
+      \pgftransformxshift{+\pgfdecoratedremainingdistance}%
+      \pgfpathlineto%
+      {%
+        \pgfqpoint%
+        {-3.3333\pgfdecorationsegmentamplitude}%
+        {\pgfdecorationsegmentamplitude}%
+      }%
+      \pgfpathcurveto%
+      {%
+        \pgfqpoint%
+        {-2.3333\pgfdecorationsegmentamplitude}%
+        {\pgfdecorationsegmentamplitude}%
+      }%
+      {%
+        \pgfqpoint%
+        {-.76604\pgfdecorationsegmentamplitude}%
+        {.64279\pgfdecorationsegmentamplitude}%
+      }%
+      {\pgfqpoint{0pt}{0pt}}%
+    }%
+    \tikzset{%
+      taper width=.5\pgflinewidth,%
+      taper%
+    }%
+    \pgfsyssoftpath@getcurrentpath\cal@tmp@path%
+    \CopperplatePath{\cal@tmp@path}%
+  }%
   \state{final}{}%
 }
 \pgfdeclaredecoration{calligraphic curved parenthesis}{brace}
 {
-  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
-  {
-    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
-    \pgfpathmoveto{\pgfpointorigin}
-    \pgf@xa=\pgfdecoratedremainingdistance\relax
-    \advance\pgf@xa by -1.5890\pgfdecorationsegmentamplitude\relax
-    \edef\cgrphy@xa{\the\pgf@xa}
-    \pgfpathcurveto
-    {\pgfqpoint{1.5890\pgfdecorationsegmentamplitude}{1.3333\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{\cgrphy@xa}{1.3333\pgfdecorationsegmentamplitude}}
-    {\pgfqpoint{\pgfdecoratedremainingdistance}{0pt}}
-    \tikzset{
-      taper width=.5\pgflinewidth,
-      taper
+  \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]%
+  {%
+    \pgfsyssoftpath@setcurrentpath{\pgfutil@empty}%
+    \pgfpathmoveto{\pgfpointorigin}%
+    \pgf@xa=\pgfdecoratedremainingdistance\relax%
+    \advance\pgf@xa by -1.5890\pgfdecorationsegmentamplitude\relax%
+    \edef\cgrphy@xa{\the\pgf@xa}%
+    \pgfpathcurveto%
+    {%
+      \pgfqpoint%
+      {1.5890\pgfdecorationsegmentamplitude}%
+      {1.3333\pgfdecorationsegmentamplitude}%
     }%
-    \pgfsyssoftpath@getcurrentpath\cal@tmp@path
-    \CopperplatePath{\cal@tmp@path}
-  }
+    {\pgfqpoint{\cgrphy@xa}{1.3333\pgfdecorationsegmentamplitude}}%
+    {\pgfqpoint{\pgfdecoratedremainingdistance}{0pt}}%
+    \tikzset{%
+      taper width=.5\pgflinewidth,%
+      taper%
+    }%
+    \pgfsyssoftpath@getcurrentpath\cal@tmp@path%
+    \CopperplatePath{\cal@tmp@path}%
+  }%
   \state{final}{}%
 }
 \fi
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+%% Copyright (C) 2011-2021 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
@@ -720,7 +897,7 @@
 %% This work is "maintained" (as per LPPL maintenance status) by
 %% Andrew Stacey.
 %% 
-%% This work consists of the files  spath3.dtx
+%% This work consists of the files  spath3_code.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
 %%                                  spath3.tex
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
index 5872a71fdf3..c6ae085925a 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryknots.code.tex
@@ -45,6 +45,7 @@
 \dim_new:N \l__knot_tmpa_dim
 \dim_new:N \l__knot_tmpb_dim
 \dim_new:N \l__knot_tolerance_dim
+\dim_new:N \l__knot_redraw_tolerance_dim
 \dim_new:N \l__knot_clip_bg_radius_dim
 \dim_new:N \l__knot_clip_draw_radius_dim
 
@@ -247,6 +248,11 @@
 {
   \pgfscope
   \pgftransformreset
+  \dim_set:Nn \l__knot_redraw_tolerance_dim {\fp_to_dim:n
+    {
+      sqrt(2) * max(\l__knot_clip_bg_radius_dim, \l__knot_clip_draw_radius_dim)
+    }
+  }
   \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_draw_strand:n
   \bool_if:NF \l__knot_super_draft_bool
   {
@@ -267,13 +273,21 @@
     {
       \tl_set:Nn \l__knot_node_tl {
         \exp_not:N \node[coordinate,
-          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]
+          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
+            ]
             }]
       }
     }
     \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
+      \int_step_variable:nnnNn
+      {\tl_use:N \l__knot_tmpa_tl + 1}
+      {1}
+      {\l__knot_tmpa_int} \l__knot_tmpb_tl
       {
         \knot_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
       }
@@ -290,7 +304,12 @@
   \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}
+  \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
@@ -303,11 +322,15 @@
     \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};
+    \node[
+      knot~ diagram/draft/strand~label
+    ] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
     \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};
+    \node[
+      knot~ diagram/draft/strand~label
+    ] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1};
   }
   \bool_if:nT {
     \l__knot_self_intersections_bool
@@ -316,6 +339,8 @@
   }
   {
     \tl_clear:N \l__knot_tmpa_tl
+    \spath_initialpoint:Nv \l__knot_tmpa_tl {knot strand #1}
+    \tl_put_left:NV \l__knot_tmpa_tl \c_spath_moveto_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
@@ -330,23 +355,29 @@
     {
       \fp_set:Nn \l__knot_tmpa_fp
       {
-        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6}
+        + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
         *
         (3 * \tl_item:nn {#1} {8} - 3 * \tl_item:nn {#1} {11})
         -
-        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5}
+        + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
         *
         (3 * \tl_item:nn {#1} {9} - 3 * \tl_item:nn {#1} {12})
       }
       \fp_set:Nn \l__knot_tmpb_fp
       {
-        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
+        (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5}
+        + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11})
         *
-        (3 * \tl_item:nn {#1} {6} - 6 * \tl_item:nn {#1} {9} + 3 * \tl_item:nn {#1} {12})
+        (3 * \tl_item:nn {#1} {6} - 6 * \tl_item:nn {#1} {9}
+        + 3 * \tl_item:nn {#1} {12})
         -
-        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
+        (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6}
+        + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12})
         *
-        (3 * \tl_item:nn {#1} {5} - 6 * \tl_item:nn {#1} {8} + 3 * \tl_item:nn {#1} {11})
+        (3 * \tl_item:nn {#1} {5} - 6 * \tl_item:nn {#1} {8}
+        + 3 * \tl_item:nn {#1} {11})
       }
       \fp_compare:nTF
       {
@@ -359,7 +390,11 @@
           0 < \l__knot_tmpa_fp && \l__knot_tmpa_fp < 1
         }
         {
-          \spath_split_curve:NNnV \l__knot_tmpc_tl \l__knot_tmpd_tl {#1} \l__knot_tmpa_fp
+          \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}
@@ -411,19 +446,33 @@
   \bool_if:nTF {
     \l__knot_save_bool
     &&
-    \tl_if_exist_p:c {knot~ intersections~ \tl_use:N \l__knot_name_tl - \tl_use:N \l__knot_tmpa_tl -  \tl_use:N \l__knot_tmpb_tl}
+    \tl_if_exist_p:c {
+      knot~ intersections~
+      \tl_use:N \l__knot_name_tl -
+      \tl_use:N \l__knot_tmpa_tl -
+      \tl_use:N \l__knot_tmpb_tl
+    }
   }
   {
-    \tl_use:c {knot~ intersections~ \tl_use:N \l__knot_name_tl - \tl_use:N \l__knot_tmpa_tl -  \tl_use:N \l__knot_tmpb_tl}
+    \tl_use:c
+    {
+      knot~ intersections~ \tl_use:N \l__knot_name_tl -
+      \tl_use:N \l__knot_tmpa_tl -
+      \tl_use:N \l__knot_tmpb_tl
+    }
   }
   {
-\pgfintersectionofpaths{\pgfsetpath\l__knot_tmpc_tl}{\pgfsetpath\l__knot_tmpd_tl}
+    \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
+    \int_step_function:nnnN
+    {1}
+    {1}
+    {\pgfintersectionsolutions}
+    \knot_do_intersection:n
   }
 
   \knot_save_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl
@@ -455,7 +504,16 @@
         }
         \tl_put_right:Nx \l__knot_aux_tl
         {
-          {\exp_not:N \pgf@x=\dim_use:N \l__knot_tmpa_dim\exp_not:N\relax\exp_not:N \pgf@y =\dim_use:N \l__knot_tmpb_dim\relax}
+          {
+            \exp_not:N \pgf@x
+            =
+            \dim_use:N \l__knot_tmpa_dim
+            \exp_not:N \relax
+            \exp_not:N \pgf@y
+            =
+            \dim_use:N \l__knot_tmpb_dim
+            \exp_not:N \relax
+          }
         }
       }
       \tl_set:Nn \l__knot_auxa_tl {\expandafter \gdef \csname knot~ intersections~}
@@ -480,7 +538,7 @@
     \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}
+      \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpb_tl {final point}
       {
         \bool_set_true:N \l__knot_skip_bool
       }
@@ -491,7 +549,7 @@
     \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}
+      \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpa_tl {final point}
       {
         \bool_set_true:N \l__knot_skip_bool
       }
@@ -499,19 +557,19 @@
   }
   \bool_if:NT \l__knot_ignore_ends_bool
   {
-    \knot_test_endpoint:VnT \l__knot_tmpa_tl {initial point}
+    \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpa_tl {initial point}
     {
       \bool_set_true:N \l__knot_skip_bool
     }
-    \knot_test_endpoint:VnT \l__knot_tmpa_tl {final point}
+    \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpa_tl {final point}
     {
       \bool_set_true:N \l__knot_skip_bool
     }
-    \knot_test_endpoint:VnT \l__knot_tmpb_tl {initial point}
+    \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpb_tl {initial point}
     {
       \bool_set_true:N \l__knot_skip_bool
     }
-    \knot_test_endpoint:VnT \l__knot_tmpb_tl {final point}
+    \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpb_tl {final point}
     {
       \bool_set_true:N \l__knot_skip_bool
     }
@@ -545,14 +603,16 @@
       }
       \bool_if:NT \l__knot_self_intersections_bool
       {
-        \knot_test_endpoint:VnT \l__knot_tmpg_tl {initial point}
+        \knot_test_endpoint:NVnT
+        \l__knot_redraw_tolerance_dim \l__knot_tmpg_tl {initial point}
         {
           \bool_set_true:N \l__knot_prepend_prev_bool
         }
         {
           \bool_set_false:N \l__knot_prepend_prev_bool
         }
-        \knot_test_endpoint:VnT \l__knot_tmpg_tl {final point}
+        \knot_test_endpoint:NVnT
+        \l__knot_redraw_tolerance_dim \l__knot_tmpg_tl {final point}
         {
           \bool_set_true:N \l__knot_append_next_bool
         }
@@ -565,10 +625,14 @@
         }
         {
           \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_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}
+          \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
           {
@@ -579,7 +643,9 @@
             !\tl_if_empty_p: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}}
+            \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
@@ -589,10 +655,18 @@
               !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
             }
             {
-              \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {initial point}
+              \knot_test_endpoint:NvnT
+              \l__knot_redraw_tolerance_dim
+              {knot previous \tl_use:N \l__knot_tmpg_tl}
+              {initial point}
               {
-
-                \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}}}
+                \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}
               }
             }
@@ -606,7 +680,9 @@
             !\tl_if_empty_p:c {knot previous \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}}
+            \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
@@ -617,42 +693,61 @@
               !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl}
             }
             {
-              \knot_test_endpoint:vnT {knot previous \tl_use:N \l__knot_tmpg_tl} {final point}
+              \knot_test_endpoint:NvnT
+              \l__knot_redraw_tolerance_dim
+              {knot previous \tl_use:N \l__knot_tmpg_tl}
+              {final point}
               {
-                \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}}}
-
+                \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}
+                  }
+                }
               }
             }
           }
-
           \tl_set:Nn \l__knot_tmpg_tl {\tl_use:N \l__knot_prefix_tl -1}
         }
       }
       \pgfscope
       \group_begin:
-      \tikzset{knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \g__knot_intersections_int/.try}
+      \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);
+      \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
     }
     \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) {};}
+      \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) {};
+      }
     }
   }
 }
 
 \cs_generate_variant:Nn \knot_intersections:nn {VV}
-\prg_new_conditional:Npnn \knot_test_endpoint:N #1 {p,T,F,TF}
+\prg_new_conditional:Npnn \knot_test_endpoint:NN #1#2 {p,T,F,TF}
 {
   \dim_compare:nTF
   {
-    \dim_abs:n { \l__knot_tmpa_dim - \tl_item:Nn #1 {1}}
+    \dim_abs:n { \l__knot_tmpa_dim - \tl_item:Nn #2 {1}}
     +
-    \dim_abs:n { \l__knot_tmpb_dim - \tl_item:Nn #1 {2}}
+    \dim_abs:n { \l__knot_tmpb_dim - \tl_item:Nn #2 {2}}
     <
-    \l__knot_tolerance_dim
+    #1
   }
   {
     \prg_return_true:
@@ -661,10 +756,10 @@
     \prg_return_false:
   }
 }
-\prg_new_protected_conditional:Npnn \knot_test_endpoint:nn #1#2 {T,F,TF}
+\prg_new_protected_conditional:Npnn \knot_test_endpoint:Nnn #1#2#3 {T,F,TF}
 {
-  \use:c {spath_#2:Nv} \l__knot_tmpd_tl {knot #1}
-  \knot_test_endpoint:NTF \l__knot_tmpd_tl
+  \use:c {spath_#3:Nv} \l__knot_tmpd_tl {knot #2}
+  \knot_test_endpoint:NNTF #1 \l__knot_tmpd_tl
   {
     \prg_return_true:
   }
@@ -673,34 +768,44 @@
   }
 }
 
-\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_generate_variant:Nn \knot_test_endpoint:NnnT {NVnT,NvnT}
+\cs_generate_variant:Nn \knot_test_endpoint:NnnF {NVnF,NvnF}
+\cs_generate_variant:Nn \knot_test_endpoint:NnnTF {NVnTF,NvnTF}
 \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];
+  \path[knot~ diagram/background~ clip] (#2, #3)
+  circle[radius=\l__knot_clip_bg_radius_dim];
 
   \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__knot_tmpa_tl {l__knot_options_ #1}
   }
-  \tl_put_right:Nn \l__knot_tmpa_tl {,knotbg,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth}
+  \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];
+  \path[knot~ diagram/clip] (#2, #3)
+  circle[radius=\l__knot_clip_draw_radius_dim];
 
   \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__knot_tmpa_tl {l__knot_options_ #1}
   }
-  \tl_put_right:Nn \l__knot_tmpa_tl {,knot~ diagram/only~ when~ rendering/.try,only~ when~ rendering/.try}
+  \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
@@ -752,12 +857,14 @@
       \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_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 \g__knot_filaments_int} {filament \int_eval:n {\g__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}}
       }
     }
     \c_spath_curvetoa_tl
@@ -766,12 +873,15 @@
       \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_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 \g__knot_filaments_int} {filament \int_eval:n {\g__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}}
       }
     }
     \c_spath_closepath_tl
@@ -779,18 +889,26 @@
       \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: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_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 \g__knot_filaments_int} {filament \int_eval:n {\g__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 \g__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}
     }
   }
   {
@@ -1008,7 +1126,7 @@
  }
 }
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+%% Copyright (C) 2011-2021 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
@@ -1020,7 +1138,7 @@
 %% This work is "maintained" (as per LPPL maintenance status) by
 %% Andrew Stacey.
 %% 
-%% This work consists of the files  spath3.dtx
+%% This work consists of the files  spath3_code.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
 %%                                  spath3.tex
diff --git a/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex b/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
index 32d0d9fea08..9c1c158e52a 100644
--- a/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
+++ b/Master/texmf-dist/tex/latex/spath3/tikzlibraryspath3.code.tex
@@ -24,6 +24,8 @@
 \seq_new:N \g__spath_tmpa_seq
 \seq_new:N \g__spath_tmpb_seq
 \bool_new:N \l__spath_draft_bool
+\msg_new:nnn { spath3 } { missing soft path } { Soft~ path~ #1~ doesn't~ exist }
+\msg_new:nnn { spath3 } { empty soft path } { Soft~ path~ #1~ is~ empty }
 \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
@@ -53,6 +55,20 @@
   }
 }
 \cs_generate_variant:Nn \spath_gsave_path:Nn {cn, NV, cV}
+\cs_new_protected_nopar:Npn \__spath_process_tikz_point:Nn #1#2
+{
+  \group_begin:
+  \use:c {tikz@scan@one@point} \use:n #2 \scan_stop:
+  \tl_gset:Nx \g__spath_output_tl
+  {
+    { \dim_use:c {pgf@x} }
+    { \dim_use:c {pgf@y} }
+  }
+  \group_end:
+  \tl_set_eq:NN #1 \g__spath_output_tl
+  \tl_gclear:N \g__spath_output_tl
+}
+\cs_set_eq:NN \getComponentOf \clist_item:Nn
 \tikzset{
   spath/.is~family,
   spath/.cd,
@@ -74,11 +90,14 @@
     \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
+      \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_if_exist:cTF
+    {\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}
@@ -86,9 +105,13 @@
       {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+    }
   },
   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_if_exist:cTF
+    {\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}
@@ -96,6 +119,9 @@
       {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+    }
   },
   save~ global/.code={
     \tikz@addmode{
@@ -107,19 +133,75 @@
     }
   },
   save~ to~ aux/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   restore/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     {
-      \spath_set_current_path:c
+      \tl_if_empty:cTF
       {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
-      \spath_set_tikz_coords:v
+      {
+        \tl_clear:N \l__spath_tmpa_tl
+        \tl_put_right:NV \l__spath_tmpa_tl \c_spath_moveto_tl
+        \tl_put_right:Nn \l__spath_tmpa_tl {{0pt}{0pt}}
+        \spath_set_current_path:V \l__spath_tmpa_tl
+        \spath_set_tikz_data:V \l__spath_tmpa_tl
+        \msg_warning:nnn { spath3 } { empty soft path } { #1 }
+      }
+      {
+        \spath_set_current_path:c
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        \spath_set_tikz_data:v
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+    {
+      \tl_clear:N \l__spath_tmpa_tl
+      \tl_put_right:NV \l__spath_tmpa_tl \c_spath_moveto_tl
+      \tl_put_right:Nn \l__spath_tmpa_tl {{0pt}{0pt}}
+      \spath_set_current_path:V \l__spath_tmpa_tl
+      \spath_set_tikz_data:V \l__spath_tmpa_tl
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  restore~ reverse/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_empty:cTF
       {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {
+        \tl_clear:N \l__spath_tmpa_tl
+        \tl_put_right:NV \l__spath_tmpa_tl \c_spath_moveto_tl
+        \tl_put_right:Nn \l__spath_tmpa_tl {{0pt}{0pt}}
+        \spath_set_current_path:V \l__spath_tmpa_tl
+        \spath_set_tikz_data:V \l__spath_tmpa_tl
+        \msg_warning:nnn { spath3 } { empty soft path } { #1 }
+      }
+      {
+        \spath_reverse:Nv
+        \l__spath_reverse_tl
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        \spath_set_current_path:N \l__spath_reverse_tl
+        \spath_set_tikz_data:V \l__spath_reverse_tl
+      }
+    }
+    {
+      \tl_clear:N \l__spath_tmpa_tl
+      \tl_put_right:NV \l__spath_tmpa_tl \c_spath_moveto_tl
+      \tl_put_right:Nn \l__spath_tmpa_tl {{0pt}{0pt}}
+      \spath_set_current_path:V \l__spath_tmpa_tl
+      \spath_set_tikz_data:V \l__spath_tmpa_tl
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   show~current~path/.code={
@@ -130,73 +212,142 @@
     }
   },
   show/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
+      \tl_if_empty:cTF
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {
+        \msg_warning:nnn { spath3 } { empty soft path } { #1 }
+      }
+      {
+        \iow_term:n {---~ soft~ path~ #1~ ---}
+        \spath_show:v
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   append/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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
+      \spath_finalpoint:NV \l__spath_tmpa_tl \l__spath_current_tl
+      \tl_set_eq:Nc
+      \l__spath_tmpb_tl
       {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \spath_translate_to:NV \l__spath_tmpb_tl \l__spath_tmpa_tl
+      \spath_append_no_move:NV \l__spath_current_tl \l__spath_tmpb_tl
       \spath_set_current_path:N \l__spath_current_tl
-      \spath_set_tikz_coords:V \l__spath_current_tl
+      \spath_set_tikz_data:V \l__spath_tmpb_tl
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   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:cTF
+    {\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}
+      \tl_if_exist:cTF
+      {\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}
       }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   spot~ weld/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  spot~ weld~ globally/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_spot_gweld_components:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   reverse/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  reverse~ globally/.code={
+    \tl_if_exist:cTF
+    {\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}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   append~ reverse/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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_finalpoint:NV \l__spath_tmpa_tl \l__spath_current_tl
+      \spath_translate_to:NV \l__spath_reverse_tl \l__spath_tmpa_tl
+      \spath_append_no_move: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
+      \spath_set_tikz_data:V \l__spath_reverse_tl
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   insert/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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
+      \spath_set_tikz_data:v
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   insert~ reverse/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     {
       \spath_reverse:Nv
       \l__spath_reverse_tl
@@ -204,48 +355,391 @@
       \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
+      \spath_set_tikz_data:V \l__spath_reverse_tl
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  append~ no~ move/.code={
+    \tl_if_exist:cTF
+    {\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_no_move: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_data:v
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  append~ reverse~ no~ move/.code={
+    \tl_if_exist:cTF
+    {\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_no_move:NV \l__spath_current_tl \l__spath_reverse_tl
+      \spath_set_current_path:N \l__spath_current_tl
+      \spath_set_tikz_data:V \l__spath_reverse_tl
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  span/.code ~n~ args={3}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \__spath_process_tikz_point:Nn \l__spath_tmpa_tl {#2}
+      \__spath_process_tikz_point:Nn \l__spath_tmpb_tl {#3}
+      \spath_span:cVV
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \l__spath_tmpa_tl \l__spath_tmpb_tl
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  span~ global/.code ~n~ args={3}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \__spath_process_tikz_point:Nn \l__spath_tmpa_tl {#2}
+      \__spath_process_tikz_point:Nn \l__spath_tmpb_tl {#3}
+      \spath_gspan:cVV
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \l__spath_tmpa_tl \l__spath_tmpb_tl
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  to/.style={
+    to~path={
+      [
+        spath/span={#1}{(\tikztostart)}{(\tikztotarget)},
+        spath/append~no~move={#1},
+      ]
+      \tikztonodes
+    }
+  },
+  splice/.code ~n~ args={3}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \tl_if_exist:cTF
+        {\tl_use:N \l__spath_prefix_tl #3 \tl_use:N \l__spath_suffix_tl}
+        {
+          \spath_splice_between:cvv
+          {\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}
+          {\tl_use:N \l__spath_prefix_tl #3 \tl_use:N \l__spath_suffix_tl}
+        }
+        {
+          \msg_warning:nnn { spath3 } { missing soft path } { #3 }
+        }
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  splice~ global/.code ~n~ args={3}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \tl_if_exist:cTF
+        {\tl_use:N \l__spath_prefix_tl #3 \tl_use:N \l__spath_suffix_tl}
+        {
+          \spath_gsplice_between:cvv
+          {\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}
+          {\tl_use:N \l__spath_prefix_tl #3 \tl_use:N \l__spath_suffix_tl}
+        }
+        {
+          \msg_warning:nnn { spath3 } { missing soft path } { #3 }
+        }
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  join~ components~ with/.code~2~args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \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}
+
+        \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_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpa_tl
+
+        \seq_map_inline:Nn \l__spath_tmpa_seq
+        {
+          \spath_splice_between:Nvn \l__spath_tmpa_tl
+          {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+          {##1}
+        }
+        \tl_set_eq:cN
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        \l__spath_tmpa_tl
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  join~ components~ globally~ with/.code~2~args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_spot_gweld_components:c
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+
+        \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_pop_left:NN \l__spath_tmpa_seq \l__spath_tmpa_tl
+
+        \seq_map_inline:Nn \l__spath_tmpa_seq
+        {
+          \spath_gsplice_between:Nvn \l__spath_tmpa_tl
+          {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+          {##1}
+        }
+        \tl_set_eq:cN
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+        \l__spath_tmpa_tl
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  close/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_close:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  close~ globally/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gclose:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  close~ with/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_close_with: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}
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  close~ globally~ with/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_gclose_with: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}
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   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}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   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}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   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}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  shorten~ globally~ at~ end/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gshorten_at_end:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  shorten~ globally~ at~ start/.code~ 2~ args ={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gshorten_at_start:cn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl} {#2}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  shorten~ globally~ at~ both~ ends/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\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}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   translate/.code~ n~ args={3}{
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  translate~ globally/.code~ n~ args={3}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gtranslate:cnn
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{#2}{#3}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  normalise/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_normalise:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  normalise~ globally/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gnormalise:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   export~ to~ svg/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     {
-      \spath_export_to_svg:c
+      \spath_export_to_svg:nv {#1}
       {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   transform/.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:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     {
       \group_begin:
       \pgftransformreset
@@ -260,9 +754,13 @@
       \group_end:
       \tl_use:N \g__spath_smuggle_tl
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
-  transform~global/.code~ 2~ args={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+  transform~globally/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     {
       \group_begin:
       \pgftransformreset
@@ -277,27 +775,111 @@
       \group_end:
       \tl_use:N \g__spath_smuggle_tl
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  split~ at~ intersections~ with/.code~ n~ args={2}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_split_path_at_intersections: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}
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  split~ globally~ at~ intersections~ with/.code~ n~ args={2}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_gsplit_path_at_intersections: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}
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   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:cTF
+    {\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}
+      \tl_if_exist:cTF
+      {\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}
       }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  split~ globally~ at~ intersections/.code~ n~ args={2}{
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #2 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_gsplit_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}
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #2 }
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
     }
   },
   split~ at~ self~ intersections/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  split~ globally~ at~ self~ intersections/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gsplit_at_self_intersections:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   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}
+    \tl_if_exist:cTF
+    {\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
@@ -306,16 +888,58 @@
       \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_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}
+        {
+          \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
       }
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  get~ components~ of~ globally/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \clist_gclear_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_gset: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_gput_right:Nx #2 {anonymous_\int_use:N \g__spath_anon_int}
+        \int_gincr:N \g__spath_anon_int
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   render~ components/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
     {
       \group_begin:
       \spath_components_to_seq:Nv
@@ -338,17 +962,29 @@
       }
       \group_end:
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   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}
+    \tl_if_exist:cTF
+    {\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
+      \spath_numberofcomponents:Nv \l__spath_tmpa_int
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
       \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 }}
+        \seq_gput_right:Nx
+        \g__spath_tmpb_seq
+        {\int_eval:n
+          {
+            \int_mod:nn { \l__spath_tmpa_tl }{ \l__spath_tmpa_int } + 1
+          }
+        }
       }
       \spath_components_to_seq:Nv
       \l__spath_tmpa_seq
@@ -374,9 +1010,62 @@
       \g__spath_output_tl
       \tl_gclear:N \g__spath_output_tl
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  insert~ gaps~ globally~ after~ components/.code~ n~ args={3}{
+    \tl_if_exist:cTF
+    {\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
+      \spath_numberofcomponents:Nv \l__spath_tmpa_int
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      \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
+          {
+            \int_mod:nn { \l__spath_tmpa_tl }{ \l__spath_tmpa_int } + 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_gset_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
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   join~ components/.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:cTF
+    {\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}
@@ -395,13 +1084,144 @@
         {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{##1}
       }
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  join~ components~ globally/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\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_gjoin_component:cn
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}{##1}
+      }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   remove~ empty~ components/.code={
-    \tl_if_exist:cT {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    \tl_if_exist:cTF
+    {\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}
     }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  remove~ empty~ components~ globally/.code={
+    \tl_if_exist:cTF
+    {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    {
+      \spath_gremove_empty_components:c
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  remove~ components/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\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: }
+      }
+      \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_gpop_left:NNF \g__spath_tmpa_seq \l__spath_tmpa_tl
+      {
+        \tl_clear:N \l__spath_tmpa_tl
+      }
+      \seq_clear:N \l__spath_tmpb_seq
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+      {
+        \tl_set:Nn \l__spath_tmpb_tl {##1}
+        \tl_if_eq:NNTF \l__spath_tmpb_tl \l__spath_tmpa_tl
+        {
+          \seq_gpop_left:NNF \g__spath_tmpa_seq \l__spath_tmpa_tl
+          {
+            \tl_clear:N \l__spath_tmpa_tl
+          }
+        }
+        {
+          \seq_put_right:Nn \l__spath_tmpb_seq {##2}
+        }
+      }
+      \tl_set:cx {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {\seq_use:Nn \l__spath_tmpb_seq {} }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
+  },
+  remove~ components~ globally/.code~ 2~ args={
+    \tl_if_exist:cTF
+    {\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: }
+      }
+      \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_gpop_left:NNF \g__spath_tmpa_seq \l__spath_tmpa_tl
+      {
+        \tl_clear:N \l__spath_tmpa_tl
+      }
+      \seq_clear:N \l__spath_tmpb_seq
+      \seq_map_indexed_inline:Nn \l__spath_tmpa_seq
+      {
+        \tl_set:Nn \l__spath_tmpb_tl {##1}
+        \tl_if_eq:NNTF \l__spath_tmpb_tl \l__spath_tmpa_tl
+        {
+          \seq_gpop_left:NNF \g__spath_tmpa_seq \l__spath_tmpa_tl
+          {
+            \tl_clear:N \l__spath_tmpa_tl
+          }
+        }
+        {
+          \seq_put_right:Nn \l__spath_tmpb_seq {##2}
+        }
+      }
+      \tl_gset:cx {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {\seq_use:Nn \l__spath_tmpb_seq {} }
+    }
+    {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+    }
   },
   draft~ mode/.is~ choice,
   draft~ mode/true/.code={
@@ -413,11 +1233,29 @@
   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}
+      \tl_if_exist:cTF
+      {\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}
       }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+      }
+    }
+  },
+  maybe~ spot~ weld~ globally/.code={
+    \bool_if:NF \l__spath_draft_bool
+    {
+      \tl_if_exist:cTF
+      {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      {
+        \spath_spot_gweld_components:c
+        {\tl_use:N \l__spath_prefix_tl #1 \tl_use:N \l__spath_suffix_tl}
+      }
+      {
+        \msg_warning:nnn { spath3 } { missing soft path } { #1 }
+      }
     }
   },
   transform~ to/.code~ 2~ args={
@@ -449,6 +1287,7 @@
       \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpc_tl
     }
     {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
       \tl_gset_eq:NN \g__spath_smuggle_tl { {1}{0}{0}{1}{0pt}{0pt} }
     }
     \group_end:
@@ -484,6 +1323,7 @@
       \tl_gset_eq:NN \g__spath_smuggle_tl \l__spath_tmpc_tl
     }
     {
+      \msg_warning:nnn { spath3 } { missing soft path } { #1 }
       \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}
@@ -503,11 +1343,18 @@
     \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
+    spath/split~ at~ self~ intersections=#1,
+    spath/remove~ empty~ components=#1,
+    spath/insert~ gaps~ after~ components={#1}{#2}{#3},
+    spath/maybe~ spot~ weld=#1,
+    spath/render~ components=#1
+  },
+  global~ knot/.style~ n~ args={3}{
+    spath/split~ globally~ at~ self~ intersections=#1,
+    spath/remove~ empty~ components~ globally=#1,
+    spath/insert~ gaps~ globally ~after~ components={#1}{#2}{#3},
+    spath/maybe~ spot~ weld~ globally=#1,
+    spath/render~ components=#1
   },
 }
 \tikzdeclarecoordinatesystem{spath}{%
@@ -556,15 +1403,20 @@
     }
   }
   {
+    \msg_warning:nnx { spath3 } { missing soft path } { \tl_use:N \l__spath_tmpa_tl }
     \tl_gset_eq:NN \g__spath_smuggle_tl \pgfpointorigin
   }
-    \group_end:
+  \group_end:
+  \use:c {pgf@process}{%
     \tl_use:N \g__spath_smuggle_tl
+    \pgftransforminvert
+    \use:c {pgf@pos@transform@glob}
+  }
 }
 
 \ExplSyntaxOff
 %% 
-%% Copyright (C) 2011-2019 by Andrew Stacey <loopspace@mathforge.org>
+%% Copyright (C) 2011-2021 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
@@ -576,7 +1428,7 @@
 %% This work is "maintained" (as per LPPL maintenance status) by
 %% Andrew Stacey.
 %% 
-%% This work consists of the files  spath3.dtx
+%% This work consists of the files  spath3_code.dtx
 %%                                  calligraphy_doc.tex
 %%                                  knots_doc.tex
 %%                                  spath3.tex