%%
%% This is file `spath3.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% spath3.dtx  (with options: `spath3')
%% ----------------------------------------------------------------
%% spath3 --- Functions for manipulating PGF soft paths
%% E-mail: stacey@math.ntnu.no
%% Released under the LaTeX Project Public License v1.3c or later
%% See http://www.latex-project.org/lppl.txt
%% ----------------------------------------------------------------
%% 
\NeedsTeXFormat{LaTeX2e}
\RequirePackage{expl3}
\RequirePackage{pgf}
\ProvidesExplPackage {spath3} {2016/02/19} {1.1} {Functions for
manipulating PGF soft paths}
\RequirePackage{xparse}
\tl_new:N \l__spath_tmpa_tl
\tl_new:N \l__spath_tmpb_tl
\tl_new:N \l__spath_tmpc_tl
\tl_new:N \l__spath_tmpd_tl
\tl_new:N \l__spath_smuggle_tl
\dim_new:N \l__spath_tmpa_dim
\dim_new:N \l__spath_tmpb_dim
\fp_new:N \l__spath_tmpa_fp
\fp_new:N \l__spath_tmpb_fp
\int_new:N \l__spath_tmpa_int
\tl_new:N \g__spath_moveto_tl
\tl_new:N \g__spath_lineto_tl
\tl_new:N \g__spath_curveto_tl
\tl_new:N \g__spath_curvetoa_tl
\tl_new:N \g__spath_curvetob_tl
\tl_new:N \g__spath_closepath_tl
\tl_set:Nn \g__spath_moveto_tl {\pgfsyssoftpath@movetotoken}
\tl_set:Nn \g__spath_lineto_tl {\pgfsyssoftpath@linetotoken}
\tl_set:Nn \g__spath_curveto_tl {\pgfsyssoftpath@curvetotoken}
\tl_set:Nn \g__spath_curvetoa_tl {\pgfsyssoftpath@curvetosupportatoken}
\tl_set:Nn \g__spath_curvetob_tl {\pgfsyssoftpath@curvetosupportbtoken}
\tl_set:Nn \g__spath_closepath_tl {\pgfsyssoftpath@closepathtoken}
\tl_new:N \g__spath_attributes
\tl_new:N \g__spath_moveable_attributes
\tl_new:N \g__spath_path_attributes
\tl_set:Nn \g__spath_attributes {
  {path}
  {reverse path}
  {length}
  {real length}
  {number of components}
  {initial point}
  {final point}
  {initial action}
  {final action}
  {min bb}
  {max bb}
}
\tl_set:Nn \g__spath_moveable_attributes {
  {initial point}
  {final point}
  {min bb}
  {max bb}
}
\tl_set:Nn \g__spath_path_attributes {
  {path}
  {reverse path}
}
\cs_new_nopar:Npn \spath_new:n #1
{
  \prop_new:c {l__spath_#1}
}
\cs_new_nopar:Npn \spath_clear:n #1
{
  \prop_gclear:c {l__spath_#1}
}
\cs_new_nopar:Npn \spath_clear_new:n #1
{
  \prop_gclear_new:c {l__spath_#1}
}
\cs_new_nopar:Npn \spath_show:n #1
{
  \prop_show:c {l__spath_#1}
}
\cs_new_nopar:Npn \spath_put:nnn #1#2#3
{
  \prop_gput:cnn {l__spath_#1} {#2} {#3}
}
\cs_new_nopar:Npn \spath_remove:nn #1#2
{
  \prop_gremove:cn {l__spath_#1} {#2}
}
\cs_new_nopar:Npn \__spath_get:nn #1#2
{
  \prop_item:cn {l__spath_#1} {#2}
}
\cs_new_nopar:Npn \__spath_get:nnN #1#2#3
{
  \prop_get:cnN {l__spath_#1} {#2} #3
}
\prg_new_conditional:Npnn \spath_if_in:nn #1#2 {p, T, F, TF}
{
  \prop_if_in:cnTF {l__spath_#1} {#2}
  { \prg_return_true: }
  { \prg_return_false: }
}
\cs_generate_variant:Nn \__prop_split:NnTF {cnTF}
\prg_new_protected_conditional:Npnn \__spath_get:nnN #1#2#3 {T, F, TF}
{
  \__prop_split:cnTF {l__spath_#1} {#2}
  {
    \tl_set:Nn #3 {##2}
    \prg_return_true:
  }
  { \prg_return_false: }
}
\cs_generate_variant:Nn \spath_put:nnn {nnV, nnx, nno}
\cs_generate_variant:Nn \__spath_get:nn {Vn}
\cs_generate_variant:Nn \__spath_get:nnN {VnN}
\prg_new_conditional:Npnn \spath_if_exist:n #1 {p,T,F,TF}
{
  \prop_if_exist:cTF {l__spath_#1}
  {
    \prg_return_true:
  }
  {
    \prg_return_false:
  }
}
\cs_new_nopar:Npn \spath_clone:nn #1 #2
{
  \spath_clear_new:n {#2}
  \tl_map_inline:Nn \g__spath_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
      \spath_put:nnV {#2} {##1} \l__spath_tmpa_tl
    }
  }
}
\cs_new_protected_nopar:Npn \spath_get_current_path:n #1
{
  \pgfsyssoftpath@getcurrentpath\l__spath_tmpa_tl
  \spath_clear_new:n {#1}
  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
}
\cs_new_protected_nopar:Npn \spath_set_current_path:n #1
{
  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl

  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl

  \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \pgfsyssoftpath@setcurrentpath\l__spath_tmpa_tl
  \pgfsyssoftpath@flushcurrentpath
}
\cs_new_protected_nopar:Npn \spath_use_path:nn #1#2
{
  \spath_set_current_path:n {#1}
  \pgfusepath{#2}
}
\cs_new_protected_nopar:Npn \spath_protocol_path:n #1
{
  \spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl

  \spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
  \exp_last_unbraced:NV \pgf@protocolsizes\l__spath_tmpa_tl
}
\cs_new_protected_nopar:Npn \spath_tikz_path:nn #1#2
{
  \path[#1] \pgfextra{
    \spath_get:nnN {#2} {path} \l__spath_tmpa_tl
    \pgfsyssoftpath@setcurrentpath \l__spath_tmpa_tl
  };
}
\cs_generate_variant:Nn \spath_tikz_path:nn {Vn}
\cs_new_nopar:Npn \spath_get:nn #1#2
{
  \spath_if_in:nnF {#1} {#2}
  {
    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
  }
  \__spath_get:nn {#1} {#2}
}
\cs_new_nopar:Npn \spath_get:nnN #1#2#3
{
  \spath_if_in:nnF {#1} {#2}
  {
    \cs_if_exist_use:cT {spath_generate_#2:n} {{#1}}
  }
  \__spath_get:nnN {#1} {#2} #3
}
\cs_generate_variant:Nn \spath_get:nnN {nnV,VnN,VnV}
\cs_new_nopar:Npn \spath_generate_length:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \spath_put:nnx {#1} {length} {\int_eval:n {\tl_count:N \l__spath_tmpa_tl /3 }}
}
\cs_new_nopar:Npn \spath_generate_reallength:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \int_set:Nn \l__spath_tmpa_int {0}
  \tl_map_inline:Nn \l__spath_tmpa_tl {
    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@linetotoken}
    {
      \int_incr:N \l__spath_tmpa_int
    }
    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@curvetotoken}
    {
      \int_incr:N \l__spath_tmpa_int
    }
  }
  \spath_put:nnx {#1} {real length} {\int_use:N \l__spath_tmpa_int}
}
\cs_new_nopar:Npn \spath_generate_numberofcomponents:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \int_set:Nn \l__spath_tmpa_int {0}
  \tl_map_inline:Nn \l__spath_tmpa_tl {
    \tl_if_eq:nnT {##1} {\pgfsyssoftpath@movetotoken}
    {
      \int_incr:N \l__spath_tmpa_int
    }
  }
  \spath_put:nnx {#1} {number of components} {\int_use:N \l__spath_tmpa_int}
}
\cs_new_nopar:Npn \spath_generate_initialpoint:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \tl_clear:N \l__spath_tmpb_tl
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
  \spath_put:nnV {#1} {initial point} \l__spath_tmpb_tl
}
\cs_new_nopar:Npn \spath_generate_finalpoint:n #1
{
  \tl_clear:N \l__spath_tmpb_tl
  \spath_if_in:nnTF {#1} {reverse path}
  {
    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
  }
  {
    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
    \tl_reverse:N \l__spath_tmpa_tl
    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \tl_put_left:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
  }
  \spath_put:nnV {#1} {final point} \l__spath_tmpb_tl
}
\cs_generate_variant:Nn \spath_generate_finalpoint:n {V}
\cs_new_nopar:Npn \spath_generate_reversepath:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \tl_clear:N \l__spath_tmpb_tl
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_put_left:Nx \l__spath_tmpb_tl
  {
    {\dim_use:N \l__spath_tmpa_dim}
    {\dim_use:N \l__spath_tmpb_dim}
  }
  \bool_until_do:nn {
    \tl_if_empty_p:N \l__spath_tmpa_tl
  }
  {
    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nn \l__spath_tmpd_tl {}
    \tl_case:NnF \l__spath_tmpc_tl
    {
      \g__spath_moveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl }
      \g__spath_lineto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl }
      \g__spath_curveto_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl }
      \g__spath_curvetoa_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl }
      \g__spath_curvetob_tl {\tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl }
    }
    {
      \tl_show:N \l__spath_tmpc_tl
    }
    \tl_put_left:NV \l__spath_tmpb_tl \l__spath_tmpd_tl
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \tl_put_left:Nx \l__spath_tmpb_tl
    {
      {\dim_use:N \l__spath_tmpa_dim}
      {\dim_use:N \l__spath_tmpb_dim}
    }
  }
  \tl_put_left:NV \l__spath_tmpb_tl \g__spath_moveto_tl
  \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
}
\cs_new_nopar:Npn \spath_generate_initialaction:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \tl_clear:N \l__spath_tmpb_tl
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_if_empty:NF \l__spath_tmpa_tl {
    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
  }
  \spath_put:nnV {#1} {initial action} \l__spath_tmpb_tl
}
\cs_new_nopar:Npn \spath_generate_finalaction:n #1
{
  \tl_clear:N \l__spath_tmpb_tl
  \spath_if_in:nnTF {#1} {reverse path}
  {
    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  }
  {
    \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
    \tl_reverse:N \l__spath_tmpa_tl
  }
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_if_empty:NF \l__spath_tmpa_tl {
    \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
  }
  \tl_if_eq:NNT \l__spath_tmpa_tl \g__spath_curvetoa_tl
  {
    \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_curveto_tl
  }
  \spath_put:nnV {#1} {final action} \l__spath_tmpb_tl
}
\cs_new_nopar:Npn \spath_generate_minbb:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \bool_until_do:nn {
    \tl_if_empty_p:N \l__spath_tmpa_tl
  }
  {
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  }
  \tl_clear:N \l__spath_tmpb_tl
  \tl_put_right:Nx \l__spath_tmpb_tl
  {
    {\dim_use:N \l__spath_tmpa_dim}
    {\dim_use:N \l__spath_tmpb_dim}
  }
  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
}
\cs_new_nopar:Npn \spath_generate_maxbb:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \bool_until_do:nn {
    \tl_if_empty_p:N \l__spath_tmpa_tl
  }
  {
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpa_dim}}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\tl_head:N \l__spath_tmpa_tl} {\l__spath_tmpb_dim}}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  }
  \tl_clear:N \l__spath_tmpb_tl
  \tl_put_right:Nx \l__spath_tmpb_tl
  {
    {\dim_use:N \l__spath_tmpa_dim}
    {\dim_use:N \l__spath_tmpb_dim}
  }
  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
}
\tl_new:N \l__spath_rp_tl
\int_new:N \l__spath_l_int
\int_new:N \l__spath_rl_int
\int_new:N \l__spath_nc_int
\tl_new:N \l__spath_ip_tl
\tl_new:N \l__spath_fp_tl
\tl_new:N \l__spath_ia_tl
\tl_new:N \l__spath_fa_tl
\dim_new:N \l__spath_minx_dim
\dim_new:N \l__spath_miny_dim
\dim_new:N \l__spath_maxx_dim
\dim_new:N \l__spath_maxy_dim

\cs_new_nopar:Npn \spath_generate_all:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl

  \tl_clear:N \l__spath_rp_tl
  \int_set:Nn \l__spath_l_int {1}
  \int_zero:N \l__spath_rl_int
  \int_set:Nn \l__spath_nc_int {1}
  \tl_clear:N \l__spath_ip_tl
  \tl_clear:N \l__spath_fp_tl
  \tl_clear:N \l__spath_ia_tl
  \tl_clear:N \l__spath_fa_tl
  \dim_zero:N \l__spath_minx_dim
  \dim_zero:N \l__spath_miny_dim
  \dim_zero:N \l__spath_maxx_dim
  \dim_zero:N \l__spath_maxy_dim

  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

  \tl_clear:N \l__spath_ip_tl
  \tl_put_right:Nx \l__spath_ip_tl
  {
    {\dim_use:N \l__spath_tmpa_dim}
    {\dim_use:N \l__spath_tmpb_dim}
  }

  \dim_set_eq:NN \l__spath_minx_dim \l__spath_tmpa_dim
  \dim_set_eq:NN \l__spath_miny_dim \l__spath_tmpb_dim
  \dim_set_eq:NN \l__spath_maxx_dim \l__spath_tmpa_dim
  \dim_set_eq:NN \l__spath_maxy_dim \l__spath_tmpb_dim

  \tl_put_left:Nx \l__spath_rp_tl
  {
    {\dim_use:N \l__spath_tmpa_dim}
    {\dim_use:N \l__spath_tmpb_dim}
  }

  \tl_set:Nx \l__spath_ia_tl {\tl_head:N \l__spath_tmpa_tl}

  \bool_until_do:nn {
    \tl_if_empty_p:N \l__spath_tmpa_tl
  }
  {
    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nn \l__spath_tmpd_tl {}
    \tl_set_eq:NN \l__spath_fa_tl \l__spath_tmpc_tl
    \int_incr:N \l__spath_l_int

    \tl_case:NnF \l__spath_tmpc_tl
    {
      \g__spath_moveto_tl {
        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_moveto_tl
        \int_incr:N \l__spath_nc_int
      }
      \g__spath_lineto_tl {
        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_lineto_tl
        \int_incr:N \l__spath_rl_int
      }
      \g__spath_curveto_tl {
        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetoa_tl
        \int_incr:N \l__spath_rl_int
      }
      \g__spath_curvetoa_tl {
        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curveto_tl
      }
      \g__spath_curvetob_tl {
        \tl_set_eq:NN \l__spath_tmpd_tl \g__spath_curvetob_tl
      }
    }
    {
      \tl_show:N \l__spath_tmpc_tl
    }
    \tl_put_left:NV \l__spath_rp_tl \l__spath_tmpd_tl
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

    \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

    \dim_set:Nn \l__spath_minx_dim {\dim_min:nn { \l__spath_minx_dim} {\l__spath_tmpa_dim}}
    \dim_set:Nn \l__spath_miny_dim {\dim_min:nn { \l__spath_miny_dim} {\l__spath_tmpb_dim}}
    \dim_set:Nn \l__spath_maxx_dim {\dim_max:nn { \l__spath_maxx_dim} {\l__spath_tmpa_dim}}
    \dim_set:Nn \l__spath_maxy_dim {\dim_max:nn { \l__spath_maxy_dim} {\l__spath_tmpb_dim}}

    \tl_put_left:Nx \l__spath_rp_tl
    {
      {\dim_use:N \l__spath_tmpa_dim}
      {\dim_use:N \l__spath_tmpb_dim}
    }

    \tl_set:Nx \l__spath_fp_tl
    {
      {\dim_use:N \l__spath_tmpa_dim}
      {\dim_use:N \l__spath_tmpb_dim}
    }

  }

  \tl_put_left:NV \l__spath_rp_tl \g__spath_moveto_tl

  \spath_put:nnV {#1} {reverse path} \l__spath_rp_tl
  \spath_put:nnV {#1} {length} \l__spath_l_int
  \spath_put:nnV {#1} {real length} \l__spath_rl_int
  \spath_put:nnV {#1} {number of components} \l__spath_nc_int
  \spath_put:nnV {#1} {initial point} \l__spath_ip_tl
  \spath_put:nnV {#1} {final point} \l__spath_fp_tl
  \spath_put:nnV {#1} {initial action} \l__spath_ia_tl
  \spath_put:nnV {#1} {final action} \l__spath_fa_tl

  \tl_clear:N \l__spath_tmpb_tl
  \tl_put_right:Nx \l__spath_tmpb_tl
  {
    {\dim_use:N \l__spath_minx_dim}
    {\dim_use:N \l__spath_miny_dim}
  }
  \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl

  \tl_clear:N \l__spath_tmpb_tl
  \tl_put_right:Nx \l__spath_tmpb_tl
  {
    {\dim_use:N \l__spath_maxx_dim}
    {\dim_use:N \l__spath_maxy_dim}
  }
  \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl

}
\cs_new_nopar:Npn \spath_translate:nnn #1#2#3
{
  \tl_map_inline:Nn \g__spath_moveable_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl

      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
      \tl_clear:N \l__spath_tmpb_tl
      \tl_put_right:Nx \l__spath_tmpb_tl
      {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
    }
  }
  \tl_map_inline:Nn \g__spath_path_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
      \tl_clear:N \l__spath_tmpb_tl
      \bool_until_do:nn {
        \tl_if_empty_p:N \l__spath_tmpa_tl
      }
      {
        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl + #2}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl + #3}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \tl_put_right:Nx \l__spath_tmpb_tl
        {
          {\dim_use:N \l__spath_tmpa_dim}
          {\dim_use:N \l__spath_tmpb_dim}
        }
      }
      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
    }
  }
}

\cs_generate_variant:Nn \spath_translate:nnn {nxx}
\cs_new_nopar:Npn \spath_translate:nn #1#2
{
  \spath_translate:nnn {#1} #2
}

\cs_generate_variant:Nn \spath_translate:nn {nV}
\cs_new_nopar:Npn \spath_scale:nnn #1#2#3
{
  \tl_map_inline:Nn \g__spath_moveable_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl

      \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
      \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
      \tl_clear:N \l__spath_tmpb_tl
      \tl_put_right:Nx \l__spath_tmpb_tl
      {
        {\fp_to_dim:N \l__spath_tmpa_fp}
        {\fp_to_dim:N \l__spath_tmpb_fp}
      }
      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
    }
  }
  \tl_map_inline:Nn \g__spath_path_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
      \tl_clear:N \l__spath_tmpb_tl
      \bool_until_do:nn {
        \tl_if_empty_p:N \l__spath_tmpa_tl
      }
      {
        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \fp_set:Nn \l__spath_tmpa_fp {\tl_head:N \l__spath_tmpa_tl * #2}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \fp_set:Nn \l__spath_tmpb_fp {\tl_head:N \l__spath_tmpa_tl * #3}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \tl_put_right:Nx \l__spath_tmpb_tl
        {
          {\fp_to_dim:N \l__spath_tmpa_fp}
          {\fp_to_dim:N \l__spath_tmpb_fp}
        }
      }
      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
    }
  }
}
\cs_generate_variant:Nn \spath_scale:nnn {nxx}
\cs_new_nopar:Npn \spath_scale:nn #1#2
{
  \spath_scale:nnn {#1} #2
}

\cs_generate_variant:Nn \spath_scale:nn {nV}
\cs_new_nopar:Npn \spath_transform:nnnnnnn #1#2#3#4#5#6#7
{
  \tl_map_inline:Nn \g__spath_moveable_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpa_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
      \fp_set:Nn \l__spath_tmpa_fp {\l__spath_tmpa_tl * #2 + \l__spath_tmpb_tl * #3 + #6}
      \fp_set:Nn \l__spath_tmpb_fp {\l__spath_tmpa_tl * #4 + \l__spath_tmpb_tl * #5 + #7}
      \tl_clear:N \l__spath_tmpb_tl
      \tl_put_right:Nx \l__spath_tmpb_tl
      {
        {\fp_to_dim:N \l__spath_tmpa_fp}
        {\fp_to_dim:N \l__spath_tmpb_fp}
      }
      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
    }
  }
  \tl_map_inline:Nn \g__spath_path_attributes
  {
    \spath_if_in:nnT {#1} {##1}
    {
      \__spath_get:nnN {#1} {##1} \l__spath_tmpa_tl
      \tl_clear:N \l__spath_tmpb_tl
      \bool_until_do:nn {
        \tl_if_empty_p:N \l__spath_tmpa_tl
      }
      {
        \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
        \tl_set:Nx \l_tmpa_tl {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
        \tl_set:Nx \l_tmpb_tl {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \fp_set:Nn \l__spath_tmpa_fp {\l_tmpa_tl * #2 + \l_tmpb_tl * #3 + #6}
        \fp_set:Nn \l__spath_tmpb_fp {\l_tmpa_tl * #4 + \l_tmpb_tl * #5 + #7}
        \tl_put_right:Nx \l__spath_tmpb_tl
        {
          {\fp_to_dim:N \l__spath_tmpa_fp}
          {\fp_to_dim:N \l__spath_tmpb_fp}
        }
      }
      \spath_put:nnV {#1} {##1} \l__spath_tmpb_tl
    }
  }
}

\cs_generate_variant:Nn \spath_transform:nnnnnnn {nxxxxxx}
\cs_new_nopar:Npn \spath_transform:nn #1#2
{
  \spath_transform:nnnnnnn {#1} #2
}

\cs_generate_variant:Nn \spath_transform:nn {nV}
\cs_new_nopar:Npn \spath_reverse:n #1
{
  \spath_if_in:nnF {#1} {reverse path} {
    \use:c {spath_generate_reverse path:n} {#1}
  }
  \spath_swap:nnn {#1} {path} {reverse path}
  \spath_swap:nnn {#1} {initial point} {final point}
  \spath_swap:nnn {#1} {initial action} {final action}
}
\cs_new_nopar:Npn \spath_swap:nnn #1#2#3
{
  \__spath_get:nnNF {#1} {#2} \l__spath_tmpa_tl {\tl_clear:N \l__spath_tmpa_tl}
  \__spath_get:nnNF {#1} {#3} \l__spath_tmpb_tl {\tl_clear:N \l__spath_tmpb_tl}
  \tl_if_empty:NTF \l__spath_tmpb_tl
  {\spath_remove:nn {#1} {#2}}
  {\spath_put:nnV {#1} {#2} \l__spath_tmpb_tl}
  \tl_if_empty:NTF \l__spath_tmpa_tl
  {\spath_remove:nn {#1} {#3}}
  {\spath_put:nnV {#1} {#3} \l__spath_tmpa_tl}
}
\cs_new_nopar:Npn \spath_weld:nn #1#2
{
  \spath_clone:nn {#2} {tmp_path}
  \spath_get:nnN {#1} {final point} \l__spath_tmpa_tl

  \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}

  \spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl

  \dim_sub:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \dim_sub:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}

  \spath_translate:nxx {tmp_path} {\dim_use:N \l__spath_tmpa_dim} {\dim_use:N \l__spath_tmpb_dim}

  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \__spath_get:nnN {tmp_path} {path} \l__spath_tmpb_tl
  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
  \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl

  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl

  \__spath_get:nnNTF {tmp_path} {final point} \l__spath_tmpa_tl
  {
    \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
  }
  {
    \spath_remove:nn {#1} {final point}
  }

  \__spath_get:nnNTF {tmp_path} {final action} \l__spath_tmpa_tl
  {
    \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
  }
  {
    \spath_remove:nn {#1} {final action}
  }

  \__spath_get:nnNT {tmp_path} {min bb} \l__spath_tmpa_tl
  {
    \__spath_get:nnNT {#1} {min bb} \l__spath_tmpb_tl
    {
      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}

      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}

      \tl_clear:N \l__spath_tmpb_tl
      \tl_put_right:Nx \l__spath_tmpb_tl
      {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
      \spath_put:nnV {#1} {min bb} \l__spath_tmpb_tl
    }
  }

  \__spath_get:nnNT {tmp_path} {max bb} \l__spath_tmpa_tl
  {
    \__spath_get:nnNT {#1} {max bb} \l__spath_tmpb_tl
    {
      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}

      \dim_set:Nn \l__spath_tmpa_dim {\dim_max:nn {\l__spath_tmpa_dim} {\tl_head:N           \l__spath_tmpb_tl}}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \dim_set:Nn \l__spath_tmpb_dim {\dim_max:nn {\l__spath_tmpb_dim} {\tl_head:N \l__spath_tmpb_tl}}

      \tl_clear:N \l__spath_tmpb_tl
      \tl_put_right:Nx \l__spath_tmpb_tl
      {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
      \spath_put:nnV {#1} {max bb} \l__spath_tmpb_tl
    }
  }

  \__spath_get:nnNT {tmp_path} {reverse path} \l__spath_tmpa_tl
  {
    \__spath_get:nnNT {#1} {reverse path} \l__spath_tmpb_tl
    {
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl

      \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
    }
  }

  \__spath_get:nnNT {tmp_path} {length} \l__spath_tmpa_tl
  {
    \__spath_get:nnNT {#1} {length} \l__spath_tmpb_tl
    {
      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
      \spath_put:nnV {#1} {length} \l__spath_tmpa_int
    }
  }

  \__spath_get:nnNT {tmp_path} {real length} \l__spath_tmpa_tl
  {
    \__spath_get:nnNT {#1} {real length} \l__spath_tmpb_tl
    {
      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl}
      \spath_put:nnV {#1} {real length} \l__spath_tmpa_int
    }
  }

  \__spath_get:nnNT {tmp_path} {number of components} \l__spath_tmpa_tl
  {
    \__spath_get:nnNT {#1} {number of components} \l__spath_tmpb_tl
    {
      \int_set:Nn \l__spath_tmpa_int {\l__spath_tmpa_tl + \l__spath_tmpb_tl - 1}
      \spath_put:nnV {#1} {number of components} \l__spath_tmpa_int
    }
  }

}
\cs_new_nopar:Npn \spath_prepend_no_move:nn #1#2
{
  \spath_if_exist:nT {#2}
  {
    \__spath_get:nnN {#2} {path} \l__spath_tmpa_tl
    \__spath_get:nnN {#1} {path} \l__spath_tmpb_tl
    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl

    \spath_if_in:nnTF {#2} {initial point}
    {
      \__spath_get:nnN {#2} {initial point} \l__spath_tmpa_tl
      \spath_put:nnV {#1} {initial point} \l__spath_tmpa_tl
    }
    {
      \spath_remove:nn {#1} {initial point}
    }

    \spath_if_in:nnTF {#2} {initial action}
    {
      \__spath_get:nnN {#2} {initial action} \l__spath_tmpa_tl
      \spath_put:nnV {#1} {initial action} \l__spath_tmpa_tl
    }
    {
      \spath_remove:nn {#1} {initial action}
    }

    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {length}
      &&
      \spath_if_in_p:nn {#2} {length}
    }
    {
      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
          \l__spath_tmpb_tl - 1}}
    }
    {
      \spath_remove:nn {#1} {length}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {real length}
      &&
      \spath_if_in_p:nn {#2} {real length}
    }
    {
      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
          \l__spath_tmpb_tl }}
    }
    {
      \spath_remove:nn {#1} {real length}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {number of components}
      &&
      \spath_if_in_p:nn {#2} {number of components}
    }
    {
      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
          \l__spath_tmpb_tl - 1}}
    }
    {
      \spath_remove:nn {#1} {number of components}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {min bb}
      &&
      \spath_if_in_p:nn {#2} {min bb}
    }
    {
      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {1}} {\tl_item:Nn
          \l__spath_tmpb_tl {1}}}
      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {2}} {\tl_item:Nn
          \l__spath_tmpb_tl {2}}}
      \spath_put:nnx {#1} {min bb} {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
    }
    {
      \spath_remove:nn {#1} {min bb}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {max bb}
      &&
      \spath_if_in_p:nn {#2} {max bb}
    }
    {
      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {1}} {\tl_item:Nn
          \l__spath_tmpb_tl {1}}}
      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {2}} {\tl_item:Nn
          \l__spath_tmpb_tl {2}}}
      \spath_put:nnx {#1} {max bb} {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
    }
    {
      \spath_remove:nn {#1} {max bb}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {reverse path}
      &&
      \spath_if_in_p:nn {#2} {reverse path}
    }
    {
      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpb_tl
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
    }
    {
      \spath_remove:nn {#1} {reverse path}
    }

  }
}
\cs_new_nopar:Npn \spath_append_no_move:nn #1#2
{
  \spath_if_exist:nT {#2}
  {
    \spath_get:nnN {#1} {path} \l__spath_tmpa_tl
    \spath_get:nnN {#2} {path} \l__spath_tmpb_tl
    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
    \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
    \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
    \spath_if_in:nnTF {#2} {final point}
    {
      \__spath_get:nnN {#2} {final point} \l__spath_tmpa_tl
      \spath_put:nnV {#1} {final point} \l__spath_tmpa_tl
    }
    {
      \spath_remove:nn {#1} {final point}
    }
    \spath_if_in:nnTF {#2} {final action}
    {
      \__spath_get:nnN {#2} {final action} \l__spath_tmpa_tl
      \spath_put:nnV {#1} {final action} \l__spath_tmpa_tl
    }
    {
      \spath_remove:nn {#1} {final action}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {length}
      &&
      \spath_if_in_p:nn {#2} {length}
    }
    {
      \__spath_get:nnN {#1} {length} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {length} \l__spath_tmpb_tl
      \spath_put:nnx {#1} {length} {\int_eval:n {\l__spath_tmpa_tl +
          \l__spath_tmpb_tl - 1}}
    }
    {
      \spath_remove:nn {#1} {length}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {real length}
      &&
      \spath_if_in_p:nn {#2} {real length}
    }
    {
      \__spath_get:nnN {#1} {real length} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {real length} \l__spath_tmpb_tl
      \spath_put:nnx {#1} {real length} {\int_eval:n {\l__spath_tmpa_tl +
          \l__spath_tmpb_tl }}
    }
    {
      \spath_remove:nn {#1} {real length}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {number of components}
      &&
      \spath_if_in_p:nn {#2} {number of components}
    }
    {
      \__spath_get:nnN {#1} {number of components} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {number of components} \l__spath_tmpb_tl
      \spath_put:nnx {#1} {number of components} {\int_eval:n {\l__spath_tmpa_tl +
          \l__spath_tmpb_tl - 1}}
    }
    {
      \spath_remove:nn {#1} {number of components}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {min bb}
      &&
      \spath_if_in_p:nn {#2} {min bb}
    }
    {
      \__spath_get:nnN {#1} {min bb} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {min bb} \l__spath_tmpb_tl
      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {1}} {\tl_item:Nn
          \l__spath_tmpb_tl {1}}}
      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {2}} {\tl_item:Nn
          \l__spath_tmpb_tl {2}}}
      \spath_put:nnx {#1} {min bb} {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
    }
    {
      \spath_remove:nn {#1} {min bb}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {max bb}
      &&
      \spath_if_in_p:nn {#2} {max bb}
    }
    {
      \__spath_get:nnN {#1} {max bb} \l__spath_tmpa_tl
      \__spath_get:nnN {#2} {max bb} \l__spath_tmpb_tl
      \dim_set:Nn \l__spath_tmpa_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {1}} {\tl_item:Nn
          \l__spath_tmpb_tl {1}}}
      \dim_set:Nn \l__spath_tmpb_dim {\dim_min:nn {\tl_item:Nn
          \l__spath_tmpa_tl {2}} {\tl_item:Nn
          \l__spath_tmpb_tl {2}}}
      \spath_put:nnx {#1} {max bb} {
        {\dim_use:N \l__spath_tmpa_dim}
        {\dim_use:N \l__spath_tmpb_dim}
      }
    }
    {
      \spath_remove:nn {#1} {max bb}
    }
    \bool_if:nTF
    {
      \spath_if_in_p:nn {#1} {reverse path}
      &&
      \spath_if_in_p:nn {#2} {reverse path}
    }
    {
      \__spath_get:nnN {#2} {reverse path} \l__spath_tmpa_tl
      \__spath_get:nnN {#1} {reverse path} \l__spath_tmpb_tl
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_set:Nx \l__spath_tmpb_tl {\tl_tail:N \l__spath_tmpb_tl}
      \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
      \spath_put:nnV {#1} {reverse path} \l__spath_tmpb_tl
    }
    {
      \spath_remove:nn {#1} {reverse path}
    }
  }
}
\cs_new_nopar:Npn \spath_bake_round:n #1
{
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \pgf@@processround\l__spath_tmpa_tl\l__spath_tmpb_tl
  \spath_put:nnV {#1} {path} \l__spath_tmpb_tl
}
\cs_new_nopar:Npn \spath_close_path:n #1
{
  \spath_get:nnN {#1} {initial point} \l__spath_tmpb_tl
  \__spath_get:nnN {#1} {path} \l__spath_tmpa_tl
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
  \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
  \spath_put:nnV {#1} {path} \l__spath_tmpa_tl
  \spath_if_in:nnT {#1} {reverse path}
  {
    \spath_get:nnN {#1} {final point} \l__spath_tmpb_tl
    \__spath_get:nnN {#1} {reverse path} \l__spath_tmpa_tl
    \tl_put_right:NV \l__spath_tmpa_tl \g__spath_closepath_tl
    \tl_put_right:NV \l__spath_tmpa_tl \l__spath_tmpb_tl
    \spath_put:nnV {#1} {reverse path} \l__spath_tmpa_tl
  }
}
\cs_new_nopar:Npn \spath_map_component:Nn #1#2
{
  \int_gincr:N \g__prg_map_int
  \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 {#2}
  \tl_set:NV \l__spath_tmpa_tl #1
  \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_moveto_tl
  \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
  \bool_until_do:nn {
    \tl_if_empty_p:N \l__spath_tmpa_tl
  }
  {
    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
    \tl_if_eq:NNT \l__spath_tmpc_tl \g__spath_moveto_tl
    {
      \exp_args:NnV \use:c { __prg_map_ \int_use:N \g__prg_map_int :w } \l__spath_tmpb_tl
\tl_clear:N \l__spath_tmpb_tl
    }
    \tl_if_single:NTF \l__spath_tmpc_tl
    {
      \tl_put_right:NV \l__spath_tmpb_tl \l__spath_tmpc_tl
    }
    {
      \tl_put_right:Nx \l__spath_tmpb_tl {{\l__spath_tmpc_tl}}
    }
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
  }
}
\cs_new_nopar:Npn \spath_map_segment_inline:Nn #1#2
{
  \int_gincr:N \g__prg_map_int
  \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 ##2 {#2}
  \spath_map_segment_function:Nc #1 { __prg_map_ \int_use:N \g__prg_map_int :w }
}
\cs_new_nopar:Npn \spath_map_segment_inline:nn #1#2
{
  \int_gincr:N \g__prg_map_int
  \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 ##2 {#2}
  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
  \spath_map_segment_function:Nc \l__spath_tmpd_tl { __prg_map_ \int_use:N \g__prg_map_int :w }
}
\cs_new_nopar:Npn \spath_map_segment_function:nN #1#2
{
  \spath_get:nnN {#1} {path} \l__spath_tmpd_tl
  \spath_map_segment_function:NN \l__spath_tmpd_tl #2
}
\cs_new_nopar:Npn \spath_map_segment_function:NN #1#2
{
  \tl_set_eq:NN \l__spath_tmpa_tl #1
  \tl_clear:N \l__spath_tmpb_tl
  \dim_zero:N \l__spath_tmpa_dim
  \dim_zero:N \l__spath_tmpb_dim

  \bool_until_do:nn {
    \tl_if_empty_p:N \l__spath_tmpa_tl
  }
  {
    \tl_set:Nx \l__spath_tmpc_tl {\tl_head:N \l__spath_tmpa_tl}
    \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
    \tl_case:NnF \l__spath_tmpc_tl
    {
      \g__spath_lineto_tl
      {
        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
        \tl_put_right:Nx \l__spath_tmpb_tl
        {
          {\dim_use:N \l__spath_tmpa_dim}
          {\dim_use:N \l__spath_tmpb_dim}
        }
        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_lineto_tl

        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

      }

      \g__spath_curvetoa_tl
      {
        \tl_set_eq:NN \l__spath_tmpb_tl \g__spath_moveto_tl
        \tl_put_right:Nx \l__spath_tmpb_tl
        {
          {\dim_use:N \l__spath_tmpa_dim}
          {\dim_use:N \l__spath_tmpb_dim}
        }
        \tl_put_right:NV \l__spath_tmpb_tl \g__spath_curvetoa_tl

        \prg_replicate:nn {2} {
          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
          \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N               \l__spath_tmpa_tl}}
          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
          \tl_put_right:Nx \l__spath_tmpb_tl {\tl_head:N             \l__spath_tmpa_tl}
          \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}
        }

        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
        \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

        \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
        \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
        \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

      }
    }
    {

      \tl_set_eq:NN \l__spath_tmpb_tl \l__spath_tmpc_tl
      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
      \dim_set:Nn \l__spath_tmpa_dim {\tl_head:N \l__spath_tmpa_tl}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

      \tl_put_right:Nx \l__spath_tmpb_tl {{\tl_head:N \l__spath_tmpa_tl}}
      \dim_set:Nn \l__spath_tmpb_dim {\tl_head:N \l__spath_tmpa_tl}
      \tl_set:Nx \l__spath_tmpa_tl {\tl_tail:N \l__spath_tmpa_tl}

    }

    #2 \l__spath_tmpc_tl \l__spath_tmpb_tl
    \tl_clear:N \l__spath_tmpb_tl

  }
}
\cs_generate_variant:Nn \spath_map_segment_function:NN {Nc}
\NewDocumentCommand \MakeSPath { m m }
{
  \spath_clear_new:n {#1}
  \spath_put:nno {#1} {path} {#2}
}
\NewDocumentCommand \MakeSPathList { m m }
{
  \tl_gclear_new:c {l__spath_list_#1}
  \int_zero:N \l__spath_tmpa_int
  \spath_map_component:Nn #2 {
    \spath_clear_new:n {#1 _ \int_use:N \l__spath_tmpa_int}
    \spath_put:nnn  {#1 _ \int_use:N \l__spath_tmpa_int} {path} {##1}
    \tl_gput_right:cx {l__spath_list_#1} {{#1 _ \int_use:N \l__spath_tmpa_int}}
    \int_incr:N \l__spath_tmpa_int
  }
}
\NewDocumentCommand \CloneSPath { m m }
{
  \spath_clone:nn {#1} {#2}
}
\NewDocumentCommand \SPathInfo { m m }
{
  \spath_get:nn {#1} {#2}
}
\NewDocumentCommand \SPathPrepare { m }
{
  \spath_generate_all:n {#1}
}
\NewDocumentCommand \SPathListPrepare { m }
{
  \tl_map_inline:cn {l__spath_list_#1}
  {
    \spath_generate_all:n {##1}
  }
}
\NewDocumentCommand \SPathInfoInto { m m m }
{
  \tl_set:Nn \l_tmpa_tl #3
  \spath_get:nnV {#1} {#2} \l_tmpa_tl
}
\NewDocumentCommand \SPathShow { m }
{
  \spath_show:n {#1}
}
\NewDocumentCommand \SPathTranslate { m m m }
{
  \spath_translate:nnn {#1} {#2} {#3}
}
\NewDocumentCommand \SPathTranslateInto { m m m m }
{
  \spath_clone:nn {#1} {#2}
  \spath_translate:nnn {#2} {#3} {#4}
}
\NewDocumentCommand \SPathScale { m m m }
{
  \spath_scale:nnn {#1} {#2} {#3}
}
\NewDocumentCommand \SPathScaleInto { m m m m }
{
  \spath_clone:nn {#1} {#2}
  \spath_scale:nnn {#2} {#3} {#4}
}
\NewDocumentCommand \SPathWeld { m m }
{
  \spath_weld:nn {#1} {#2}
}
\NewDocumentCommand \SPathWeldInto { m m m }
{
  \spath_clone:nn {#1} {#2}
  \spath_weld:nn {#2} {#3}
}
\tikzset{
  save~spath/.code={
    \tikz@addmode{
      \spath_get_current_path:n {#1}
    }
  },
  restore~spath/.code={
    \spath_set_current_path:n {#1}
  }
}
\cs_new_nopar:Npn \spath_split_curve:nnNN #1#2#3#4
{
  \group_begin:
  \tl_gclear:N \l__spath_smuggle_tl
  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
  \tl_put_right:Nx \l__spath_tmpa_tl {
    {\tl_item:nn {#2} {3}}
    {\tl_item:nn {#2} {4}}
  }
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
  \tl_put_right:Nx \l__spath_tmpa_tl
  {
    {\fp_to_dim:n
    {
      (1 - #1) * \tl_item:nn {#2} {2} + (#1) * \tl_item:nn {#2} {5}
    }}
    {\fp_to_dim:n
    {
      (1 - #1) * \tl_item:nn {#2} {3} + (#1) * \tl_item:nn {#2} {6}
    }}
  }
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
  \tl_put_right:Nx \l__spath_tmpa_tl
  {
    {\fp_to_dim:n
    {
      (1 - #1)^2 * \tl_item:nn {#2} {2} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {5} + (#1)^2 * \tl_item:nn {#2} {8}
    }}
    {\fp_to_dim:n
    {
      (1 - #1)^2 * \tl_item:nn {#2} {3} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {6} + (#1)^2 * \tl_item:nn {#2} {9}
    }}
  }
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
  \tl_put_right:Nx \l__spath_tmpa_tl
  {
    {\fp_to_dim:n
      {
      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
    }}
    {\fp_to_dim:n
    {
      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
    }}
  }
  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
  \group_end:
  \tl_set_eq:NN #3 \l__spath_smuggle_tl
  \group_begin:
  \tl_set_eq:NN \l__spath_tmpa_tl \g__spath_moveto_tl
  \tl_put_right:Nx \l__spath_tmpa_tl
  {
    {\fp_to_dim:n
      {
      (1 - #1)^3 * \tl_item:nn {#2} {2} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {5} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {8} + (#1)^3 * \tl_item:nn {#2} {11}
    }}
    {\fp_to_dim:n
    {
      (1 - #1)^3 * \tl_item:nn {#2} {3} + 3 * (1 - #1)^2 * (#1) * \tl_item:nn {#2} {6} + 3 * (1 - #1) * (#1)^2 * \tl_item:nn {#2} {9} + (#1)^3 * \tl_item:nn {#2} {12}
    }}
  }
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetoa_tl
  \tl_put_right:Nx \l__spath_tmpa_tl
  {
    {\fp_to_dim:n
    {
      (1 - #1)^2 * \tl_item:nn {#2} {5} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {8} + (#1)^2 * \tl_item:nn {#2} {11}
    }}
    {\fp_to_dim:n
    {
      (1 - #1)^2 * \tl_item:nn {#2} {6} + 2 * (1 - #1) * (#1) * \tl_item:nn {#2} {9} + (#1)^2 * \tl_item:nn {#2} {12}
    }}
  }
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curvetob_tl
  \tl_put_right:Nx \l__spath_tmpa_tl
  {
    {\fp_to_dim:n
    {
      (1 - #1) * \tl_item:nn {#2} {8} + (#1) * \tl_item:nn {#2} {11}
    }}
    {\fp_to_dim:n
    {
      (1 - #1) * \tl_item:nn {#2} {9} + (#1) * \tl_item:nn {#2} {12}
    }}
  }
  \tl_put_right:NV \l__spath_tmpa_tl \g__spath_curveto_tl
  \tl_put_right:Nx \l__spath_tmpa_tl {
    {\tl_item:nn {#2} {11}}
    {\tl_item:nn {#2} {12}}
  }
  \tl_gset_eq:NN \l__spath_smuggle_tl \l__spath_tmpa_tl
  \group_end:
  \tl_set_eq:NN #4 \l__spath_smuggle_tl
}

\cs_generate_variant:Nn \spath_split_curve:nnNN {nVNN, VVNN}
%% 
%% Copyright (C) 2011 by Andrew Stacey <stacey@math.ntnu.no>
%% 
%% This work may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License (LPPL), either
%% version 1.3c of this license or (at your option) any later
%% version.  The latest version of this license is in the file:
%% 
%% http://www.latex-project.org/lppl.txt
%% 
%% This work is "maintained" (as per LPPL maintenance status) by
%% Andrew Stacey.
%% 
%% This work consists of the files  spath3.dtx
%%                                  calligraphy_doc.tex
%%                                  knot_doc.tex
%% and the derived files            spath3.ins,
%%                                  spath3.pdf,
%%                                  spath3.sty,
%%                                  tikzlibrarycalligraphy.code.tex
%%                                  tikzlibraryknots.code.tex
%%                                  calligraphy_doc.pdf
%%                                  knots_doc.pdf
%%                                  README.txt
%% 
%%
%% End of file `spath3.sty'.