%%
%% This is file `tikzlibraryspath3.code.tex',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% spath3_code.dtx  (with options: `tikzspath3')
%% ----------------------------------------------------------------
%% spath3 --- Functions for manipulating PGF soft paths
%% E-mail: Andrew Stacey <loopspace@mathforge.org>
%% Released under the LaTeX Project Public License v1.3c or later
%% See http://www.latex-project.org/lppl.txt
%% ----------------------------------------------------------------
%% 
\RequirePackage{spath3}
\RequirePackage{expl3}
\ExplSyntaxOn

\tl_new:N \l__tikzspath_tmpa_tl
\tl_new:N \l__tikzspath_tmpb_tl
\tl_new:N \l__tikzspath_tmpc_tl
\tl_new:N \l__tikzspath_tmpd_tl
\tl_new:N \l__tikzspath_tmpe_tl
\tl_new:N \l__tikzspath_tmpf_tl

\int_new:N \l__tikzspath_tmpa_int
\seq_new:N \l__tikzspath_tmpa_seq
\seq_new:N \l__tikzspath_tmpb_seq
\seq_new:N \l__tikzspath_tmpc_seq
\seq_new:N \l__tikzspath_tmpd_seq

\tl_new:N \l__tikzspath_current_tl
\tl_new:N \l__tikzspath_reverse_tl
\tl_new:N \l__tikzspath_prefix_tl
\tl_new:N \l__tikzspath_suffix_tl
\tl_new:N \g__tikzspath_smuggle_tl
\tl_new:N \g__tikzspath_output_tl
\tl_new:N \l__tikzspath_check_tl
\clist_new:N \g__tikzspath_output_clist
\seq_new:N \g__tikzspath_tmpa_seq
\seq_new:N \g__tikzspath_tmpb_seq
\seq_new:N \g__tikzspath_output_seq
\bool_new:N \l__tikzspath_draft_bool
\msg_new:nnn { spath3 } { missing soft path }
{ Soft~ path~ #1~ doesn't~ exist~ \msg_line_context:}
\msg_new:nnnn { spath3 } { empty soft path }
{ Soft~ path~ #1~ is~ empty~ \msg_line_context:}
{If~ it~ was~ defined~ inside~ a~ group,~ try~ using~ "save~ global". }
\msg_new:nnn { spath3 } { load intersections }
{ You~ need~ to~ load~ the~ "intersections"~ library~
  to~ work~ with~ intersections }
\tl_set:Nn \l__tikzspath_prefix_tl {tikz@intersect@path@name@}
\tl_set:Nn \l__tikzspath_suffix_tl {}
\tl_new:N \g__tikzspath_tikzfinish_tl
\tl_new:N \l__tikzspath_tikzfinish_outside_tl
\cs_new_protected_nopar:Npn \spath_at_end_of_path:
{
  \tl_use:N \g__tikzspath_tikzfinish_tl
  \tl_gclear:N \g__tikzspath_tikzfinish_tl
}
\tl_put_right:Nn \tikz@finish {\spath_at_end_of_path:}

\tikzset{
  every~ scope/.append~ style={
    execute~ at~ begin~ scope={
      \tl_set_eq:NN \l__tikzspath_tikzfinish_outside_tl \g__tikzspath_tikzfinish_tl
    },
    execute~ at~ end~ scope={
      \tl_use:N \g__tikzspath_tikzfinish_tl
      \tl_gclear:N \g__tikzspath_tikzfinish_tl
      \tl_gset_eq:NN \g__tikzspath_tikzfinish_tl \l__tikzspath_tikzfinish_outside_tl
    },
  },
}
\tl_new:N \l__tikzspath_tikzpath_finish_tl

\cs_new_protected_nopar:Npn \__tikzspath_at_end_of_path_construction:
{
  \tl_use:N \l__tikzspath_tikzpath_finish_tl
  \tl_clear:N \l__tikzspath_tikzpath_finish_tl
}

\tl_put_left:Nn \tikz@finish {\__tikzspath_at_end_of_path_construction:}
\cs_new_protected_nopar:Npn \spath_save_path:Nn #1#2
{
  \tl_if_empty:NF \g__tikzspath_tikzfinish_tl
  {
    \tl_use:N \g__tikzspath_tikzfinish_tl
  }
  \tl_gput_right:Nn \g__tikzspath_tikzfinish_tl
  {
    \tl_clear_new:N #1
    \tl_set:Nn #1 {#2}
  }
}
\cs_generate_variant:Nn \spath_save_path:Nn {cn, NV, cV}

\cs_new_protected_nopar:Npn \spath_gsave_path:Nn #1#2
{
  \tl_gput_right:Nn \g__tikzspath_tikzfinish_tl
  {
    \tl_gclear_new:N #1
    \tl_gset:Nn #1 {#2}
  }
}
\cs_generate_variant:Nn \spath_gsave_path:Nn {cn, NV, cV}
\cs_new_protected_nopar:Npn \__tikzspath_process_tikz_point:Nn #1#2
{
  \group_begin:
  \use:c {tikz@scan@one@point} \use:n #2 \scan_stop:
  \tl_gset:Nx \g__tikzspath_output_tl
  {
    { \dim_use:c {pgf@x} }
    { \dim_use:c {pgf@y} }
  }
  \group_end:
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_set_eq:NN \__tikzspath_tikzset:n \tikzset
\cs_generate_variant:Nn \__tikzspath_tikzset:n {V, v}
\cs_new_protected_nopar:Npn \__tikzspath_check_path:nnn #1#2#3
{
  \tl_set:Nn \l__tikzspath_check_tl {#3}
  \tl_if_exist:cTF {\__tikzspath_path_name:n {#2}}
  {
    \tl_if_empty:cTF {\__tikzspath_path_name:n {#2}}
    {
      \msg_warning:nnn { spath3 } { empty soft path } { #2 }
    }
    {
      \tl_set:Nn \l__tikzspath_check_tl {
        #1 {\__tikzspath_path_name:n {#2}}
      }
    }
  }
  {
    \msg_warning:nnx { spath3 } { missing soft path } { #2 }
  }
  \tl_use:N \l__tikzspath_check_tl
}
\cs_new_protected_nopar:Npn \__tikzspath_check_two_paths:nnnn #1#2#3#4
{
  \__tikzspath_check_path:nnn {
    \__tikzspath_check_path:nnn {#1}{#2}{#4}
  }{#3}{#4}
}
\cs_new_protected_nopar:Npn \__tikzspath_check_three_paths:nnnnn #1#2#3#4#5
{
  \__tikzspath_check_path:nnn {
    \__tikzspath_check_path:nnn {
      \__tikzspath_check_path:nnn {#1}{#2}{#5}
    }{#3}{#5}
  }{#4}{#5}
}
\cs_generate_variant:Nn \__tikzspath_check_path:nnn {nVn}
\cs_generate_variant:Nn \__tikzspath_check_two_paths:nnnn {nnVn}
\cs_new_protected_nopar:Npn \__tikzspath_maybe_current_path:nn #1#2
{
  \tl_if_eq:nnT {#2} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#2}}
  }
  #1 {#2}
}
\cs_new_protected_nopar:Npn \__tikzspath_maybe_current_path_reuse:nnn #1#2#3
{
  \bool_set_true:N \l_spath_movetorelevant_bool
  \tl_if_eq:nnT {#2} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#2}}
  }
  #1 {#2} #3
  \tl_if_eq:nnT {#2} {current}
  {
    \tl_if_empty:cF {\__tikzspath_path_name:n {#2}}
    {
      \spath_set_current_path:c {\__tikzspath_path_name:n {#2}}
      \spath_set_tikz_data:v {\__tikzspath_path_name:n {#2}}
    }
  }
}
\cs_new_protected_nopar:Npn \__tikzspath_maybe_current_two_paths_reuse_both:nnnn #1#2#3#4
{
  \bool_set_true:N \l_spath_movetorelevant_bool
  \tl_if_eq:nnT {#2} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#2}}
  }
  \tl_if_eq:nnT {#3} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#3}}
  }
  #1 {#2} {#3} #4
  \tl_if_eq:nnT {#2} {current}
  {
    \tl_if_empty:cF {\__tikzspath_path_name:n {#2}}
    {
      \spath_set_current_path:c {\__tikzspath_path_name:n {#2}}
      \spath_set_tikz_data:v {\__tikzspath_path_name:n {#2}}
    }
  }
  \tl_if_eq:nnT {#3} {current}
  {
    \tl_if_empty:cF {\__tikzspath_path_name:n {#3}}
    {
      \spath_set_current_path:c {\__tikzspath_path_name:n {#3}}
      \spath_set_tikz_data:v {\__tikzspath_path_name:n {#3}}
    }
  }
}
\cs_new_protected_nopar:Npn \__tikzspath_maybe_current_two_paths_reuse_first:nnnn #1#2#3#4
{
  \bool_set_true:N \l_spath_movetorelevant_bool
  \tl_if_eq:nnT {#2} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#2}}
  }
  \tl_if_eq:nnT {#3} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#3}}
  }
  #1 {#2} {#3} #4
  \tl_if_eq:nnT {#2} {current}
  {
    \tl_if_empty:cF {\__tikzspath_path_name:n {#2}}
    {
      \spath_set_current_path:c {\__tikzspath_path_name:n {#2}}
      \spath_set_tikz_data:v {\__tikzspath_path_name:n {#2}}
    }
  }
}
\cs_new_protected_nopar:Npn \__tikzspath_maybe_current_two_paths_reuse_second:nnnn #1#2#3#4
{
  \bool_set_true:N \l_spath_movetorelevant_bool
  \tl_if_eq:nnT {#2} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#2}}
  }
  \tl_if_eq:nnT {#3} {current}
  {
    \spath_get_current_path:c {\__tikzspath_path_name:n {#3}}
  }
  #1 {#2} {#3} #4
  \tl_if_eq:nnT {#3} {current}
  {
    \tl_if_empty:cF {\__tikzspath_path_name:n {#3}}
    {
      \spath_set_current_path:c {\__tikzspath_path_name:n {#3}}
      \spath_set_tikz_data:v {\__tikzspath_path_name:n {#3}}
    }
  }
}
\cs_generate_variant:Nn \__tikzspath_maybe_current_path:nn {nV}
\cs_generate_variant:Nn \__tikzspath_maybe_current_path_reuse:nnn {nVn}
\cs_new_protected_nopar:Npn \__tikzspath_seq_from_foreach:Nnn #1#2#3
{
  \group_begin:
  \seq_gclear:N \g__tikzspath_output_seq

  \tl_if_empty:nTF {#3}
  {
    \int_step_inline:nnnn {1}{1} {#2}
    {
      \seq_gput_right:Nn \g__tikzspath_output_seq {##1}
    }
  }
  {
    \foreach \l__tikzspath_tmpa_tl in {#3}
    {
      \int_compare:nTF { \l__tikzspath_tmpa_tl > 0 }
      {
        \seq_gput_right:NV \g__tikzspath_output_seq \l__tikzspath_tmpa_tl
      }
      {
        \seq_gput_right:Nx \g__tikzspath_output_seq
        {\int_eval:n {#2 - \l__tikzspath_tmpa_tl}}
      }
    }
    \seq_gsort:Nn \g__tikzspath_output_seq
    {
      \int_compare:nNnTF {##1} < {##2}
      { \sort_return_same: }
      { \sort_return_swapped: }
    }
  }
  \group_end:
  \seq_set_eq:NN #1 \g__tikzspath_output_seq
  \seq_gclear:N \g__tikzspath_output_seq
}
\cs_generate_variant:Nn \__tikzspath_seq_from_foreach:Nnn {NVV, NVn}
\cs_new:Npn \__tikzspath_path_name:n #1
{
  \tl_use:N \l__tikzspath_prefix_tl
  #1
  \tl_use:N \l__tikzspath_suffix_tl
}
\cs_generate_variant:Nn \__tikzspath_path_name:n {V}
\bool_new:N \l__tikzspath_reverse_bool
\bool_new:N \l__tikzspath_weld_bool
\bool_new:N \l__tikzspath_move_bool
\bool_new:N \l__tikzspath_global_bool
\bool_new:N \l__tikzspath_current_transformation_bool
\tl_new:N \l__tikzspath_joinpath_tl
\tl_new:N \l__tikzspath_transformation_tl

\cs_new_protected_nopar:Npn \__tikzspath_set_bool:Nn #1#2
{
  \tl_if_eq:nnTF {#2}{false}
  {
    \bool_set_false:N #1
  }
  {
    \bool_set_true:N #1
  }
}
\tikzset {
  spath/join/.is~ family,
  spath/join/.cd,
  reverse/.code = {
    \__tikzspath_set_bool:Nn \l__tikzspath_reverse_bool {#1}
  },
  reverse/.default = true,
  weld/.code = {
    \__tikzspath_set_bool:Nn \l__tikzspath_weld_bool {#1}
  },
  weld/.default = true,
  no~ weld/.code = {
    \__tikzspath_set_bool:Nn \l__tikzspath_weld_bool {#1}
    \bool_set:Nn \l__tikzspath_weld_bool {! \l__tikzspath_weld_bool}
  },
  no~ weld/.default = true,
  move/.code = {
    \__tikzspath_set_bool:Nn \l__tikzspath_move_bool {#1}
  },
  move/.default = true,
  no~ move/.code = {
    \__tikzspath_set_bool:Nn \l__tikzspath_move_bool {#1}
    \bool_set:Nn \l__tikzspath_move_bool {! \l__tikzspath_move_bool}
  },
  no~ move/.default = true,
  global/.code = {
    \__tikzspath_set_bool:Nn \l__tikzspath_global_bool {#1}
  },
  global/.default = true,
  use~ current~ transformation/.code={
    \__tikzspath_set_bool:Nn \l__tikzspath_current_transformation_bool {#1}
  },
  use~ current~ transformation/.default = true,
  transform/.store~in=\l__tikzspath_transformation_tl,
  .unknown/.code = {
    \tl_set_eq:NN \l__tikzspath_joinpath_tl \pgfkeyscurrentname
  }
}
\cs_set_eq:NN \getComponentOf \clist_item:Nn
\cs_new_protected_nopar:Npn \__tikzspath_use_path:n #1
{
  \tl_set:Nn \l__tikzspath_joinpath_tl {#1}
  \spath_get_current_path:N \l__tikzspath_current_tl

  \bool_if:NT \l__tikzspath_reverse_bool
  {
    \spath_reverse:N \l__tikzspath_joinpath_tl
  }

  \bool_if:NT \l__tikzspath_current_transformation_bool
  {
    \pgfgettransform \l__tikzspath_tmpa_tl
    \spath_transform:NV
    \l__tikzspath_joinpath_tl
    \l__tikzspath_tmpa_tl
  }

  \tl_if_empty:NF \l__tikzspath_transformation_tl
  {
    \group_begin:
    \pgftransformreset
    \__tikzspath_tikzset:V \l__tikzspath_transformation_tl
    \pgfgettransform \l__tikzspath_tmpa_tl
    \tl_gset:Nn \g__tikzspath_smuggle_tl
    {
      \spath_transform:Nnnnnnn
      \l__tikzspath_joinpath_tl
    }
    \tl_gput_right:NV \g__tikzspath_smuggle_tl \l__tikzspath_tmpa_tl
    \group_end:
    \tl_use:N \g__tikzspath_smuggle_tl
  }

  \bool_if:NT \l__tikzspath_move_bool
  {
    \tl_if_empty:NTF \l__tikzspath_current_tl
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl { {0pt} {0pt} }
    }
    {
      \spath_finalpoint:NV
      \l__tikzspath_tmpc_tl
      \l__tikzspath_current_tl
    }
    \spath_translate_to:NV \l__tikzspath_joinpath_tl \l__tikzspath_tmpc_tl
  }

  \tl_if_empty:NTF \l__tikzspath_current_tl
  {
    \tl_if_empty:NTF \l__tikzspath_joinpath_tl
    {
      \tl_set_eq:NN \l__tikzspath_current_tl \c_spath_moveto_tl
      \tl_put_right:Nn \l__tikzspath_current_tl {{0pt}{0pt}}
    }
    {
      \tl_set_eq:NN \l__tikzspath_current_tl \l__tikzspath_joinpath_tl
    }
  }
  {

    \tl_clear:N \l__tikzspath_tmpa_tl
    \tl_set:Nn \l__tikzspath_tmpa_tl {spath_}

    \tl_put_right:Nn \l__tikzspath_tmpa_tl {append}

    \bool_if:NT \l__tikzspath_weld_bool
    {
      \tl_put_right:Nn \l__tikzspath_tmpa_tl {_no_move}
      \spath_numberofcomponents:NV \l__tikzspath_tmpa_int \l__tikzspath_joinpath_tl
      \int_compare:nT {\l__tikzspath_tmpa_int == 1}
      {
        \bool_set_false:N \l_spath_movetorelevant_bool
      }
    }
    \tl_put_right:Nn \l__tikzspath_tmpa_tl {:NV}

    \use:c {\tl_use:N \l__tikzspath_tmpa_tl }
    \l__tikzspath_current_tl
    \l__tikzspath_joinpath_tl
  }

  \spath_set_current_path:N \l__tikzspath_current_tl
  \spath_set_tikz_data:V \l__tikzspath_joinpath_tl
}
\cs_generate_variant:Nn \__tikzspath_use_path:n {V, v}
\cs_new_protected_nopar:Npn \__tikzspath_join_with:Nn #1#2
{
  \tl_set:Nn \l__tikzspath_joinpath_tl {#2}

  \bool_if:NT \l__tikzspath_reverse_bool
  {
    \spath_reverse:N \l__tikzspath_joinpath_tl
  }

  \tl_if_empty:NF \l__tikzspath_transformation_tl
  {
    \group_begin:
    \pgftransformreset
    \__tikzspath_tikzset:V \l__tikzspath_transformation_tl
    \pgfgettransform \l__tikzspath_tmpa_tl
    \tl_gset:Nn \g__tikzspath_smuggle_tl
    {
      \spath_transform:Nnnnnnn
      \l__tikzspath_joinpath_tl
    }
    \tl_gput_right:NV \g__tikzspath_smuggle_tl \l__tikzspath_tmpa_tl
    \group_end:
    \tl_use:N \g__tikzspath_smuggle_tl
  }

  \bool_if:NT \l__tikzspath_move_bool
  {
    \spath_finalpoint:NV
    \l__tikzspath_tmpc_tl
    #1
    \spath_translate_to:NV \l__tikzspath_joinpath_tl \l__tikzspath_tmpc_tl
  }

  \tl_clear:N \l__tikzspath_tmpa_tl
  \tl_set:Nn \l__tikzspath_tmpa_tl {spath_}

  \bool_if:NT \l__tikzspath_global_bool
  {
    \tl_put_right:Nn \l__tikzspath_tmpa_tl {g}
  }

  \tl_put_right:Nn \l__tikzspath_tmpa_tl {append}

  \bool_if:NT \l__tikzspath_weld_bool
  {
    \tl_put_right:Nn \l__tikzspath_tmpa_tl {_no_move}
  }
  \tl_put_right:Nn \l__tikzspath_tmpa_tl {:NV}

  \cs_if_exist:cF {\tl_use:N \l__tikzspath_tmpa_tl}
  {
    \tl_show:N \l__tikzspath_tmpa_tl
  }

  \use:c {\tl_use:N \l__tikzspath_tmpa_tl } #1
  \l__tikzspath_joinpath_tl
}
\cs_generate_variant:Nn \__tikzspath_join_with:Nn {cv, cn}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_with_aux:nnn #1#2#3
{
  \group_begin:
  \tl_set:Nn \l__tikzspath_tmpc_tl {#1}
  \tl_if_empty:nT {#3}
  {
    \spath_spot_weld_components:N \l__tikzspath_tmpc_tl
  }

  \spath_numberofcomponents:NV \l__tikzspath_tmpa_int \l__tikzspath_tmpc_tl
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpb_seq \l__tikzspath_tmpa_int {#3}

  \spath_components_to_seq:NV \l__tikzspath_tmpa_seq \l__tikzspath_tmpc_tl

  \seq_pop_left:NN \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_tl
  \seq_pop_left:NN \l__tikzspath_tmpb_seq \l__tikzspath_tmpb_tl

  \seq_map_indexed_inline:Nn \l__tikzspath_tmpa_seq
  {
    \int_compare:nTF
    {
      ##1 == \l__tikzspath_tmpb_tl
    }
    {
      \seq_pop_left:NNF \l__tikzspath_tmpb_seq \l__tikzspath_tmpb_tl
      {
        \tl_set:Nn \l__tikzspath_tmpb_tl {-1}
      }
      \spath_splice_between:Nnn \l__tikzspath_tmpa_tl {#2} {##2}
    }
    {
      \tl_put_right:Nn \l__tikzspath_tmpa_tl {##2}
    }
  }
  \tl_gset_eq:NN \g__tikzspath_output_tl \l__tikzspath_tmpa_tl
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_with:Nnnn #1#2#3#4
{
  \__tikzspath_join_components_with_aux:nnn {#2}{#3}{#4}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_join_components_with:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_with:Nnn #1#2#3
{
  \__tikzspath_join_components_with:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_join_components_with:Nnn {cvV}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components_with:Nnnn #1#2#3#4
{
  \__tikzspath_join_components_with_aux:nnn {#2}{#3}{#4}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components_with:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components_with:Nnn #1#2#3
{
  \__tikzspath_gjoin_components_with:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components_with:Nnn {cvV}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_upright_with_aux:nnn #1#2#3
{
  \group_begin:
  \tl_set:Nn \l__tikzspath_tmpc_tl {#1}
  \tl_if_empty:nT {#3}
  {
    \spath_spot_weld_components:N \l__tikzspath_tmpc_tl
  }

  \spath_numberofcomponents:NV \l__tikzspath_tmpa_int \l__tikzspath_tmpc_tl
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpb_seq \l__tikzspath_tmpa_int {#3}

  \spath_components_to_seq:NV \l__tikzspath_tmpa_seq \l__tikzspath_tmpc_tl

  \seq_pop_left:NN \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_tl
  \seq_pop_left:NN \l__tikzspath_tmpb_seq \l__tikzspath_tmpb_tl

  \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
  \spath_transform:NVnnnnnn \l__tikzspath_tmpd_tl \l__tikzspath_tmpc_tl {1}{0}{0}{-1}{0pt}{0pt}

  \seq_map_indexed_inline:Nn \l__tikzspath_tmpa_seq
  {
    \int_compare:nTF
    {
      ##1 == \l__tikzspath_tmpb_tl
    }
    {
      \seq_pop_left:NNF \l__tikzspath_tmpb_seq \l__tikzspath_tmpb_tl
      {
        \tl_set:Nn \l__tikzspath_tmpb_tl {-1}
      }

      \spath_finalpoint:NV \l__tikzspath_tmpe_tl \l__tikzspath_tmpa_tl
      \spath_initialpoint:Nn \l__tikzspath_tmpf_tl {##2}

      \dim_compare:nTF
      {
        \tl_item:Nn \l__tikzspath_tmpe_tl {1}
        >
        \tl_item:Nn \l__tikzspath_tmpf_tl {1}
      }
      {
        \spath_splice_between:NVn
        \l__tikzspath_tmpa_tl
        \l__tikzspath_tmpd_tl
        {##2}
      }
      {
        \spath_splice_between:NVn
        \l__tikzspath_tmpa_tl
        \l__tikzspath_tmpc_tl
        {##2}
      }
    }
    {
      \tl_put_right:Nn \l__tikzspath_tmpa_tl {##2}
    }
  }
  \tl_gset_eq:NN \g__tikzspath_output_tl \l__tikzspath_tmpa_tl
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_upright_with:Nnnn #1#2#3#4
{
  \__tikzspath_join_components_upright_with_aux:nnn {#2}{#3}{#4}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_join_components_upright_with:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_upright_with:Nnn #1#2#3
{
  \__tikzspath_join_components_upright_with:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_join_components_upright_with:Nnn {cvV}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components_upright_with:Nnnn #1#2#3#4
{
  \__tikzspath_join_components_upright_with_aux:nnn {#2}{#3}{#4}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components_upright_with:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components_upright_with:Nnn #1#2#3
{
  \__tikzspath_gjoin_components_upright_with:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components_upright_with:Nnn {cvV}
\cs_new_protected_nopar:Npn \__tikzspath_get_components_aux:n #1
{
  \clist_gclear_new:N \g__tikzspath_output_clist
  \spath_components_to_seq:Nn \l__tikzspath_tmpa_seq {#1}

  \seq_map_inline:Nn \l__tikzspath_tmpa_seq
  {
    \spath_anonymous:N \l__tikzspath_tmpa_tl
    \tl_new:c {\__tikzspath_path_name:V \l__tikzspath_tmpa_tl}
    \tl_set:cn {\__tikzspath_path_name:V \l__tikzspath_tmpa_tl} {##1}
    \clist_gput_right:NV \g__tikzspath_output_clist \l__tikzspath_tmpa_tl
  }
}
\cs_new_protected_nopar:Npn \__tikzspath_get_components:Nn #1#2
{
  \clist_clear_new:N #1
  \__tikzspath_get_components_aux:n {#2}
  \clist_set_eq:NN #1 \g__tikzspath_output_clist
  \clist_gclear:N \g__tikzspath_output_clist
}
\cs_generate_variant:Nn \__tikzspath_get_components:Nn {NV, Nv}
\cs_new_protected_nopar:Npn \__tikzspath_gget_components:Nn #1#2
{
  \clist_gclear_new:N #1
  \__tikzspath_get_components_aux:n {#2}
  \clist_gset_eq:NN #1 \g__tikzspath_output_clist
  \clist_gclear:N \g__tikzspath_output_clist
}
\cs_generate_variant:Nn \__tikzspath_gget_components:Nn {NV, Nv}
\cs_new_protected_nopar:Npn \__tikzspath_render_components:nn #1#2
{
  \group_begin:
  \spath_components_to_seq:Nn \l__tikzspath_tmpa_seq {#2}
  \seq_map_indexed_inline:Nn \l__tikzspath_tmpa_seq
  {
    \spath_tikz_path:nn
    {
      every~ spath~ component/.try,
      spath ~component~ ##1/.try,
      spath ~component/.try={##1},
      every~ #1~ component/.try,
      #1 ~component~ ##1/.try,
      #1 ~component/.try={##1},
    }
    {
      ##2
    }
  }
  \group_end:
}
\cs_generate_variant:Nn \__tikzspath_render_components:nn {nv}
\cs_new_protected_nopar:Npn \__tikzspath_insert_gaps_after_components_aux:nnn #1#2#3
{
  \group_begin:
  \spath_numberofcomponents:Nn \l__tikzspath_tmpa_int {#1}
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_int {#3}

  \tl_if_empty:nT {#3}
  {
    \seq_pop_right:NN \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_tl
  }

  \seq_clear:N \l__tikzspath_tmpb_seq
  \seq_map_inline:Nn \l__tikzspath_tmpa_seq {
    \seq_put_right:Nx
    \l__tikzspath_tmpb_seq
    {\int_eval:n
      {
        \int_mod:nn { ##1 }{ \l__tikzspath_tmpa_int } + 1
      }
    }
  }

  \spath_components_to_seq:Nn \l__tikzspath_tmpc_seq {#1}

  \seq_clear:N \l__tikzspath_tmpd_seq
  \seq_map_indexed_inline:Nn \l__tikzspath_tmpc_seq
  {
    \tl_set:Nn \l__tikzspath_tmpa_tl {##2}
    \seq_if_in:NnT \l__tikzspath_tmpa_seq {##1}
    {
      \spath_shorten_at_end:Nn \l__tikzspath_tmpa_tl {(#2)/2}
    }
    \seq_if_in:NnT \l__tikzspath_tmpb_seq {##1}
    {
      \spath_shorten_at_start:Nn \l__tikzspath_tmpa_tl {(#2)/2}
    }
    \seq_put_right:NV \l__tikzspath_tmpd_seq \l__tikzspath_tmpa_tl
  }
  \tl_gset:Nx \g__tikzspath_output_tl {\seq_use:Nn \l__tikzspath_tmpd_seq {} }
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_insert_gaps_after_components:Nnnn #1#2#3#4
{
  \__tikzspath_insert_gaps_after_components_aux:nnn {#2}{#3}{#4}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_insert_gaps_after_components:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_insert_gaps_after_components:Nnn #1#2#3
{
  \__tikzspath_insert_gaps_after_components:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_insert_gaps_after_components:Nnn {cnn, cVV}
\cs_new_protected_nopar:Npn \__tikzspath_ginsert_gaps_after_components:Nnnn #1#2#3#4
{
  \__tikzspath_insert_gaps_after_components_aux:nnn {#2}{#3}{#4}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_ginsert_gaps_after_components:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_ginsert_gaps_after_components:Nnn #1#2#3
{
  \__tikzspath_ginsert_gaps_after_components:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_ginsert_gaps_after_components:Nnn {cnn, cVV}
\cs_new_protected_nopar:Npn \__tikzspath_insert_gaps_after_segments_aux:nnn #1#2#3
{
  \group_begin:
  \spath_reallength:Nn \l__tikzspath_tmpa_int {#1}
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_int {#3}

  \tl_if_empty:nT {#3}
  {
    \seq_pop_right:NN \l__tikzspath_tmpb_seq \l__tikzspath_tmpa_tl
  }

  \seq_clear:N \l__tikzspath_tmpb_seq
  \seq_map_inline:Nn \l__tikzspath_tmpa_seq {
    \seq_put_right:Nx
    \l__tikzspath_tmpb_seq
    {\int_eval:n
      {
        \int_mod:nn { ##1 }{ \l__tikzspath_tmpa_int } + 1
      }
    }
  }

  \spath_segments_to_seq:Nn \l__tikzspath_tmpc_seq {#1}

  \seq_clear:N \l__tikzspath_tmpd_seq
  \seq_map_indexed_inline:Nn \l__tikzspath_tmpc_seq
  {
    \tl_set:Nn \l__tikzspath_tmpa_tl {##2}
    \seq_if_in:NnT \l__tikzspath_tmpa_seq {##1}
    {
      \spath_shorten_at_end:Nn \l__tikzspath_tmpa_tl {(#2)/2}
    }
    \seq_if_in:NnT \l__tikzspath_tmpb_seq {##1}
    {
      \spath_shorten_at_start:Nn \l__tikzspath_tmpa_tl {(#2)/2}
    }
    \seq_put_right:NV \l__tikzspath_tmpd_seq \l__tikzspath_tmpa_tl
  }
  \tl_gset:Nx \g__tikzspath_output_tl {\seq_use:Nn \l__tikzspath_tmpd_seq {} }
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_insert_gaps_after_segments:Nnnn #1#2#3#4
{
  \__tikzspath_insert_gaps_after_segments_aux:nnn {#2}{#3}{#4}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_insert_gaps_after_segments:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_insert_gaps_after_segments:Nnn #1#2#3
{
  \__tikzspath_insert_gaps_after_segments:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_insert_gaps_after_segments:Nnn {cnn, cVV}
\cs_new_protected_nopar:Npn \__tikzspath_ginsert_gaps_after_segments:Nnnn #1#2#3#4
{
  \__tikzspath_insert_gaps_after_segments_aux:nnn {#2}{#3}{#4}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_ginsert_gaps_after_segments:Nnnn {NVnn}
\cs_new_protected_nopar:Npn \__tikzspath_ginsert_gaps_after_segments:Nnn #1#2#3
{
  \__tikzspath_ginsert_gaps_after_segments:NVnn #1#1{#2}{#3}
}
\cs_generate_variant:Nn \__tikzspath_ginsert_gaps_after_segments:Nnn {cnn, cVV}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_aux:nn #1#2
{
  \group_begin:

  \tl_set:Nn \l__tikzspath_tmpa_tl {#1}
  \spath_numberofcomponents:NV \l__tikzspath_tmpa_int \l__tikzspath_tmpa_tl
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_int {#2}

  \seq_reverse:N \l__tikzspath_tmpa_seq

  \seq_map_inline:Nn \l__tikzspath_tmpa_seq
  {
    \spath_join_component:Nn \l__tikzspath_tmpa_tl {##1}
  }
  \tl_gset_eq:NN \g__tikzspath_output_tl \l__tikzspath_tmpa_tl
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_join_components:Nnn #1#2#3
{
  \__tikzspath_join_components_aux:nn {#2}{#3}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_join_components:Nnn {NVn}
\cs_new_protected_nopar:Npn \__tikzspath_join_components:Nn #1#2
{
  \__tikzspath_join_components:NVn #1#1{#2}
}
\cs_generate_variant:Nn \__tikzspath_join_components:Nn {cn}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components:Nnn #1#2#3
{
  \__tikzspath_join_components_aux:nn {#2}{#3}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components:Nnn {NVn}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components:Nn #1#2
{
  \__tikzspath_gjoin_components:NVn #1#1{#2}
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components:Nn {cn}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_with_bezier_aux:nn #1#2
{
  \group_begin:
  \tl_set:Nn \l__tikzspath_tmpc_tl {#1}
  \tl_if_empty:nT {#2}
  {
    \spath_spot_weld_components:N \l__tikzspath_tmpc_tl
  }

  \spath_numberofcomponents:NV \l__tikzspath_tmpa_int \l__tikzspath_tmpc_tl
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpb_seq \l__tikzspath_tmpa_int {#2}

  \spath_components_to_seq:NV \l__tikzspath_tmpa_seq \l__tikzspath_tmpc_tl

  \seq_pop_left:NN \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_tl
  \seq_pop_left:NN \l__tikzspath_tmpb_seq \l__tikzspath_tmpb_tl

  \seq_map_indexed_inline:Nn \l__tikzspath_tmpa_seq
  {
    \int_compare:nTF
    {
      ##1 == \l__tikzspath_tmpb_tl
    }
    {
      \seq_pop_left:NNF \l__tikzspath_tmpb_seq \l__tikzspath_tmpb_tl
      {
        \tl_set:Nn \l__tikzspath_tmpb_tl {-1}
      }
      \spath_curve_between:Nn \l__tikzspath_tmpa_tl {##2}
    }
    {
      \tl_put_right:Nn \l__tikzspath_tmpa_tl {##2}
    }
  }
  \tl_gset_eq:NN \g__tikzspath_output_tl \l__tikzspath_tmpa_tl
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_with_bezier:Nnn #1#2#3
{
  \__tikzspath_join_components_with_bezier_aux:nn {#2}{#3}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_join_components_with_bezier:Nnn {NVn}
\cs_new_protected_nopar:Npn \__tikzspath_join_components_with_bezier:Nn #1#2
{
  \__tikzspath_join_components_with_bezier:NVn #1#1{#2}
}
\cs_generate_variant:Nn \__tikzspath_join_components_with_bezier:Nn {cV}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components_with_bezier:Nnn #1#2#3
{
  \__tikzspath_join_components_with_bezier_aux:nn {#2}{#3}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components_with_bezier:Nnn {NVn}
\cs_new_protected_nopar:Npn \__tikzspath_gjoin_components_with_bezier:Nn #1#2
{
  \__tikzspath_gjoin_components_with_bezier:NVn #1#1{#2}
}
\cs_generate_variant:Nn \__tikzspath_gjoin_components_with_bezier:Nn {cV}
\cs_new_protected_nopar:Npn \__tikzspath_remove_components_aux:nn #1#2
{
  \group_begin:

  \spath_numberofcomponents:Nn \l__tikzspath_tmpa_int {#1}
  \__tikzspath_seq_from_foreach:NVn \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_int {#2}

  \spath_components_to_seq:Nn \l__tikzspath_tmpb_seq {#1}

  \seq_pop_left:NNF \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_tl
  {
    \tl_clear:N \l__tikzspath_tmpa_tl
  }

  \seq_clear:N \l__tikzspath_tmpc_seq
  \seq_map_indexed_inline:Nn \l__tikzspath_tmpb_seq
  {
    \tl_set:Nn \l__tikzspath_tmpb_tl {##1}
    \tl_if_eq:NNTF \l__tikzspath_tmpb_tl \l__tikzspath_tmpa_tl
    {
      \seq_pop_left:NNF \l__tikzspath_tmpa_seq \l__tikzspath_tmpa_tl
      {
        \tl_clear:N \l__tikzspath_tmpa_tl
      }
    }
    {
      \seq_put_right:Nn \l__tikzspath_tmpc_seq {##2}
    }
  }

  \tl_gset:Nx \g__tikzspath_output_tl {\seq_use:Nn \l__tikzspath_tmpc_seq {} }
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_remove_components:Nnn #1#2#3
{
  \__tikzspath_remove_components_aux:nn {#2}{#3}
  \tl_set_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_remove_components:Nnn {NVn}
\cs_new_protected_nopar:Npn \__tikzspath_remove_components:Nn #1#2
{
  \__tikzspath_remove_components:NVn #1#1{#2}
}
\cs_generate_variant:Nn \__tikzspath_remove_components:Nn {cn}
\cs_new_protected_nopar:Npn \__tikzspath_gremove_components:Nnn #1#2#3
{
  \__tikzspath_remove_components_aux:nn {#2}{#3}
  \tl_gset_eq:NN #1 \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_gremove_components:Nnn {NVn}
\cs_new_protected_nopar:Npn \__tikzspath_gremove_components:Nn #1#2
{
  \__tikzspath_gremove_components:NVn #1#1{#2}
}
\cs_generate_variant:Nn \__tikzspath_gremove_components:Nn {cn}
\cs_new_protected_nopar:Npn \__tikzspath_transform_to_aux:nn #1#2
{
  \group_begin:
  \spath_reallength:Nn \l__tikzspath_tmpa_int {#2}

  \tl_set:Nx \l__tikzspath_tmpb_tl
  {\fp_to_decimal:n {(#1) * (\l__tikzspath_tmpa_int)}}
  \spath_transformation_at:NnV \l__tikzspath_tmpc_tl {#2} \l__tikzspath_tmpb_tl
  \tl_gset_eq:NN \g__tikzspath_output_tl \l__tikzspath_tmpc_tl
  \group_end:
}
\cs_new_protected_nopar:Npn \__tikzspath_transform_to:nn #1#2
{
  \__tikzspath_transform_to_aux:nn {#1}{#2}
  \exp_last_unbraced:NV \pgfsettransformentries \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_transform_to:nn {nv}
\cs_new_protected_nopar:Npn \__tikzspath_transform_upright_to:nn #1#2
{
  \__tikzspath_transform_to_aux:nn {#1}{#2}
  \fp_compare:nT { \tl_item:Nn \g__tikzspath_output_tl {4} < 0}
  {
    \tl_gset:Nx \g__tikzspath_output_tl
    {
      { \fp_eval:n { - (\tl_item:Nn \g__tikzspath_output_tl {1})} }
      { \fp_eval:n { - (\tl_item:Nn \g__tikzspath_output_tl {2})} }
      { \fp_eval:n { - (\tl_item:Nn \g__tikzspath_output_tl {3})} }
      { \fp_eval:n { - (\tl_item:Nn \g__tikzspath_output_tl {4})} }
      { \tl_item:Nn \g__tikzspath_output_tl {5} }
      { \tl_item:Nn \g__tikzspath_output_tl {6} }
    }
  }
  \exp_last_unbraced:NV \pgfsettransformentries \g__tikzspath_output_tl
  \tl_gclear:N \g__tikzspath_output_tl
}
\cs_generate_variant:Nn \__tikzspath_transform_upright_to:nn {nv}
\tikzset{
  spath/.is~family,
  spath/.cd,
  set~ prefix/.store~ in=\l__tikzspath_prefix_tl,
  prefix/.is~choice,
  prefix/default/.style={
    /tikz/spath/set~ prefix=tikz@intersect@path@name@
  },
  set~ suffix/.store~ in=\l__tikzspath_suffix_tl,
  suffix/.is~choice,
  suffix/default/.style={
    /tikz/spath/set~ suffix={}
  },
  set~ name/.style={
    /tikz/spath/prefix=#1,
    /tikz/spath/suffix=#1
  },
  at~ end~ path~ construction/.code={
    \tl_put_right:Nn \l__tikzspath_tikzpath_finish_tl {#1}
  },
  save/.code={
    \tikz@addmode{
      \spath_get_current_path:N \l__tikzspath_tmpa_tl
      \spath_bake_round:NV \l__tikzspath_tmpa_tl \l__tikzspath_tmpa_tl
      \spath_bake_shorten:NV \l__tikzspath_tmpa_tl \l__tikzspath_tmpa_tl
      \spath_save_path:cV {\__tikzspath_path_name:n {#1}}
      \l__tikzspath_tmpa_tl
    }
  },
  save~ global/.code={
    \tikz@addmode{
      \spath_get_current_path:N \l__tikzspath_tmpa_tl
      \spath_bake_round:NV \l__tikzspath_tmpa_tl \l__tikzspath_tmpa_tl
      \spath_bake_shorten:NV \l__tikzspath_tmpa_tl \l__tikzspath_tmpa_tl
      \spath_gsave_path:cV {\__tikzspath_path_name:n {#1}}
      \l__tikzspath_tmpa_tl
    }
  },
  clone/.code~ 2~ args={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \tl_clear_new:c {\__tikzspath_path_name:n {#1}}
        \tl_set_eq:cc {\__tikzspath_path_name:n {#1}}
      }
    }
    {#2}{}
  },
  clone~ global/.code~ 2~ args={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \tl_gclear_new:c {\__tikzspath_path_name:n {#1}}
        \tl_gset_eq:cc {\__tikzspath_path_name:n {#1}}
      }
    }
    {#2}{}
  },
  save~ to~ aux/.code={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \spath_save_to_aux:c
      }
    }
    {#1}
    {}
  },
  export~ to~ svg/.code={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \spath_export_to_svg:nv {#1}
      }
    }
    {#1}
    {}
  },
  use/.code={
    \bool_set_false:N \l__tikzspath_reverse_bool
    \bool_set_false:N \l__tikzspath_weld_bool
    \bool_set_false:N \l__tikzspath_move_bool
    \bool_set_false:N \l__tikzspath_current_transformation_bool
    \bool_set_true:N \l_spath_movetorelevant_bool
    \tl_clear:N \l__tikzspath_joinpath_tl
    \tl_clear:N \l__tikzspath_transformation_tl
    \tikzset{
      spath/join/.cd,
      #1
    }

    \__tikzspath_check_path:nVn
    {
      \__tikzspath_use_path:v
    } \l__tikzspath_joinpath_tl {}

  },
  restore/.style={/tikz/spath/use={#1}},
  restore~ reverse/.style={/tikz/spath/use={reverse, #1}},
  append/.style={/tikz/spath/use={move, weld, #1}},
  append~ no~ move/.style={/tikz/spath/use={weld, #1}},
  append~ reverse/.style={/tikz/spath/use={move, weld, reverse, #1}},
  append~ reverse~ no~ move/.style={/tikz/spath/use={weld, reverse, #1}},
  insert/.style={/tikz/spath/use={#1}},
  insert~ reverse/.style={/tikz/spath/use={reverse, #1}},
  show~current~path/.code={
    \tikz@addmode{
      \pgfsyssoftpath@getcurrentpath\l__tikzspath_tmpa_tl
      \iow_term:n {---~ current~ soft~ path~ ---}
      \spath_show:V \l__tikzspath_tmpa_tl
    }
  },
  show/.code={
    \__tikzspath_check_path:nnn {
      \iow_term:n {---~ soft~ path~ #1~ ---}
      \spath_show:v
    } {#1} {}
  },
  join~ with/.code~ 2~ args={
    \bool_set_false:N \l__tikzspath_reverse_bool
    \bool_set_false:N \l__tikzspath_weld_bool
    \bool_set_false:N \l__tikzspath_move_bool
    \bool_set_false:N \l__tikzspath_global_bool
    \bool_set_false:N \l__tikzspath_current_transformation_bool
    \tl_clear:N \l__tikzspath_joinpath_tl
    \tl_clear:N \l__tikzspath_transformation_tl
    \tikzset{
      spath/join/.cd,
      #2
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnVn
      {
        \__tikzspath_join_with:cv
      }
    } {#1} { \l__tikzspath_joinpath_tl {} }
  },
  spot~ weld/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_spot_weld_components:c
      }
    } {#1} { {} }
  },
  spot~ weld~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_spot_gweld_components:c
      }
    } {#1} { {} }
  },
  reverse/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_reverse:c
      }
    } {#1} { {} }
  },
  reverse~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_greverse:c
      }
    } {#1} { {} }
  },
  span/.code ~n~ args={3}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_process_tikz_point:Nn \l__tikzspath_tmpa_tl {#2}
        \__tikzspath_process_tikz_point:Nn \l__tikzspath_tmpb_tl {#3}
        \spath_span:cVV
      }
    } {#1} { {} \l__tikzspath_tmpa_tl \l__tikzspath_tmpb_tl }
  },
  span~ global/.code ~n~ args={3}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_process_tikz_point:Nn \l__tikzspath_tmpa_tl {#2}
        \__tikzspath_process_tikz_point:Nn \l__tikzspath_tmpb_tl {#3}
        \spath_span:cVV
      }
    } {#1} { {} \l__tikzspath_tmpa_tl \l__tikzspath_tmpb_tl }
  },
  to/.style={
    to~path={
      [
        spath/span={#1}{(\tikztostart)}{(\tikztotarget)},
        spath/use={#1,weld},
      ]
      \tikztonodes
    }
  },
  splice/.code ~n~ args={3}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_three_paths:nnnnn
      {
        \spath_splice_between:cvv
      }
    } {#1} { {#2} {#3} {} }
  },
  splice~ global/.code ~n~ args={3}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_three_paths:nnnnn
      {
        \spath_gsplice_between:cvv
      }
    } {#1} { {#2} {#3} {} }
  },
  join~ components~ with/.code~2~args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnVn
      {
        \__tikzspath_join_components_with:cvV
      }
    } {#1} { \l__tikzspath_tmpc_tl {} \l__tikzspath_tmpd_tl  }
  },
  join~ components~ globally~ with/.code~2~args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnVn
      {
        \__tikzspath_gjoin_components_with:cvV
      }
    } {#1} { \l__tikzspath_tmpc_tl {} \l__tikzspath_tmpd_tl  }
  },
  join~ components~ upright~ with/.code~2~args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnVn
      {
        \__tikzspath_join_components_upright_with:cvV
      }
    } {#1} { \l__tikzspath_tmpc_tl {} \l__tikzspath_tmpd_tl  }
  },
  join~ components~ globally~ upright~ with/.code~2~args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnVn
      {
        \__tikzspath_gjoin_components_upright_with:cvV
      }
    } {#1} { \l__tikzspath_tmpc_tl {} \l__tikzspath_tmpd_tl  }
  },
  join~ components~ with~ bezier/.code={
    \tl_if_head_is_group:nTF {#1}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#1} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#1} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#1}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nVn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_join_components_with_bezier:cV
      }
    } \l__tikzspath_tmpc_tl { {} \l__tikzspath_tmpd_tl }
  },
  join~ components~ globally~ with~ bezier/.code~2~args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_gjoin_components_with_bezier:cn
      }
    } {#1} { {} {#2} }
  },
  close/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_close:c
      }
    } {#1} { {} }
  },
  close~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gclose:c
      }
    } {#1} { {} }
  },
  open/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_open:c
      }
    } {#1} { {} }
  },
  open~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gopen:c
      }
    } {#1} { {} }
  },
  adjust~ and~ close/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_adjust_close:c
      }
    } {#1} { {} }
  },
  adjust~ and~ close~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_adjust_gclose:c
      }
    } {#1} { {} }
  },
  close~ with/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnnn
      {
        \spath_close_with:cv
      }
    } {#1} { {#2} {} }
  },
  close~ globally~ with/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_two_paths:nnnn
      {
        \spath_gclose_with:cv
      }
    } {#1} { {#2} {} }
  },
  close~ with~ curve/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_close_with_curve:c
      }
    } {#1} { {} }
  },
  close~ globally~ with~ curve/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gclose_with_curve:c
      }
    } {#1} { {} }
  },
  shorten~ at~ end/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_shorten_at_end:cn
      }
    } {#1} { {} {#2} }
  },
  shorten~ at~ start/.code~ 2~ args ={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_shorten_at_start:cn
      }
    } {#1} { {} {#2} }
  },
  shorten~ at~ both~ ends/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_shorten_at_both_ends:cn
      }
    } {#1} { {} {#2} }
  },
  shorten~ globally~ at~ end/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gshorten_at_end:cn
      }
    } {#1} { {} {#2} }
  },
  shorten~ globally~ at~ start/.code~ 2~ args ={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gshorten_at_start:cn
      }
    } {#1} { {} {#2} }
  },
  shorten~ globally~ at~ both~ ends/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gshorten_at_both_ends:cn
      }
    } {#1} { {} {#2} }
  },
  split~ at/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_split_at_normalised:cn
      }
    } {#1} { {} {#2} }
  },
  split~ globally~ at/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gsplit_at_normalised:cn
      }
    } {#1} { {} {#2} }
  },
  split~ at~ into/.code~ n~ args={4}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_split_at_normalised:ccvn {\__tikzspath_path_name:n {#1}}
        {\__tikzspath_path_name:n {#2}}
      }
    } {#3} { {} {#4} }
  },
  split~ globally~ at~ into/.code~ n~ args={4}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gsplit_at_normalised:ccvn {\__tikzspath_path_name:n {#1}}
        {\__tikzspath_path_name:n {#2}}
      }
    } {#3} { {} {#4} }
  },
  split~ at~ keep~ start/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_split_at_normalised_keep_start:cn
      }
    } {#1} { {} {#2} }
  },
  split~ globally~ at~ keep~ start/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gsplit_at_normalised_keep_start:cn
      }
    } {#1} { {} {#2} }
  },
  split~ at~ keep~ end/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_split_at_normalised_keep_end:cn
      }
    } {#1} { {} {#2} }
  },
  split~ globally~ at~ keep~ end/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gsplit_at_normalised_keep_end:cn
      }
    } {#1} { {} {#2} }
  },
  split~ at~ keep~ middle/.style~ n~ args={3}{
    /tikz/spath/split~ at~ keep~ start={#1}{#3},
    /tikz/spath/split~ at~ keep~ end={#1}{(#2)/(#3)},
  },
  split~ globally~ at~ keep~ middle/.style~ n~ args={3}{
    /tikz/spath/split~ globally~ at~ keep~ start={#1}{#3},
    /tikz/spath/split~ globally~ at~ keep~ end={#1}{(#2)/(#3)},
  },
  translate/.code~ n~ args={3}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_translate:cnn
      }
    } {#1} { {} {#2}{#3} }
  },
  translate~ globally/.code~ n~ args={3}{
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gtranslate:cnn
      }
    } {#1} { {} {#2}{#3} }
  },
  normalise/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_normalise:c
      }
    } {#1} { {} }
  },
  normalise~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gnormalise:c
      }
    } {#1} { {} }
  },
  transform/.code~ 2~ args={
    \group_begin:
    \pgftransformreset
    \tikzset{#2}
    \pgfgettransform \l__tikzspath_tmpa_tl
    \tl_gset_eq:NN \g__tikzspath_smuggle_tl \l__tikzspath_tmpa_tl
    \group_end:

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_transform:cV
      }
    } {#1} { {} \g__tikzspath_smuggle_tl }
  },
  transform~globally/.code~ 2~ args={
    \group_begin:
    \pgftransformreset
    \tikzset{#2}
    \pgfgettransform \l__tikzspath_tmpa_tl
    \tl_gset_eq:NN \g__tikzspath_smuggle_tl \l__tikzspath_tmpa_tl
    \group_end:

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gtransform:cV
      }
    } {#1} { {} \g__tikzspath_smuggle_tl }
  },
  split~ at~ intersections~ with/.code~ 2~ args={
    \tl_if_exist:cTF
    {
      tikz@library@intersections@loaded
    }
    {
      \__tikzspath_maybe_current_two_paths_reuse_first:nnnn
      {
        \__tikzspath_check_two_paths:nnnn
        {
          \spath_split_path_at_intersections:cv
        }
      } {#1} {#2} { {} }
    }
    {
      \msg_warning:nn { spath3 } { load intersections }
    }
  },
  split~ globally~ at~ intersections~ with/.code~ n~ args={2}{
    \tl_if_exist:cTF
    {
      tikz@library@intersections@loaded
    }
    {
      \__tikzspath_maybe_current_two_paths_reuse_first:nnnn
      {
        \__tikzspath_check_two_paths:nnnn
        {
          \spath_gsplit_path_at_intersections:cv
        }
      } {#1} {#2} { {} }
    }
    {
      \msg_warning:nn { spath3 } { load intersections }
    }
  },
  split~ at~ intersections/.code~ n~ args={2}{
    \tl_if_exist:cTF
    {
      tikz@library@intersections@loaded
    }
    {
      \__tikzspath_maybe_current_two_paths_reuse_both:nnnn
      {
        \__tikzspath_check_two_paths:nnnn
        {
          \spath_split_at_intersections:cc
        }
      } {#1} {#2} { {} }
    }
    {
      \msg_warning:nn { spath3 } { load intersections }
    }
  },
  split~ globally~ at~ intersections/.code~ n~ args={2}{
    \tl_if_exist:cTF
    {
      tikz@library@intersections@loaded
    }
    {
      \__tikzspath_maybe_current_two_paths_reuse_both:nnnn
      {
        \__tikzspath_check_two_paths:nnnn
        {
          \spath_gsplit_at_intersections:cc
        }
      } {#1} {#2} { {} }
    }
    {
      \msg_warning:nn { spath3 } { load intersections }
    }
  },
  split~ at~ self~ intersections/.code={
    \tl_if_exist:cTF
    {
      tikz@library@intersections@loaded
    }
    {
      \__tikzspath_maybe_current_path_reuse:nnn
      {
        \__tikzspath_check_path:nnn
        {
          \spath_split_at_self_intersections:c
        }
      } {#1} { {} }
    }
    {
      \msg_warning:nn { spath3 } { load intersections }
    }
  },
  split~ globally~ at~ self~ intersections/.code={
    \tl_if_exist:cTF
    {
      tikz@library@intersections@loaded
    }
    {
      \__tikzspath_maybe_current_path_reuse:nnn
      {
        \__tikzspath_check_path:nnn
        {
          \spath_gsplit_at_self_intersections:c
        }
      } {#1} { {} }
    }
    {
      \msg_warning:nn { spath3 } { load intersections }
    }
  },
  get~ components~ of/.code~ 2~ args={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \__tikzspath_get_components:Nv #2
      }
    }
    {#1}
    {}
  },
  get~ components~ of~ globally/.code~ 2~ args={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \__tikzspath_gget_components:Nv #2
      }
    }
    {#1}
    {}
  },
  render~ components/.code={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \__tikzspath_render_components:nv {#1}
      }
    }
    {#1}
    {}
  },
  insert~ gaps~ after~ components/.code~ 2~ args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_insert_gaps_after_components:cVV
      }
    } {#1} { {} \l__tikzspath_tmpc_tl \l__tikzspath_tmpd_tl  }
  },
  insert~ gaps~ globally~ after~ components/.code~ 2~ args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_ginsert_gaps_after_components:cVV
      }
    } {#1} { {} \l__tikzspath_tmpc_tl \l__tikzspath_tmpd_tl  }
  },
  insert~ gaps~ after~ segments/.code~ 2~ args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_insert_gaps_after_segments:cVV
      }
    } {#1} { {} \l__tikzspath_tmpc_tl \l__tikzspath_tmpd_tl  }
  },
  insert~ gaps~ globally~ after~ segments/.code~ 2~ args={
    \tl_if_head_is_group:nTF {#2}
    {
      \tl_set:Nx \l__tikzspath_tmpc_tl { \tl_item:nn {#2} {1} }
      \tl_set:Nx \l__tikzspath_tmpd_tl { \tl_item:nn {#2} {2} }
    }
    {
      \tl_set:Nn \l__tikzspath_tmpc_tl {#2}
      \tl_clear:N \l__tikzspath_tmpd_tl
    }

    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_ginsert_gaps_after_segments:cVV
      }
    } {#1} { {} \l__tikzspath_tmpc_tl \l__tikzspath_tmpd_tl  }
  },
  join~ components/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_join_components:cn
      }
    } {#1} { {} {#2} }
  },
  join~ components~ globally/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_gjoin_components:cn
      }
    } {#1} { {} {#2} }
  },
  remove~ empty~ components/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_remove_empty_components:c
      }
    } {#1} { {} }
  },
  remove~ empty~ components~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_gremove_empty_components:c
      }
    } {#1} { {} }
  },
  replace~ lines/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_replace_lines:c
      }
    } {#1} { {} }
  },
  replace~ lines~ globally/.code={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \spath_greplace_lines:c
      }
    } {#1} { {} }
  },
  remove~ components/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_remove_components:cn
      }
    } {#1} { {} {#2} }
  },
  remove~ components~ globally/.code~ 2~ args={
    \__tikzspath_maybe_current_path_reuse:nnn
    {
      \__tikzspath_check_path:nnn
      {
        \__tikzspath_gremove_components:cn
      }
    } {#1} { {} {#2} }
  },
  draft~ mode/.code={
    \__tikzspath_set_bool:Nn \l__tikzspath_draft_bool {#1}
  },
  maybe~ spot~ weld/.code={
    \bool_if:NF \l__tikzspath_draft_bool
    {
      \__tikzspath_maybe_current_path_reuse:nnn
      {
        \__tikzspath_check_path:nnn
        {
          \spath_spot_weld_components:c
        }
      } {#1} { {} }
    }
  },
  maybe~ spot~ weld~ globally/.code={
    \bool_if:NF \l__tikzspath_draft_bool
    {
      \__tikzspath_maybe_current_path_reuse:nnn
      {
        \__tikzspath_check_path:nnn
        {
          \spath_spot_gweld_components:c
        }
      } {#1} { {} }
    }
  },
  transform~ to/.code~ 2~ args={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \__tikzspath_transform_to:nv {#2}
      }
    }
    {#1}
    {
      \pgfsettransformentries {1}{0}{0}{1}{0pt}{0pt}
    }
  },
  upright~ transform~ to/.code~ 2~ args={
    \__tikzspath_maybe_current_path:nn
    {
      \__tikzspath_check_path:nnn {
        \__tikzspath_transform_upright_to:nv {#2}
      }
    }
    {#1}
    {
      \pgfsettransformentries {1}{0}{0}{1}{0pt}{0pt}
    }
  },
  knot/.style~ n~ args={3}{
    /tikz/spath/split~ at~ self~ intersections=#1,
    /tikz/spath/remove~ empty~ components=#1,
    /tikz/spath/insert~ gaps~ after~ components={#1}{#2}{#3},
    /tikz/spath/maybe~ spot~ weld=#1,
    /tikz/spath/render~ components=#1
  },
  global~ knot/.style~ n~ args={3}{
    /tikz/spath/split~ globally~ at~ self~ intersections=#1,
    /tikz/spath/remove~ empty~ components~ globally=#1,
    /tikz/spath/insert~ gaps~ globally ~after~ components={#1}{#2}{#3},
    /tikz/spath/maybe~ spot~ weld~ globally=#1,
    /tikz/spath/render~ components=#1
  },
  arrow~ shortening/.code={
    \__tikzspath_set_bool:Nn \l_spath_arrow_shortening_bool {#1}
  },
  show/.default=current,
  spot~ weld/.default=current,
  spot~ weld~ globally/.default=current,
  reverse/.default=current,
  reverse~ globally/.default=current,
  close/.default=current,
  close~ globally/.default=current,
  open/.default=current,
  open~ globally/.default=current,
  adjust~ and~ close/.default=current,
  adjust~ and~ close~ globally/.default=current,
  close~ with~ curve/.default=current,
  close~ globally~ with~ curve/.default=current,
  remove~ empty~ components/.default=current,
  remove~ empty~ components~ globally/.default=current,
  replace~ lines/.default=current,
  replace~ lines~ globally/.default=current,
  maybe~ spot~ weld/.default=current,
  maybe~ spot~ weld~ globally/.default=current,
}
\cs_new_protected_nopar:Npn \__tikzspath_get_point_at:nn #1#2
{
  \group_begin:
  \spath_reallength:Nn \l__tikzspath_tmpa_int {#2}
  \tl_set:Nx \l__tikzspath_tmpb_tl
  {\fp_to_decimal:n {(#1) * (\l__tikzspath_tmpa_int)}}
  \spath_point_at:NnV \l__tikzspath_tmpc_tl {#2} \l__tikzspath_tmpb_tl

  \tl_clear:N \l__tikzspath_tmpd_tl
  \tl_put_right:Nn \l__tikzspath_tmpd_tl {\pgf@x=}
  \tl_put_right:Nx \l__tikzspath_tmpd_tl {\tl_item:Nn \l__tikzspath_tmpc_tl {1}}
  \tl_put_right:Nn \l__tikzspath_tmpd_tl {\relax}
  \tl_put_right:Nn \l__tikzspath_tmpd_tl {\pgf@y=}
  \tl_put_right:Nx \l__tikzspath_tmpd_tl {\tl_item:Nn \l__tikzspath_tmpc_tl {2}}
  \tl_put_right:Nn \l__tikzspath_tmpd_tl {\relax}

  \tl_gset_eq:NN \g__tikzspath_output_tl \l__tikzspath_tmpd_tl
  \group_end:
 }
\cs_generate_variant:Nn \__tikzspath_get_point_at:nn {VV, Vn, Vv}

\tikzdeclarecoordinatesystem{spath}{%
  \group_begin:
  \tl_set:Nn \l__tikzspath_tmpa_tl {#1}
  \tl_trim_spaces:N \l__tikzspath_tmpa_tl

  \seq_set_split:NnV \l__tikzspath_tmpa_seq {~} \l__tikzspath_tmpa_tl
  \seq_pop_right:NN \l__tikzspath_tmpa_seq \l__tikzspath_tmpb_tl

  \tl_set:Nx \l__tikzspath_tmpa_tl { \seq_use:Nn \l__tikzspath_tmpa_seq {~} }

  \__tikzspath_maybe_current_path:nV
  {
    \__tikzspath_check_path:nnn {
      \__tikzspath_get_point_at:Vv \l__tikzspath_tmpb_tl
    }
  }
  \l__tikzspath_tmpa_tl
  {
    \tl_gset_eq:NN \g__tikzspath_output_tl \pgfpointorigin
  }

  \group_end:
  \use:c {pgf@process}{%
    \tl_use:N \g__tikzspath_output_tl
    \pgftransforminvert
    \use:c {pgf@pos@transform@glob}
  }
  \tl_gclear:N \g__tikzspath_output_tl
}

\ExplSyntaxOff
%% 
%% Copyright (C) 2011-2024 by Andrew Stacey <loopspace@mathforge.org>
%% 
%% This work may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License (LPPL), either
%% version 1.3c of this license or (at your option) any later
%% version.  The latest version of this license is in the file:
%% 
%% http://www.latex-project.org/lppl.txt
%% 
%% This work is "maintained" (as per LPPL maintenance status) by
%% Andrew Stacey.
%% 
%% This work consists of the files  spath3_code.dtx
%%                                  calligraphy_doc.tex
%%                                  knots_doc.tex
%%                                  spath3.tex
%% and the derived files            spath3.ins,
%%                                  spath3_code.pdf,
%%                                  spath3.sty,
%%                                  tikzlibrarycalligraphy.code.tex
%%                                  tikzlibraryknots.code.tex
%%                                  tikzlibraryspath3.code.tex
%%                                  calligraphy.pdf
%%                                  knots.pdf
%%                                  spath3.pdf
%%                                  README.txt
%% 
%%
%% End of file `tikzlibraryspath3.code.tex'.