%% %% This is file `tikzlibraryknots.code.tex', %% generated with the docstrip utility. %% %% The original source files were: %% %% spath3_code.dtx (with options: `knots') %% ---------------------------------------------------------------- %% spath3 --- Functions for manipulating PGF soft paths %% E-mail: loopspace@mathforge.org %% Released under the LaTeX Project Public License v1.3c or later %% See http://www.latex-project.org/lppl.txt %% ---------------------------------------------------------------- %% %% \RequirePackage{spath3} \usetikzlibrary{intersections,spath3} \ExplSyntaxOn \tl_new:N \l__knot_tmpa_tl \tl_new:N \l__knot_tmpb_tl \tl_new:N \l__knot_tmpc_tl \tl_new:N \l__knot_tmpd_tl \tl_new:N \l__knot_tmpg_tl \tl_new:N \l__knot_redraws_tl \tl_new:N \l__knot_clip_width_tl \tl_new:N \l__knot_name_tl \tl_new:N \l__knot_node_tl \tl_new:N \l__knot_aux_tl \tl_new:N \l__knot_auxa_tl \tl_new:N \l__knot_prefix_tl \seq_new:N \l__knot_segments_seq \int_new:N \l__knot_tmpa_int \int_new:N \l__knot_strands_int \int_new:N \g__knot_intersections_int \int_new:N \g__knot_filaments_int \int_new:N \l__knot_component_start_int \fp_new:N \l__knot_tmpa_fp \fp_new:N \l__knot_tmpb_fp \dim_new:N \l__knot_tmpa_dim \dim_new:N \l__knot_tmpb_dim \dim_new:N \l__knot_tolerance_dim \dim_new:N \l__knot_redraw_tolerance_dim \dim_new:N \l__knot_clip_bg_radius_dim \dim_new:N \l__knot_clip_draw_radius_dim \bool_new:N \l__knot_draft_bool \bool_new:N \l__knot_ignore_ends_bool \bool_new:N \l__knot_self_intersections_bool \bool_new:N \l__knot_splits_bool \bool_new:N \l__knot_super_draft_bool \bool_new:N \l__knot_prepend_prev_bool \bool_new:N \l__knot_append_next_bool \bool_new:N \l__knot_skip_bool \bool_new:N \l__knot_save_bool \seq_new:N \g__knot_nodes_seq \bool_set_true:N \l__knot_ignore_ends_bool \tikzset{ spath/prefix/knot/.style={ spath/set~ prefix=knot strand, }, spath/suffix/knot/.style={ spath/set~ suffix={}, }, knot/.code={ \tl_if_eq:nnTF {#1} {none} { \tikz@addmode{\tikz@mode@doublefalse} } { \tikz@addmode{\tikz@mode@doubletrue} \tl_if_eq:nnTF {\pgfkeysnovalue} {#1} { \tikz@addoption{\pgfsetinnerstrokecolor{.}} } { \pgfsetinnerstrokecolor{#1} } \tikz@addoption{ \pgfsetstrokecolor{knotbg} } \tl_set:Nn \tikz@double@setup{ \pgfsetinnerlinewidth{\pgflinewidth} \pgfsetlinewidth{\dim_eval:n {\tl_use:N \l__knot_gap_tl \pgflinewidth}} } } }, knot~ gap/.store~ in=\l__knot_gap_tl, knot~ gap=3, knot~ diagram/.is~family, knot~ diagram/.unknown/.code={ \tl_set_eq:NN \l__knot_tmpa_tl \pgfkeyscurrentname \pgfkeysalso{ /tikz/\l__knot_tmpa_tl=#1 } }, background~ colour/.code={% \colorlet{knotbg}{#1}% }, background~ color/.code={% \colorlet{knotbg}{#1}% }, background~ colour=white, knot~ diagram, name/.store~ in=\l__knot_name_tl, name={knot}, save~ intersections/.is~ choice, save~ intersections/.default=true, save~ intersections/true/.code={ \bool_set_true:N \l__knot_save_bool }, save~ intersections/false/.code={ \bool_set_false:N \l__knot_save_bool }, every~ strand/.style={draw}, ignore~ endpoint~ intersections/.code={ \tl_if_eq:nnTF {#1} {true} { \bool_set_true:N \l__knot_ignore_ends_bool } { \bool_set_false:N \l__knot_ignore_ends_bool } }, ignore~ endpoint~ intersections/.default=true, consider~ self~ intersections/.is~choice, consider~ self~ intersections/true/.code={ \bool_set_true:N \l__knot_self_intersections_bool \bool_set_true:N \l__knot_splits_bool }, consider~ self~ intersections/false/.code={ \bool_set_false:N \l__knot_self_intersections_bool \bool_set_false:N \l__knot_splits_bool }, consider~ self~ intersections/no~ splits/.code={ \bool_set_true:N \l__knot_self_intersections_bool \bool_set_false:N \l__knot_splits_bool }, consider~ self~ intersections/.default={true}, clip~ radius/.code={ \dim_set:Nn \l__knot_clip_bg_radius_dim {#1} \dim_set:Nn \l__knot_clip_draw_radius_dim {#1+2pt} }, clip~ draw~ radius/.code={ \dim_set:Nn \l__knot_clip_draw_radius_dim {#1} }, clip~ background~ radius/.code={ \dim_set:Nn \l__knot_clip_bg_radius_dim {#1} }, clip~ radius=10pt, end~ tolerance/.code={ \dim_set:Nn \l__knot_tolerance_dim {#1} }, end~ tolerance=14pt, clip/.style={ clip }, background~ clip/.style={ clip }, clip~ width/.code={ \tl_set:Nn \l__knot_clip_width_tl {#1} }, clip~ width=3, flip~ crossing/.code={% \tl_clear_new:c {l__knot_crossing_#1} \tl_set:cn {l__knot_crossing_#1} {x} }, ignore~ crossing/.code={% \tl_clear_new:c {l__knot_ignore_crossing_#1} \tl_set:cn {l__knot_ignore_crossing_#1} {x} }, draft~ mode/.is~ choice, draft~ mode/off/.code={% \bool_set_false:N \l__knot_draft_bool \bool_set_false:N \l__knot_super_draft_bool }, draft~ mode/crossings/.code={% \bool_set_true:N \l__knot_draft_bool \bool_set_false:N \l__knot_super_draft_bool }, draft~ mode/strands/.code={% \bool_set_true:N \l__knot_draft_bool \bool_set_true:N \l__knot_super_draft_bool }, draft/.is~ family, draft, crossing~ label/.style={ overlay, fill=white, fill~ opacity=.5, text~ opacity=1, text=blue, pin~ edge={blue,<-} }, strand~ label/.style={ overlay, circle, draw=purple, fill=white, fill~ opacity=.5, text~ opacity=1, text=purple, inner~ sep=0pt }, } \cs_new_nopar:Npn \knot_apply_style:N #1 { \tl_if_exist:NT #1 { \exp_args:NV \tikzset #1 } } \cs_generate_variant:Nn \knot_apply_style:N {c} \NewDocumentCommand \flipcrossings {m} { \tikzset{knot~ diagram/flip~ crossing/.list={#1}}% } \NewDocumentCommand \strand { O{} } { \int_incr:N \l__knot_strands_int \tl_clear_new:c {l__knot_options_strand \int_use:N \l__knot_strands_int} \tl_set:cn {l__knot_options_strand \int_use:N \l__knot_strands_int} {#1} \path[#1,spath/set~ name=knot,spath/save=\int_use:N \l__knot_strands_int] } \NewDocumentEnvironment{knot} { O{} } { \knot_initialise:n {#1} } { \knot_render: } \cs_new_protected_nopar:Npn \knot_initialise:n #1 { \tikzset{knot~ diagram/.cd,every~ knot~ diagram/.try,#1} \int_zero:N \l__knot_strands_int \tl_clear:N \l__knot_redraws_tl \seq_gclear:N \g__knot_nodes_seq } \cs_new_protected_nopar:Npn \knot_render: { \pgfscope \pgftransformreset \dim_set:Nn \l__knot_redraw_tolerance_dim {\fp_to_dim:n { sqrt(2) * max(\l__knot_clip_bg_radius_dim, \l__knot_clip_draw_radius_dim) } } \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_draw_strand:n \bool_if:NF \l__knot_super_draft_bool { \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_draw_labels:n \bool_if:NTF \l__knot_self_intersections_bool { \knot_split_strands: \int_set_eq:NN \l__knot_tmpa_int \g__knot_filaments_int \tl_set:Nn \l__knot_prefix_tl {filament} } { \int_set_eq:NN \l__knot_tmpa_int \l__knot_strands_int \tl_set:Nn \l__knot_prefix_tl {strand} } \int_gzero:N \g__knot_intersections_int \tl_clear:N \l__knot_node_tl \bool_if:NT \l__knot_draft_bool { \tl_set:Nn \l__knot_node_tl { \exp_not:N \node[coordinate, pin={[ node~ contents={\int_use:N \g__knot_intersections_int}, knot~ diagram/draft/crossing~ label, knot~ diagram/draft/crossing~ \int_use:N \g__knot_intersections_int \c_space_tl label/.try ] }] } } \int_step_variable:nnnNn {1} {1} {\l__knot_tmpa_int - 1} \l__knot_tmpa_tl { \int_step_variable:nnnNn {\tl_use:N \l__knot_tmpa_tl + 1} {1} {\l__knot_tmpa_int} \l__knot_tmpb_tl { \knot_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl } } \tl_use:N \l__knot_redraws_tl \seq_use:Nn \g__knot_nodes_seq {} } \endpgfscope } \cs_new_protected_nopar:Npn \knot_draw_strand:n #1 { \pgfscope \group_begin: \spath_bake_round:c {knot strand #1} \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,} \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_strand #1} \tl_put_right:Nn \l__knot_tmpa_tl { , knot~ diagram/only~ when~ rendering/.try, only~ when~ rendering/.try } \spath_tikz_path:Vv \l__knot_tmpa_tl {knot strand #1} \group_end: \endpgfscope } \cs_generate_variant:Nn \tl_put_right:Nn {Nv} \cs_new_protected_nopar:Npn \knot_draw_labels:n #1 { \bool_if:NT \l__knot_draft_bool { \spath_finalpoint:Nv \l__knot_tmpb_tl {knot strand #1} \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}} \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}} \node[ knot~ diagram/draft/strand~label ] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1}; \spath_initialpoint:Nv \l__knot_tmpb_tl {knot strand #1} \dim_set:Nn \l__knot_tmpa_dim {\tl_item:Nn \l__knot_tmpb_tl {1}} \dim_set:Nn \l__knot_tmpb_dim {\tl_item:Nn \l__knot_tmpb_tl {2}} \node[ knot~ diagram/draft/strand~label ] at (\l__knot_tmpa_dim,\l__knot_tmpb_dim) {#1}; } \bool_if:nT { \l__knot_self_intersections_bool && \l__knot_splits_bool } { \tl_clear:N \l__knot_tmpa_tl \spath_initialpoint:Nv \l__knot_tmpa_tl {knot strand #1} \tl_put_left:NV \l__knot_tmpa_tl \c_spath_moveto_tl \spath_segments_to_seq:Nv \l__knot_segments_seq {knot strand #1} \seq_map_function:NN \l__knot_segments_seq \knot_split_self_intersects:N \tl_set_eq:cN {knot strand #1} \l__knot_tmpa_tl } } \cs_new_protected_nopar:Npn \knot_split_self_intersects:N #1 { \tl_set:Nx \l__knot_tmpc_tl {\tl_item:nn {#1} {4}} \tl_case:NnF \l__knot_tmpc_tl { \c_spath_curvetoa_tl { \fp_set:Nn \l__knot_tmpa_fp { (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12}) * (3 * \tl_item:nn {#1} {8} - 3 * \tl_item:nn {#1} {11}) - (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11}) * (3 * \tl_item:nn {#1} {9} - 3 * \tl_item:nn {#1} {12}) } \fp_set:Nn \l__knot_tmpb_fp { (\tl_item:nn {#1} {2} - 3 * \tl_item:nn {#1} {5} + 3 * \tl_item:nn {#1} {8} - \tl_item:nn {#1} {11}) * (3 * \tl_item:nn {#1} {6} - 6 * \tl_item:nn {#1} {9} + 3 * \tl_item:nn {#1} {12}) - (\tl_item:nn {#1} {3} - 3 * \tl_item:nn {#1} {6} + 3 * \tl_item:nn {#1} {9} - \tl_item:nn {#1} {12}) * (3 * \tl_item:nn {#1} {5} - 6 * \tl_item:nn {#1} {8} + 3 * \tl_item:nn {#1} {11}) } \fp_compare:nTF { \l__knot_tmpb_fp != 0 } { \fp_set:Nn \l__knot_tmpa_fp {.5 * \l__knot_tmpa_fp / \l__knot_tmpb_fp} \fp_compare:nTF { 0 < \l__knot_tmpa_fp && \l__knot_tmpa_fp < 1 } { \spath_split_curve:NNnV \l__knot_tmpc_tl \l__knot_tmpd_tl {#1} \l__knot_tmpa_fp \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl} \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl} \tl_set:Nx \l__knot_tmpd_tl {\tl_tail:N \l__knot_tmpd_tl} \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpd_tl } { \tl_set:Nn \l__knot_tmpc_tl {#1} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl } } { \tl_set:Nn \l__knot_tmpc_tl {#1} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl } } \c_spath_lineto_tl { \tl_set:Nn \l__knot_tmpc_tl {#1} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_set:Nx \l__knot_tmpc_tl {\tl_tail:N \l__knot_tmpc_tl} \tl_put_right:NV \l__knot_tmpa_tl \l__knot_tmpc_tl } } { \tl_put_right:Nn \l__knot_tmpa_tl {#1} } } \cs_new_protected_nopar:Npn \knot_intersections:nn #1#2 { \group_begin: \tl_set_eq:NN \l__knot_tmpa_tl \l__knot_prefix_tl \tl_put_right:Nn \l__knot_tmpa_tl {#1} \tl_set_eq:NN \l__knot_tmpb_tl \l__knot_prefix_tl \tl_put_right:Nn \l__knot_tmpb_tl {#2} \tl_set_eq:Nc \l__knot_tmpc_tl {knot \tl_use:N \l__knot_tmpa_tl} \tl_set_eq:Nc \l__knot_tmpd_tl {knot \tl_use:N \l__knot_tmpb_tl} \bool_if:nTF { \l__knot_save_bool && \tl_if_exist_p:c { knot~ intersections~ \tl_use:N \l__knot_name_tl - \tl_use:N \l__knot_tmpa_tl - \tl_use:N \l__knot_tmpb_tl } } { \tl_use:c { knot~ intersections~ \tl_use:N \l__knot_name_tl - \tl_use:N \l__knot_tmpa_tl - \tl_use:N \l__knot_tmpb_tl } } { \pgfintersectionofpaths{\pgfsetpath\l__knot_tmpc_tl}{\pgfsetpath\l__knot_tmpd_tl} } \int_compare:nT {\pgfintersectionsolutions > 0} { \int_step_function:nnnN {1} {1} {\pgfintersectionsolutions} \knot_do_intersection:n } \knot_save_intersections:VV \l__knot_tmpa_tl \l__knot_tmpb_tl \group_end: } \cs_new_protected_nopar:Npn \knot_save_intersections:nn #1#2 { \bool_if:NT \l__knot_save_bool { \tl_clear:N \l__knot_aux_tl \tl_put_right:Nn \l__knot_aux_tl { \def\pgfintersectionsolutions } \tl_put_right:Nx \l__knot_aux_tl { {\int_eval:n {\pgfintersectionsolutions}} } \int_compare:nT {\pgfintersectionsolutions > 0} { \int_step_inline:nnnn {1} {1} {\pgfintersectionsolutions} { \pgfpointintersectionsolution{##1} \dim_set:Nn \l__knot_tmpa_dim {\pgf@x} \dim_set:Nn \l__knot_tmpb_dim {\pgf@y} \tl_put_right:Nn \l__knot_aux_tl { \expandafter\def\csname pgfpoint@intersect@solution@##1\endcsname } \tl_put_right:Nx \l__knot_aux_tl { { \exp_not:N \pgf@x = \dim_use:N \l__knot_tmpa_dim \exp_not:N \relax \exp_not:N \pgf@y = \dim_use:N \l__knot_tmpb_dim \exp_not:N \relax } } } \tl_set:Nn \l__knot_auxa_tl {\expandafter \gdef \csname knot~ intersections~} \tl_put_right:Nx \l__knot_auxa_tl {\tl_use:N \l__knot_name_tl - #1 - #2} \tl_put_right:Nn \l__knot_auxa_tl {\endcsname} \tl_put_right:Nx \l__knot_auxa_tl {{\tl_to_str:N \l__knot_aux_tl}} \protected@write\@auxout{}{\tl_to_str:N \l__knot_auxa_tl} } } } \cs_generate_variant:Nn \knot_save_intersections:nn {VV} \cs_new_protected_nopar:Npn \knot_do_intersection:n #1 { \pgfpointintersectionsolution{#1} \dim_set:Nn \l__knot_tmpa_dim {\pgf@x} \dim_set:Nn \l__knot_tmpb_dim {\pgf@y} \bool_set_false:N \l__knot_skip_bool \bool_if:NT \l__knot_self_intersections_bool { \tl_set:Nn \l__knot_tmpc_tl {knot previous} \tl_put_right:NV \l__knot_tmpc_tl \l__knot_tmpa_tl \tl_set:Nv \l__knot_tmpc_tl \l__knot_tmpc_tl \tl_if_eq:NNT \l__knot_tmpc_tl \l__knot_tmpb_tl { \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpb_tl {final point} { \bool_set_true:N \l__knot_skip_bool } } \tl_set:Nn \l__knot_tmpc_tl {knot previous} \tl_put_right:NV \l__knot_tmpc_tl \l__knot_tmpb_tl \tl_set:Nv \l__knot_tmpc_tl \l__knot_tmpc_tl \tl_if_eq:NNT \l__knot_tmpc_tl \l__knot_tmpa_tl { \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpa_tl {final point} { \bool_set_true:N \l__knot_skip_bool } } } \bool_if:NT \l__knot_ignore_ends_bool { \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpa_tl {initial point} { \bool_set_true:N \l__knot_skip_bool } \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpa_tl {final point} { \bool_set_true:N \l__knot_skip_bool } \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpb_tl {initial point} { \bool_set_true:N \l__knot_skip_bool } \knot_test_endpoint:NVnT \l__knot_tolerance_dim \l__knot_tmpb_tl {final point} { \bool_set_true:N \l__knot_skip_bool } } \bool_if:NF \l__knot_skip_bool { \int_gincr:N \g__knot_intersections_int \bool_if:nF { \tl_if_exist_p:c {l__knot_ignore_crossing_ \int_use:N \g__knot_intersections_int} && ! \tl_if_empty_p:c {l__knot_ignore_crossing_ \int_use:N \g__knot_intersections_int} } { \bool_if:nTF { \tl_if_exist_p:c {l__knot_crossing_ \int_use:N \g__knot_intersections_int} && ! \tl_if_empty_p:c {l__knot_crossing_ \int_use:N \g__knot_intersections_int} } { \tl_set_eq:NN \l__knot_tmpg_tl \l__knot_tmpb_tl } { \tl_set_eq:NN \l__knot_tmpg_tl \l__knot_tmpa_tl } \bool_if:NT \l__knot_self_intersections_bool { \knot_test_endpoint:NVnT \l__knot_redraw_tolerance_dim \l__knot_tmpg_tl {initial point} { \bool_set_true:N \l__knot_prepend_prev_bool } { \bool_set_false:N \l__knot_prepend_prev_bool } \knot_test_endpoint:NVnT \l__knot_redraw_tolerance_dim \l__knot_tmpg_tl {final point} { \bool_set_true:N \l__knot_append_next_bool } { \bool_set_false:N \l__knot_append_next_bool } \bool_if:nT { \l__knot_prepend_prev_bool || \l__knot_append_next_bool } { \tl_clear_new:c {knot \tl_use:N \l__knot_prefix_tl -1} \tl_set_eq:cc {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:N \l__knot_tmpg_tl} \tl_clear_new:c {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1} \tl_set_eq:cc {l__knot_options_ \tl_use:N \l__knot_prefix_tl -1} {l__knot_options_ \tl_use:N \l__knot_tmpg_tl} \bool_if:nT { \l__knot_prepend_prev_bool && \tl_if_exist_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} && !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} } { \spath_prepend_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl}} \bool_if:nT { \l__knot_splits_bool && \tl_if_exist_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} && !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} } { \knot_test_endpoint:NvnT \l__knot_redraw_tolerance_dim {knot previous \tl_use:N \l__knot_tmpg_tl} {initial point} { \spath_prepend_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot previous \tl_use:c {knot previous \tl_use:N \l__knot_tmpg_tl} } } \tl_set_eq:Nc \l__knot_tmpa_tl {knot \tl_use:N \l__knot_prefix_tl -1} } } } \bool_if:nT { \l__knot_append_next_bool && \tl_if_exist_p:c {knot next \tl_use:N \l__knot_tmpg_tl} && !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} } { \spath_append_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl}} \bool_if:nT { \l__knot_splits_bool && \tl_if_exist_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} && !\tl_if_empty_p:c {knot previous \tl_use:N \l__knot_tmpg_tl} } { \knot_test_endpoint:NvnT \l__knot_redraw_tolerance_dim {knot previous \tl_use:N \l__knot_tmpg_tl} {final point} { \spath_append_no_move:cv {knot \tl_use:N \l__knot_prefix_tl -1} {knot \tl_use:c {knot next \tl_use:c {knot next \tl_use:N \l__knot_tmpg_tl} } } } } } \tl_set:Nn \l__knot_tmpg_tl {\tl_use:N \l__knot_prefix_tl -1} } } \pgfscope \group_begin: \tikzset{ knot~ diagram/every~ intersection/.try, every~ intersection/.try, knot~ diagram/intersection~ \int_use:N \g__knot_intersections_int/.try } \knot_draw_crossing:VVV \l__knot_tmpg_tl \l__knot_tmpa_dim \l__knot_tmpb_dim \coordinate (\l__knot_name_tl \c_space_tl \int_use:N \g__knot_intersections_int) at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim); \group_end: \endpgfscope } \tl_if_empty:NF \l__knot_node_tl { \seq_gpush:Nx \g__knot_nodes_seq { \l__knot_node_tl at (\dim_use:N \l__knot_tmpa_dim, \dim_use:N \l__knot_tmpb_dim) {}; } } } } \cs_generate_variant:Nn \knot_intersections:nn {VV} \prg_new_conditional:Npnn \knot_test_endpoint:NN #1#2 {p,T,F,TF} { \dim_compare:nTF { \dim_abs:n { \l__knot_tmpa_dim - \tl_item:Nn #2 {1}} + \dim_abs:n { \l__knot_tmpb_dim - \tl_item:Nn #2 {2}} < #1 } { \prg_return_true: } { \prg_return_false: } } \prg_new_protected_conditional:Npnn \knot_test_endpoint:Nnn #1#2#3 {T,F,TF} { \use:c {spath_#3:Nv} \l__knot_tmpd_tl {knot #2} \knot_test_endpoint:NNTF #1 \l__knot_tmpd_tl { \prg_return_true: } { \prg_return_false: } } \cs_generate_variant:Nn \knot_test_endpoint:NnnT {NVnT,NvnT} \cs_generate_variant:Nn \knot_test_endpoint:NnnF {NVnF,NvnF} \cs_generate_variant:Nn \knot_test_endpoint:NnnTF {NVnTF,NvnTF} \cs_new_protected_nopar:Npn \knot_draw_crossing:nnn #1#2#3 { \group_begin: \pgfscope \path[knot~ diagram/background~ clip] (#2, #3) circle[radius=\l__knot_clip_bg_radius_dim]; \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,} \tl_if_exist:cT {l__knot_options_ #1} { \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_ #1} } \tl_put_right:Nn \l__knot_tmpa_tl { ,knotbg ,line~ width= \tl_use:N \l__knot_clip_width_tl * \pgflinewidth } \spath_tikz_path:Vv \l__knot_tmpa_tl {knot #1} \endpgfscope \pgfscope \path[knot~ diagram/clip] (#2, #3) circle[radius=\l__knot_clip_draw_radius_dim]; \tl_set:Nn \l__knot_tmpa_tl {knot~ diagram/every~ strand/.try,} \tl_if_exist:cT {l__knot_options_ #1} { \tl_put_right:Nv \l__knot_tmpa_tl {l__knot_options_ #1} } \tl_put_right:Nn \l__knot_tmpa_tl { ,knot~ diagram/only~ when~ rendering/.try ,only~ when~ rendering/.try } \spath_tikz_path:Vv \l__knot_tmpa_tl {knot #1} \endpgfscope \group_end: } \cs_generate_variant:Nn \knot_draw_crossing:nnn {nVV, VVV} \cs_new_protected_nopar:Npn \knot_draw_crossing:nn #1#2 { \tikz@scan@one@point\pgfutil@firstofone #2 \relax \knot_draw_crossing:nVV {#1} \pgf@x \pgf@y } \cs_new_protected_nopar:Npn \knot_split_strands: { \int_gzero:N \g__knot_filaments_int \int_step_function:nnnN {1} {1} {\l__knot_strands_int} \knot_split_strand:n \int_step_function:nnnN {1} {1} {\g__knot_filaments_int} \knot_compute_nexts:n } \cs_new_protected_nopar:Npn \knot_compute_nexts:n #1 { \tl_clear_new:c {knot next \tl_use:c {knot previous filament #1}} \tl_set:cn {knot next \tl_use:c {knot previous filament #1}} {filament #1} } \cs_new_protected_nopar:Npn \knot_split_strand:n #1 { \int_set_eq:NN \l__knot_component_start_int \g__knot_filaments_int \int_incr:N \l__knot_component_start_int \tl_set_eq:Nc \l__knot_tmpa_tl {l__knot_options_strand #1} \spath_segments_to_seq:Nv \l__knot_segments_seq {knot strand #1} \seq_map_function:NN \l__knot_segments_seq \knot_save_filament:N } \cs_new_protected_nopar:Npn \knot_save_filament:N #1 { \tl_set:Nx \l__knot_tmpb_tl {\tl_item:nn {#1} {4}} \tl_case:NnF \l__knot_tmpb_tl { \c_spath_moveto_tl { \int_compare:nT {\l__knot_component_start_int < \g__knot_filaments_int} { \int_set_eq:NN \l__knot_component_start_int \g__knot_filaments_int } } \c_spath_lineto_tl { \int_gincr:N \g__knot_filaments_int \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int} \tl_set:cn {knot filament \int_use:N \g__knot_filaments_int} {#1} \tl_clear_new:c {l__knot_options_filament \int_use:N \g__knot_filaments_int} \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int} \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int} { \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}} } } \c_spath_curvetoa_tl { \int_gincr:N \g__knot_filaments_int \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int} \tl_set:cn {knot filament \int_use:N \g__knot_filaments_int} {#1} \tl_clear_new:c {l__knot_options_filament \int_use:N \g__knot_filaments_int} \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int} \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int} { \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}} } } \c_spath_closepath_tl { \int_gincr:N \g__knot_filaments_int \tl_clear_new:c {knot filament \int_use:N \g__knot_filaments_int} \tl_clear:N \l__knot_tmpa_tl \tl_put_right:Nx { \tl_item:nn {#1} {1}\tl_item:nn {#1} {2}\tl_item:nn {#1} {3} } \tl_put_right:NV \l__knot_tmpa_tl \c_spath_lineto_tl \tl_put_right:Nx {\tl_item:nn {#1} {5}\tl_item:nn {#1} {6}} \tl_set:cV {knot filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl \tl_set_eq:cN {l__knot_options_filament \int_use:N \g__knot_filaments_int} \l__knot_tmpa_tl \tl_clear_new:c {knot previous filament \int_use:N \g__knot_filaments_int} \int_compare:nF {\l__knot_component_start_int == \g__knot_filaments_int} { \tl_set:cx {knot previous filament \int_use:N \g__knot_filaments_int} {filament \int_eval:n {\g__knot_filaments_int - 1}} } \tl_set:cx {knot previous filament \int_use:N \l__knot_component_start_int} {filament \int_use:N \g__knot_filaments_int} } } { } } \NewDocumentCommand \redraw { m m } { \tl_put_right:Nn \l__knot_redraws_tl {\knot_draw_crossing:nn} \tl_put_right:Nx \l__knot_redraws_tl { {strand #1} {#2}% {\dim_use:N \pgf@x} {\dim_use:N \pgf@y} } } \ExplSyntaxOff \def\pgf@sh@@knotanchor#1#2{% \anchor{#2 north west}{% \csname pgf@anchor@knot #1@north west\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 north east}{% \csname pgf@anchor@knot #1@north east\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 south west}{% \csname pgf@anchor@knot #1@south west\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 south east}{% \csname pgf@anchor@knot #1@south east\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 north}{% \csname pgf@anchor@knot #1@north\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 east}{% \csname pgf@anchor@knot #1@east\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 west}{% \csname pgf@anchor@knot #1@west\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% \anchor{#2 south}{% \csname pgf@anchor@knot #1@south\endcsname% \pgf@x=#2\pgf@x% \pgf@y=#2\pgf@y% }% } \pgfdeclareshape{knot crossing} { \inheritsavedanchors[from=circle] % this is nearly a circle \inheritanchorborder[from=circle] \inheritanchor[from=circle]{north} \inheritanchor[from=circle]{north west} \inheritanchor[from=circle]{north east} \inheritanchor[from=circle]{center} \inheritanchor[from=circle]{west} \inheritanchor[from=circle]{east} \inheritanchor[from=circle]{mid} \inheritanchor[from=circle]{mid west} \inheritanchor[from=circle]{mid east} \inheritanchor[from=circle]{base} \inheritanchor[from=circle]{base west} \inheritanchor[from=circle]{base east} \inheritanchor[from=circle]{south} \inheritanchor[from=circle]{south west} \inheritanchor[from=circle]{south east} \inheritanchorborder[from=circle] \pgf@sh@@knotanchor{crossing}{2} \pgf@sh@@knotanchor{crossing}{3} \pgf@sh@@knotanchor{crossing}{4} \pgf@sh@@knotanchor{crossing}{8} \pgf@sh@@knotanchor{crossing}{16} \pgf@sh@@knotanchor{crossing}{32} \backgroundpath{ \pgfutil@tempdima=\radius% \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% \ifdim\pgf@xb<\pgf@yb% \advance\pgfutil@tempdima by-\pgf@yb% \else% \advance\pgfutil@tempdima by-\pgf@xb% \fi% } } \pgfdeclareshape{knot over cross} { \inheritsavedanchors[from=rectangle] % this is nearly a circle \inheritanchorborder[from=rectangle] \inheritanchor[from=rectangle]{north} \inheritanchor[from=rectangle]{north west} \inheritanchor[from=rectangle]{north east} \inheritanchor[from=rectangle]{center} \inheritanchor[from=rectangle]{west} \inheritanchor[from=rectangle]{east} \inheritanchor[from=rectangle]{mid} \inheritanchor[from=rectangle]{mid west} \inheritanchor[from=rectangle]{mid east} \inheritanchor[from=rectangle]{base} \inheritanchor[from=rectangle]{base west} \inheritanchor[from=rectangle]{base east} \inheritanchor[from=rectangle]{south} \inheritanchor[from=rectangle]{south west} \inheritanchor[from=rectangle]{south east} \inheritanchorborder[from=rectangle] \backgroundpath{ \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} } \foregroundpath{ \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}} } } \pgfdeclareshape{knot under cross} { \inheritsavedanchors[from=rectangle] % this is nearly a circle \inheritanchorborder[from=rectangle] \inheritanchor[from=rectangle]{north} \inheritanchor[from=rectangle]{north west} \inheritanchor[from=rectangle]{north east} \inheritanchor[from=rectangle]{center} \inheritanchor[from=rectangle]{west} \inheritanchor[from=rectangle]{east} \inheritanchor[from=rectangle]{mid} \inheritanchor[from=rectangle]{mid west} \inheritanchor[from=rectangle]{mid east} \inheritanchor[from=rectangle]{base} \inheritanchor[from=rectangle]{base west} \inheritanchor[from=rectangle]{base east} \inheritanchor[from=rectangle]{south} \inheritanchor[from=rectangle]{south west} \inheritanchor[from=rectangle]{south east} \inheritanchorborder[from=rectangle] \backgroundpath{ \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}} } \foregroundpath{ \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} } } \pgfdeclareshape{knot vert} { \inheritsavedanchors[from=rectangle] % this is nearly a circle \inheritanchorborder[from=rectangle] \inheritanchor[from=rectangle]{north} \inheritanchor[from=rectangle]{north west} \inheritanchor[from=rectangle]{north east} \inheritanchor[from=rectangle]{center} \inheritanchor[from=rectangle]{west} \inheritanchor[from=rectangle]{east} \inheritanchor[from=rectangle]{mid} \inheritanchor[from=rectangle]{mid west} \inheritanchor[from=rectangle]{mid east} \inheritanchor[from=rectangle]{base} \inheritanchor[from=rectangle]{base west} \inheritanchor[from=rectangle]{base east} \inheritanchor[from=rectangle]{south} \inheritanchor[from=rectangle]{south west} \inheritanchor[from=rectangle]{south east} \inheritanchorborder[from=rectangle] \backgroundpath{ \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}} } } \pgfdeclareshape{knot horiz} { \inheritsavedanchors[from=rectangle] % this is nearly a circle \inheritanchorborder[from=rectangle] \inheritanchor[from=rectangle]{north} \inheritanchor[from=rectangle]{north west} \inheritanchor[from=rectangle]{north east} \inheritanchor[from=rectangle]{center} \inheritanchor[from=rectangle]{west} \inheritanchor[from=rectangle]{east} \inheritanchor[from=rectangle]{mid} \inheritanchor[from=rectangle]{mid west} \inheritanchor[from=rectangle]{mid east} \inheritanchor[from=rectangle]{base} \inheritanchor[from=rectangle]{base west} \inheritanchor[from=rectangle]{base east} \inheritanchor[from=rectangle]{south} \inheritanchor[from=rectangle]{south west} \inheritanchor[from=rectangle]{south east} \inheritanchorborder[from=rectangle] \foregroundpath{ \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}} \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}} \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} } } %% %% Copyright (C) 2011-2021 by Andrew Stacey %% %% 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 %% %% %% End of file `tikzlibraryknots.code.tex'.