%% %% This is file `tikzlibraryceltic.code.tex', %% generated with the docstrip utility. %% %% The original source files were: %% %% celtic.dtx (with options: `library') %% ---------------------------------------------------------------- %% celtic --- TikZ library for producing Celtic knots. %% E-mail: loopspace@mathforge.org %% Released under the LaTeX Project Public License v1.3c or later %% See http://www.latex-project.org/lppl.txt %% ---------------------------------------------------------------- %% \usepackage{expl3} \usepackage{xparse} \ExplSyntaxOn \cs_new_nopar:Npn \celtic_shift:n #1 { \use:c{tikz@scan@one@point}\pgftransformshift #1\relax } \int_new:N \l__celtic_max_steps_int \int_new:N \l__celtic_int \int_new:N \l__celtic_flip_int \int_new:N \l__celtic_width_int \int_new:N \l__celtic_height_int \int_new:N \l__celtic_x \int_new:N \l__celtic_y \int_new:N \l__celtic_dx \int_new:N \l__celtic_dy \int_new:N \l__celtic_ox \int_new:N \l__celtic_oy \int_new:N \l__celtic_lout \int_new:N \l__celtic_cross_int \int_new:N \l__celtic_component_int \fp_new:N \l__celtic_clip_fp \fp_new:N \l__celtic_inner_clip_fp \fp_new:N \l__celtic_inner_fp \fp_new:N \l__celtic_outer_fp \seq_new:N \l__celtic_path_seq \seq_new:N \l__celtic_overpath_seq \seq_new:N \l__celtic_component_seq \seq_new:N \l__celtic_crossing_seq \seq_new:N \l__celtic_tmpa_seq \clist_new:N \l__celtic_tmpa_clist \tl_new:N \l__celtic_tmpa_tl \tl_new:N \l__celtic_path_tl \tl_new:N \l__celtic_bar_tl \tl_new:N \l__celtic_active_bar_tl \tl_new:N \l__celtic_start_tl \bool_new:N \l__celtic_bounce_bool \bool_new:N \l__celtic_pbounce_bool \cs_new_nopar:Npn \tl_split_after:Nnn #1#2#3 { \cs_set:Npn \tl_split_aux:nnn ##1#3##2 \q_stop: {#3##2} \tl_set:Nx #1 {\tl_split_aux:nnn #2 \q_stop:} } \cs_generate_variant:Nn \tl_split_after:Nnn {NVn} \cs_new_nopar:Npn \tl_split_before:Nnn #1#2#3 { \cs_set:Npn \tl_split_aux:nnn ##1#3##2 \q_stop: {##1#3} \tl_set:Nx #1 {\tl_split_aux:nnn #2 \q_stop:} } \cs_generate_variant:Nn \tl_split_before:Nnn {NVn} \msg_new:nnnn { celtic } { max~ steps } { Limit~ of~ number~ of~ steps~ exceeded~ \msg_line_context:.} { Paths~ may~ not~ be~ correctly~ constructed.~ Consider~ raising~ the~ limit~ from \int_use:N \l__celtic_max_steps_int.} \tl_const:Nx \c__celtic_colon_tl { \token_to_str:N : } \tl_set:Nn \l__celtic_bar_tl {|} \group_begin: \char_set_catcode_active:N \| \tl_gset:Nn \l__celtic_active_bar_tl {|} \group_end: \cs_generate_variant:Nn \tl_if_single_p:N {c} \cs_generate_variant:Nn \tl_if_single:NTF {cTF} \cs_generate_variant:Nn \tl_if_eq:nnTF {xnTF} \cs_generate_variant:Nn \tl_head:N {c} \cs_generate_variant:Nn \tl_tail:N {c} \cs_generate_variant:Nn \tl_if_eq:nnTF {vnTF} \cs_generate_variant:Nn \tl_if_in:nnTF {nVTF} \int_set:Nn \l__celtic_max_steps_int {20} \fp_set:Nn \l__celtic_inner_fp {1} \fp_set:Nn \l__celtic_outer_fp {2} \cs_new_nopar:Npn \celtic_do_crossing:nnn #1#2#3 { \tl_if_empty:nTF {#1} { \tl_clear:c {crossing used \int_eval:n {#2} - \int_eval:n {#3}} } { \tl_set:cn {crossing \int_eval:n {#2} - \int_eval:n{#3}}{#1} } } \cs_new_nopar:Npn \celtic_maybe_symmetric:nnnn #1#2#3#4 { \tl_if_empty:nTF {#1} { \celtic_do_crossing:nnn {#2}{#3}{#4} } { \celtic_do_crossing:nnn {#2}{#3}{#4} \celtic_do_crossing:nnn {#2}{\l__celtic_width_int - #3}{#4} \celtic_do_crossing:nnn {#2}{#3}{\l__celtic_height_int - #4} \celtic_do_crossing:nnn {#2}{\l__celtic_width_int - #3}{\l__celtic_height_int - #4} } } \cs_new_nopar:Npn \celtic_maybe_xrange:nnnn #1#2#3#4 { \tl_if_in:nVTF {#3} \c__celtic_colon_tl { \celtic_do_xrange:w {#1}{#2}#3\q_stop{#4} } { \celtic_maybe_yrange:nnnn {#1}{#2}{#3}{#4} } } \cs_new_nopar:Npn \celtic_maybe_yrange:nnnn #1#2#3#4 { \tl_if_in:nVTF {#4} \c__celtic_colon_tl { \celtic_do_yrange:w {#1}{#2}{#3}#4\q_stop } { \celtic_maybe_symmetric:nnnn {#1}{#2}{#3}{#4} } } \tl_set:Nx \l_tmpa_tl { \exp_not:N \cs_new_nopar:Npn \exp_not:N \celtic_do_xrange:w ##1##2##3\tl_use:N \c__celtic_colon_tl ##4\exp_not:N \q_stop##5 { \exp_not:N \int_step_inline:nnnn {##3} {2} {##4} { \exp_not:N \celtic_maybe_yrange:nnnn {##1}{##2} {####1}{##5} } } \exp_not:N \cs_new_nopar:Npn \exp_not:N \celtic_do_yrange:w ##1##2##3##4\tl_use:N \c__celtic_colon_tl ##5\exp_not:N \q_stop { \exp_not:N \int_step_inline:nnnn {##4} {2} {##5} { \exp_not:N \celtic_maybe_symmetric:nnnn {##1}{##2}{##3}{####1} } } } \tl_use:N \l_tmpa_tl \cs_new_nopar:Npn \celtic_ignore_crossings:w #1,#2\q_stop { \celtic_maybe_xrange:nnnn {}{}{#1}{#2} } \cs_new_nopar:Npn \celtic_ignore_symmetric_crossings:w #1,#2\q_stop { \celtic_maybe_xrange:nnnn {s}{}{#1}{#2} } \cs_new_nopar:Npn \celtic_set_crossings:w #1,#2,#3\q_stop { \celtic_maybe_xrange:nnnn {}{#3}{#1}{#2} } \cs_new_nopar:Npn \celtic_set_symmetric_crossings:w #1,#2,#3\q_stop { \celtic_maybe_xrange:nnnn {s}{#3}{#1}{#2} } \cs_new_nopar:Npn \celtic_next_crossing: { \int_zero:N \l__celtic_cross_int \tl_clear:N \l__celtic_crossing_tl \tl_clear:N \l__celtic_path_tl \tl_clear:N \l__celtic_overpath_tl \bool_set_false:N \l__celtic_bounce_tl \tl_set:Nx \l__celtic_start_tl {(\int_use:N \l__celtic_x, \int_use:N \l__celtic_y)} \tl_put_right:Nx \l__celtic_path_tl {(\int_use:N \l__celtic_x, \int_use:N \l__celtic_y)} \int_set:Nn \l__celtic_lout {(90 - \l__celtic_dx * 45) * \l__celtic_dy} \bool_do_until:nn {\int_compare_p:n {\l__celtic_cross_int > 1}} { \bool_set_eq:NN \l__celtic_pbounce_bool \l__celtic_bounce_bool \bool_set_false:N \l__celtic_bounce_bool \int_add:Nn \l__celtic_x {\l__celtic_dx} \int_add:Nn \l__celtic_y {\l__celtic_dy} \tl_if_exist:cT {crossing \int_use:N \l__celtic_x - \int_use:N \l__celtic_y} { \tl_if_eq:cNTF {crossing \int_use:N \l__celtic_x - \int_use:N \l__celtic_y} \l__celtic_bar_tl { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nn \l__celtic_path_tl { -| } } { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_eval:n {(90 - 45*\l__celtic_dx)*\l__celtic_dy}, in=\int_eval:n {-90*\l__celtic_dy}] } } \int_set:Nn \l__celtic_lout {90*\l__celtic_dy} \int_set:Nn \l__celtic_dx {-\l__celtic_dx} \tl_put_right:Nx \l__celtic_path_tl {(\fp_eval:n {\int_use:N \l__celtic_x + .5 * \int_use:N \l__celtic_dx}, \int_use:N \l__celtic_y)} \bool_set_true:N \l__celtic_bounce_bool } { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nn \l__celtic_path_tl { |- } } { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_eval:n {(90 - 45*\l__celtic_dx)*\l__celtic_dy}, in=\int_eval:n {90 + 90*\l__celtic_dx}] } } \int_set:Nn \l__celtic_lout {90-90*\l__celtic_dx} \int_set:Nn \l__celtic_dy {-\l__celtic_dy} \tl_put_right:Nx \l__celtic_path_tl {(\int_use:N \l__celtic_x, \fp_eval:n {\int_use:N \l__celtic_y + .5 * \int_use:N \l__celtic_dy})} \bool_set_true:N \l__celtic_bounce_bool } } \int_compare:nT {\l__celtic_x == 0} { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nn \l__celtic_path_tl { -| } } { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_eval:n {(90 - 45*\l__celtic_dx)*\l__celtic_dy}, in=\int_eval:n {-90*\l__celtic_dy}] } } \int_set:Nn \l__celtic_lout {90*\l__celtic_dy} \int_set:Nn \l__celtic_dx {-\l__celtic_dx} \tl_put_right:Nx \l__celtic_path_tl {(\fp_eval:n {\int_use:N \l__celtic_x + .5 * \int_use:N \l__celtic_dx}, \int_use:N \l__celtic_y)} \bool_set_true:N \l__celtic_bounce_bool } \int_compare:nT {\l__celtic_x == \l__celtic_width_int} { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nn \l__celtic_path_tl { -| } } { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_eval:n {(90 - 45*\l__celtic_dx)*\l__celtic_dy}, in=\int_eval:n {-90*\l__celtic_dy}] } } \int_set:Nn \l__celtic_lout {90*\l__celtic_dy} \int_set:Nn \l__celtic_dx {-\l__celtic_dx} \tl_put_right:Nx \l__celtic_path_tl {(\fp_eval:n {\int_use:N \l__celtic_x + .5 * \int_use:N \l__celtic_dx}, \int_use:N \l__celtic_y)} \bool_set_true:N \l__celtic_bounce_bool } \int_compare:nT {\l__celtic_y == 0} { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nn \l__celtic_path_tl { |- } } { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_eval:n {(90 - 45*\l__celtic_dx)*\l__celtic_dy}, in=\int_eval:n {90 + 90*\l__celtic_dx}] } } \int_set:Nn \l__celtic_lout {90-90*\l__celtic_dx} \int_set:Nn \l__celtic_dy {-\l__celtic_dy} \tl_put_right:Nx \l__celtic_path_tl {(\int_use:N \l__celtic_x, \fp_eval:n {\int_use:N \l__celtic_y + .5 * \int_use:N \l__celtic_dy})} \bool_set_true:N \l__celtic_bounce_bool } \int_compare:nT {\l__celtic_y == \l__celtic_height_int} { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nn \l__celtic_path_tl { |- } } { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_eval:n {(90 - 45*\l__celtic_dx)*\l__celtic_dy}, in=\int_eval:n {90 + 90*\l__celtic_dx}] } } \int_set:Nn \l__celtic_lout {-90+90*\l__celtic_dx} \int_set:Nn \l__celtic_dy {-\l__celtic_dy} \tl_put_right:Nx \l__celtic_path_tl {(\int_use:N \l__celtic_x, \fp_eval:n {\int_use:N \l__celtic_y + .5 * \int_use:N \l__celtic_dy})} \bool_set_true:N \l__celtic_bounce_bool } \bool_if:NF \l__celtic_bounce_bool { \bool_if:NTF \l__celtic_pbounce_bool { \tl_put_right:Nx \l__celtic_path_tl { to[out=\int_use:N \l__celtic_lout,in=\int_eval:n {(-90 - 45 * \l__celtic_dx)*\l__celtic_dy}] } } { \tl_put_right:Nn \l__celtic_path_tl { -- } } \tl_put_right:Nx \l__celtic_path_tl { (\int_use:N \l__celtic_x, \int_use:N \l__celtic_y)} \tl_if_empty:NTF \l__celtic_crossing_tl { \tl_set:Nx \l__celtic_crossing_tl {(\int_use:N \l__celtic_x, \int_use:N \l__celtic_y)} } { \tl_clear:c {crossing used \int_use:N \l__celtic_x - \int_use:N \l__celtic_y} } \int_incr:N \l__celtic_cross_int \int_set:Nn \l__celtic_lout {(90 - \l__celtic_dx * 45) * \l__celtic_dy} } } \tl_set_eq:NN \l__celtic_overpath_tl \l__celtic_path_tl \tl_set:Nx \l__celtic_tmpa_tl {(\int_use:N \l__celtic_x, \int_use:N \l__celtic_y)} \tl_if_eq:NNT \l__celtic_crossing_tl \l__celtic_tmpa_tl { \tl_reverse:N \l__celtic_overpath_tl \tl_set:Nx \l__celtic_overpath_tl {\tl_tail:N \l__celtic_overpath_tl} \tl_split_after:NVn \l__celtic_overpath_tl \l__celtic_overpath_tl {)} \tl_reverse:N \l__celtic_overpath_tl } \tl_if_eq:NNT \l__celtic_crossing_tl \l__celtic_start_tl { \tl_set:Nx \l__celtic_overpath_tl {\tl_tail:N \l__celtic_overpath_tl} \tl_split_after:NVn \l__celtic_overpath_tl \l__celtic_overpath_tl {(} } } \keys_define:nn { celtic } { max~ steps .int_set:N = \l__celtic_max_steps_int, flip .code:n = { \int_set:Nn \l__celtic_flip_int {-1} }, width .int_set:N = \l__celtic_width_int, height .int_set:N = \l__celtic_height_int, size .code:n = { \clist_set:Nn \l__celtic_tmpa_clist {#1} \clist_pop:NN \l__celtic_tmpa_clist \l__celtic_tmpa_tl \int_set:Nn \l__celtic_width_int {\l__celtic_tmpa_tl} \clist_pop:NN \l__celtic_tmpa_clist \l__celtic_tmpa_tl \int_set:Nn \l__celtic_height_int {\l__celtic_tmpa_tl} }, width .groups:n = { size }, height .groups:n = { size }, size .groups:n = { size }, crossings .code:n = { \seq_set_split:Nnn \l__celtic_tmpa_seq {;} {#1} \seq_map_inline:Nn \l__celtic_tmpa_seq { \tl_if_empty:nF {##1} { \celtic_set_crossings:w ##1 \q_stop } } }, symmetric~ crossings .code:n = { \seq_set_split:Nnn \l__celtic_tmpa_seq {;} {#1} \seq_map_inline:Nn \l__celtic_tmpa_seq { \tl_if_empty:nF {##1} { \celtic_set_symmetric_crossings:w ##1 \q_stop } } }, ignore~ crossings .code:n ={ \seq_set_split:Nnn \l__celtic_tmpa_seq {;} {#1} \seq_map_inline:Nn \l__celtic_tmpa_seq { \tl_if_empty:nF {##1} { \celtic_ignore_crossings:w ##1 \q_stop } } }, ignore~ symmetric~ crossings .code:n ={ \seq_set_split:Nnn \l__celtic_tmpa_seq {;} {#1} \seq_map_inline:Nn \l__celtic_tmpa_seq { \tl_if_empty:nF {##1} { \celtic_ignore_symmetric_crossings:w ##1 \q_stop } } }, style .code:n = { \tikzset {#1} }, at .code:n = { \celtic_shift:n {#1} }, inner~ clip .fp_set:N = \l__celtic_inner_fp, outer~ clip .fp_set:N = \l__celtic_outer_fp, } \DeclareDocumentCommand \CelticDrawPath { m } { \group_begin: \pgfscope \seq_clear:N \l__celtic_path_seq \seq_clear:N \l__celtic_overpath_seq \seq_clear:N \l__celtic_component_seq \seq_clear:N \l__celtic_crossing_seq \int_set:Nn \l__celtic_flip_int {1} \int_compare:nT {\char_value_catcode:n {`\|} = 13} { \tl_set_eq:NN \l__celtic_bar_tl \l__celtic_active_bar_tl } \int_step_inline:nnnn {1} {1} {\l__celtic_height_int-1} { \int_step_inline:nnnn {1 + \int_mod:nn {##1}{2}} {2} {\l__celtic_width_int-1} { \tl_clear_new:c {crossing used ####1 - ##1} \tl_set:cn {crossing used ####1 - ##1} {X} } } \keys_set_groups:nnn { celtic } { size } {#1} \keys_set_filter:nnn { celtic } { size } {#1} \path[celtic~ bar/.try, celtic~ surround/.try] (0,0) rectangle (\int_use:N \l__celtic_width_int, \int_use:N \l__celtic_height_int); \int_step_inline:nnnn {1} {1} {\l__celtic_height_int-1} { \int_step_inline:nnnn {1 + \int_mod:nn {##1}{2}} {2} {\l__celtic_width_int-1} { \tl_if_exist:cT {crossing ####1 - ##1} { \tl_if_eq:cNTF {crossing ####1 - ##1} \l__celtic_bar_tl { \path[celtic~ bar/.try] (####1,##1-1) -- (####1,##1+1); } { \path[celtic~ bar/.try] (####1-1,##1) -- (####1+1,##1); } } } } \int_step_inline:nnnn {1} {1} {\l__celtic_height_int-1} { \int_step_inline:nnnn {1 + \int_mod:nn {##1}{2}} {2} {\l__celtic_width_int-1} { \celtic_generate_path:nnx {####1}{##1}{\int_eval:n {\l__celtic_flip_int*(2*\int_mod:nn{####1}{2} - 1)}} } } \celtic_render_path: \endpgfscope \group_end: } \cs_new_nopar:Npn \celtic_generate_path:nnn #1#2#3 { \bool_if:nF { \tl_if_exist_p:c {crossing #1 - #2} || \tl_if_empty_p:c {crossing used #1 - #2} } { \tl_clear:c {crossing used #1 - #2} \int_incr:N \l__celtic_component_int \int_set:Nn \l__celtic_x {#1} \int_set:Nn \l__celtic_y {#2} \int_set_eq:NN \l__celtic_ox \l__celtic_x \int_set_eq:NN \l__celtic_oy \l__celtic_y \int_set:Nn \l__celtic_dx {#3} \int_set:Nn \l__celtic_dy {1} \int_zero:N \l__celtic_int \bool_do_until:nn { (\int_compare_p:n {\l__celtic_x == \l__celtic_ox} && \int_compare_p:n {\l__celtic_y == \l__celtic_oy} ) || \int_compare_p:n {\l__celtic_int > \l__celtic_max_steps_int} } { \int_incr:N \l__celtic_int \celtic_next_crossing: \seq_put_left:NV \l__celtic_path_seq \l__celtic_path_tl \seq_put_left:NV \l__celtic_overpath_seq \l__celtic_overpath_tl \seq_put_left:NV \l__celtic_crossing_seq \l__celtic_crossing_tl \seq_put_left:NV \l__celtic_component_seq \l__celtic_component_int } \int_compare:nT {\l__celtic_int > \l__celtic_max_steps_int} { \msg_warning:nn {celtic} { max~ steps } } } } \cs_generate_variant:Nn \celtic_generate_path:nnn {nnx} \cs_new_nopar:Npn \celtic_render_path: { \seq_map_inline:Nn \l__celtic_path_seq { \seq_pop:NN \l__celtic_component_seq \l__celtic_tmpa_tl \seq_put_right:NV \l__celtic_component_seq \l__celtic_tmpa_tl \path[celtic~ path/.try, celtic~ path~ \tl_use:N \l__celtic_tmpa_tl/.try] ##1; } \group_begin: \pgfscope \tikzset{celtic~ path/.try} \tl_use:c {tikz@double@setup} \tl_set:Nn \l__celtic_tmpa_tl { \endpgfscope \group_end: \fp_set:Nn \l__celtic_clip_fp } \tl_put_right:Nx \l__celtic_tmpa_tl {{\dim_use:N \pgflinewidth}} \tl_use:N \l__celtic_tmpa_tl \fp_set:Nn \l__celtic_inner_clip_fp {sqrt(2) * (\l__celtic_clip_fp + \l__celtic_inner_fp)} \fp_set:Nn \l__celtic_clip_fp {sqrt(2) * (\l__celtic_clip_fp + \l__celtic_outer_fp)} \seq_map_inline:Nn \l__celtic_overpath_seq { \seq_pop:NN \l__celtic_crossing_seq \l__celtic_crossing_tl \seq_pop:NN \l__celtic_component_seq \l__celtic_tmpa_tl \seq_put_right:NV \l__celtic_component_seq \l__celtic_tmpa_tl \pgfscope \clip \l__celtic_crossing_tl +(-\fp_to_dim:N \l__celtic_inner_clip_fp,0) -- +(0,\fp_to_dim:N \l__celtic_inner_clip_fp) -- +(\fp_to_dim:N \l__celtic_inner_clip_fp,0) -- +(0,-\fp_to_dim:N \l__celtic_inner_clip_fp) -- +(-\fp_to_dim:N \l__celtic_inner_clip_fp,0); \path[celtic~ path/.try, celtic~ path~ \tl_use:N \l__celtic_tmpa_tl/.try, double~ background] ##1; \endpgfscope \pgfscope \clip \l__celtic_crossing_tl +(-\fp_to_dim:N \l__celtic_clip_fp,0) -- +(0,\fp_to_dim:N \l__celtic_clip_fp) -- +(\fp_to_dim:N \l__celtic_clip_fp,0) -- +(0,-\fp_to_dim:N \l__celtic_clip_fp) -- +(-\fp_to_dim:N \l__celtic_clip_fp,0); \path[celtic~ path/.try, celtic~ path~ \tl_use:N \l__celtic_tmpa_tl/.try,double~ foreground] ##1; \endpgfscope } } \ExplSyntaxOff \tikzset{ double background/.code={% \begingroup \tikz@double@setup \global\pgf@xa=\pgflinewidth \endgroup \expandafter\tikz@semiaddlinewidth\expandafter{\the\pgf@xa}% \tikz@addmode{\tikz@mode@doublefalse}% }, double foreground/.code={% \begingroup \tikz@double@setup \global\pgf@xa=\pgfinnerlinewidth \endgroup \expandafter\tikz@semiaddlinewidth\expandafter{\the\pgf@xa}% \tikz@addmode{\tikz@mode@doublefalse}% \tikzset{color=\pgfinnerstrokecolor}% }, } %% %% Copyright (C) 2014 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 celtic.dtx %% celtic_doc.tex %% and the derived files celtic.ins %% celtic_code.pdf %% tikzlibraryceltic.code.tex %% celtic.pdf %% README %% %% %% End of file `tikzlibraryceltic.code.tex'.