%% The LaTeX package tikzfill - version 1.2.0 (2026/04/23) %% tikzlibraryfill.hexagon.code.tex: filling with hexagon patterns %% %% ------------------------------------------------------------------------------------------- %% Copyright (c) 2022-2026 by Prof. Dr. Dr. Thomas F. Sturm %% ------------------------------------------------------------------------------------------- %% %% This work may be distributed and/or modified under the %% conditions of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% The latest version of this license is in %% http://www.latex-project.org/lppl.txt %% and version 1.3c or later is part of all distributions of LaTeX %% version 2008 or later. %% %% This work has the LPPL maintenance status `author-maintained'. %% %% This work consists of all files listed in README.md %% \ProvidesFile{tikzlibraryfill.hexagon.code.tex}[2026/04/23 v1.2.0 Hexagon pattern library] \usetikzlibrary{patterns.meta} \ExplSyntaxOn \fp_zero_new:N \l__tikzfill_tmpa_fp \int_new:N \l__tikzfill_hex_ring_int \tl_new:N \l__tikzfill_hex_a_tl \tl_new:N \l__tikzfill_hex_as_tl \tl_new:N \l__tikzfill_hex_b_tl \tl_new:N \l__tikzfill_hex_bs_tl \tl_new:N \l__tikzfill_hex_linewidth_tl \tl_new:N \l__tikzfill_hex_pos_tl \pgfdeclarepattern { name = hexagon~grid, parameters = { \pgfkeysvalueof{ /pgf/pattern~keys/size }, \pgfkeysvalueof{ /pgf/pattern~keys/angle }, \pgfkeysvalueof{ /pgf/pattern~keys/xshift }, \pgfkeysvalueof{ /pgf/pattern~keys/yshift }, \pgfkeysvalueof{ /pgf/pattern~keys/line~width }, }, defaults = { size /.initial = 8mm, angle /.initial = 0, line~width /.initial = 0.4pt, xshift /.initial = 0pt, yshift /.initial = 0pt, }, set~up~code = { \fp_set:Nn \l__tikzfill_tmpa_fp { \pgfkeysvalueof{ /pgf/pattern~keys/size } } \tl_set:Nx \l__tikzfill_hex_a_tl { \fp_to_dim:N \l__tikzfill_tmpa_fp } \tl_set:Nx \l__tikzfill_hex_b_tl { \fp_to_dim:n { \l__tikzfill_tmpa_fp * sqrt(3)/2 } } \tl_set:Nx \l__tikzfill_hex_linewidth_tl { \fp_to_dim:n { \pgfkeysvalueof{ /pgf/pattern~keys/line~width } } } }, bottom~left = { \pgfpoint{ - \l__tikzfill_hex_b_tl - .1pt } { - \l__tikzfill_hex_a_tl - \l__tikzfill_hex_linewidth_tl } }, top~right = { \pgfpoint{ \l__tikzfill_hex_b_tl + .1pt } { 2 * \l__tikzfill_hex_a_tl + .1pt } }, tile~size = { \pgfpoint{ 2 * \l__tikzfill_hex_b_tl } { 3 * \l__tikzfill_hex_a_tl } }, tile~transformation = { \pgftransformrotate{ \pgfkeysvalueof{ /pgf/pattern~keys/angle } } \pgftransformshift { \pgfpoint{ \pgfkeysvalueof{ /pgf/pattern~keys/xshift } } { \pgfkeysvalueof{ /pgf/pattern~keys/yshift } } } }, code= { \pgfsetlinewidth{ \l__tikzfill_hex_linewidth_tl } \pgfpathmoveto{\pgfpoint{ 0 } { 2 * \l__tikzfill_hex_a_tl + .1pt }} \pgfpathlineto{\pgfpoint{ 0 } { \l__tikzfill_hex_a_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_b_tl } { 0.5 * \l__tikzfill_hex_a_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_b_tl } { -0.5 * \l__tikzfill_hex_a_tl }} \pgfpathlineto{\pgfpoint{ 0 } { - \l__tikzfill_hex_a_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_b_tl } { -0.5 * \l__tikzfill_hex_a_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_b_tl } { 0.5 * \l__tikzfill_hex_a_tl }} \pgfpathlineto{\pgfpoint{ 0 } { \l__tikzfill_hex_a_tl }} \pgfusepath{ stroke } } } \tikzset{ pattern~hexagon~grid /.style = { pattern= { hexagon~grid[#1] } } } \pgfdeclarepattern { name = hexagon, parameters = { \pgfkeysvalueof{ /pgf/pattern~keys/size }, \pgfkeysvalueof{ /pgf/pattern~keys/angle }, \pgfkeysvalueof{ /pgf/pattern~keys/xshift }, \pgfkeysvalueof{ /pgf/pattern~keys/yshift }, \pgfkeysvalueof{ /pgf/pattern~keys/line~width }, \pgfkeysvalueof{ /pgf/pattern~keys/pos }, \pgfkeysvalueof{ /pgf/pattern~keys/band }, \pgfkeysvalueof{ /pgf/pattern~keys/_fill_ }, }, defaults = { size /.initial = 8mm, angle /.initial = 0, xshift /.initial = 0pt, yshift /.initial = 0pt, line~width /.initial = 0.4pt, pos /.initial = 0.8, band /.initial = 0, _fill_ /.initial = 1, fill /.style = { _fill_=1 }, draw /.style = { _fill_=0 }, }, set~up~code = { \fp_set:Nn \l__tikzfill_tmpa_fp { \pgfkeysvalueof{ /pgf/pattern~keys/size } } \tl_set:Nx \l__tikzfill_hex_a_tl { \fp_to_dim:N \l__tikzfill_tmpa_fp } \tl_set:Nx \l__tikzfill_hex_b_tl { \fp_to_dim:n { \l__tikzfill_tmpa_fp * sqrt(3)/2 } } \tl_set:Nx \l__tikzfill_hex_linewidth_tl { \fp_to_dim:n { \pgfkeysvalueof{ /pgf/pattern~keys/line~width } } } \tl_set:Nx \l__tikzfill_hex_pos_tl { \fp_to_decimal:n { min ( 1 , max( 0, \pgfkeysvalueof{ /pgf/pattern~keys/pos } )) } } }, bottom~left = { \pgfpoint{ - \l__tikzfill_hex_b_tl - \l__tikzfill_hex_linewidth_tl } { - \l__tikzfill_hex_a_tl - \l__tikzfill_hex_linewidth_tl } }, top~right = { \pgfpoint{ \l__tikzfill_hex_b_tl + \l__tikzfill_hex_linewidth_tl } { 2 * \l__tikzfill_hex_a_tl + \l__tikzfill_hex_linewidth_tl } }, tile~size = { \pgfpoint{ 2 * \l__tikzfill_hex_b_tl } { 3 * \l__tikzfill_hex_a_tl } }, tile~transformation = { \pgftransformrotate{ \pgfkeysvalueof{ /pgf/pattern~keys/angle } } \int_compare:nNnTF { \pgfkeysvalueof{ /pgf/pattern~keys/band } } = { 0 } { \pgftransformshift { \pgfpoint{ \pgfkeysvalueof{ /pgf/pattern~keys/xshift } } { \pgfkeysvalueof{ /pgf/pattern~keys/yshift } } } } { \pgftransformshift { \pgfpoint{ \pgfkeysvalueof{ /pgf/pattern~keys/xshift } - \l__tikzfill_hex_b_tl } { \pgfkeysvalueof{ /pgf/pattern~keys/yshift } + 1.5 * \l__tikzfill_hex_a_tl } } } }, code= { \tl_set:Nx \l__tikzfill_hex_as_tl { \fp_to_dim:n { \l__tikzfill_hex_pos_tl * \l__tikzfill_hex_a_tl }} \tl_set:Nx \l__tikzfill_hex_bs_tl { \fp_to_dim:n { \l__tikzfill_hex_pos_tl * \l__tikzfill_hex_b_tl }} \pgfpathmoveto{\pgfpoint{ 0 } { \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_bs_tl } { 0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_bs_tl } { -0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ 0 } { - \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_bs_tl } { -0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_bs_tl } { 0.5 * \l__tikzfill_hex_as_tl }} \pgfpathclose \int_compare:nNnTF { \pgfkeysvalueof{ /pgf/pattern~keys/_fill_ } } = { 1 } { \pgfusepath{ fill } } { \pgfsetlinewidth{ \l__tikzfill_hex_linewidth_tl } \pgfusepath{ stroke } } } } \tikzset{ pattern~hexagon /.style = { preaction= { pattern= { hexagon[#1,band=1] } }, pattern= { hexagon[#1,band=0] } } } \pgfdeclarepattern { name = hexagon~cycle, parameters = { \pgfkeysvalueof{ /pgf/pattern~keys/size }, \pgfkeysvalueof{ /pgf/pattern~keys/angle }, \pgfkeysvalueof{ /pgf/pattern~keys/xshift }, \pgfkeysvalueof{ /pgf/pattern~keys/yshift }, \pgfkeysvalueof{ /pgf/pattern~keys/rings }, \pgfkeysvalueof{ /pgf/pattern~keys/gap }, \pgfkeysvalueof{ /pgf/pattern~keys/band }, }, defaults = { size /.initial = 8mm, angle /.initial = 0, xshift /.initial = 0pt, yshift /.initial = 0pt, rings /.initial = 3, gap /.initial = 1, band /.initial = 0, }, set~up~code = { \fp_set:Nn \l__tikzfill_tmpa_fp { \pgfkeysvalueof{ /pgf/pattern~keys/size } } \tl_set:Nx \l__tikzfill_hex_a_tl { \fp_to_dim:N \l__tikzfill_tmpa_fp } \tl_set:Nx \l__tikzfill_hex_b_tl { \fp_to_dim:n { \l__tikzfill_tmpa_fp * sqrt(3)/2 } } \int_set:Nn \l__tikzfill_hex_ring_int { \fp_to_int:n { max ( 0, \pgfkeysvalueof{ /pgf/pattern~keys/rings } ) }} \fp_set:Nn \l__tikzfill_tmpa_fp { max ( 0.01, \pgfkeysvalueof{ /pgf/pattern~keys/gap } ) } \tl_set:Nx \l__tikzfill_hex_linewidth_tl { \fp_to_dim:n { \l__tikzfill_hex_b_tl / (( \l__tikzfill_hex_ring_int + 0.5 )*( 1 + \l__tikzfill_tmpa_fp )) }} }, bottom~left = { \pgfpoint{ - \l__tikzfill_hex_b_tl } { - \l__tikzfill_hex_a_tl } }, top~right = { \pgfpoint{ \l__tikzfill_hex_b_tl } { 2 * \l__tikzfill_hex_a_tl } }, tile~size = { \pgfpoint{ 2 * \l__tikzfill_hex_b_tl } { 3 * \l__tikzfill_hex_a_tl } }, tile~transformation = { \pgftransformrotate{ \pgfkeysvalueof{ /pgf/pattern~keys/angle } } \int_compare:nNnTF { \pgfkeysvalueof{ /pgf/pattern~keys/band } } = { 0 } { \pgftransformshift { \pgfpoint{ \pgfkeysvalueof{ /pgf/pattern~keys/xshift } } { \pgfkeysvalueof{ /pgf/pattern~keys/yshift } } } } { \pgftransformshift { \pgfpoint{ \pgfkeysvalueof{ /pgf/pattern~keys/xshift } - \l__tikzfill_hex_b_tl } { \pgfkeysvalueof{ /pgf/pattern~keys/yshift } + 1.5 * \l__tikzfill_hex_a_tl } } } }, code= { \tl_set:Nn \l__tikzfill_hex_pos_tl { \l__tikzfill_hex_linewidth_tl / 2 / \l__tikzfill_hex_b_tl } \tl_set:Nx \l__tikzfill_hex_as_tl { \fp_to_dim:n { \l__tikzfill_hex_pos_tl * \l__tikzfill_hex_a_tl } } \tl_set:Nx \l__tikzfill_hex_bs_tl { \fp_to_dim:n { \l__tikzfill_hex_pos_tl * \l__tikzfill_hex_b_tl } } \pgfpathmoveto{\pgfpoint{ 0 } { \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_bs_tl } { 0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_bs_tl } { -0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ 0 } { - \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_bs_tl } { -0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_bs_tl } { 0.5 * \l__tikzfill_hex_as_tl }} \pgfpathclose \pgfusepath{ fill } % \pgfsetlinewidth{ \l__tikzfill_hex_linewidth_tl } \int_step_function:nN { \l__tikzfill_hex_ring_int } \__tikzfill_hex_draw_ring:n } } \cs_new_nopar:Npn \__tikzfill_hex_draw_ring:n #1 { \tl_set:Nn \l__tikzfill_hex_pos_tl { #1 / ( \l__tikzfill_hex_ring_int + 0.5 ) } \tl_set:Nx \l__tikzfill_hex_as_tl { \fp_to_dim:n { \l__tikzfill_hex_pos_tl * \l__tikzfill_hex_a_tl } } \tl_set:Nx \l__tikzfill_hex_bs_tl { \fp_to_dim:n { \l__tikzfill_hex_pos_tl * \l__tikzfill_hex_b_tl } } \pgfpathmoveto{\pgfpoint{ 0 } { \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_bs_tl } { 0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ - \l__tikzfill_hex_bs_tl } { -0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ 0 } { - \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_bs_tl } { -0.5 * \l__tikzfill_hex_as_tl }} \pgfpathlineto{\pgfpoint{ \l__tikzfill_hex_bs_tl } { 0.5 * \l__tikzfill_hex_as_tl }} \pgfpathclose \pgfusepath{ stroke } } \tikzset{ pattern~hexagon~cycle /.style = { preaction= { pattern= { hexagon~cycle[#1,band=1] }}, pattern= { hexagon~cycle[#1,band=0] } } } \ExplSyntaxOff