% File: hawkdraw-shadings.code.tex % Copyright 2026 Jasper Habicht (mail(at)jasperhabicht.de). % % This work may be distributed and/or modified under the % conditions of the LaTeX Project Public License version 1.3c, % available at http://www.latex-project.org/lppl/. % % This file is part of the `hawkdraw' package (The Work in LPPL) % and all files in that bundle must be distributed together. % % This work has the LPPL maintenance status `maintained'. % % BOF % v0.4.1 2026-07-08 % ===== % Shadings % === % Shadings are defined as rectangular PDF XObjects. There are various types of shadings, but we only define % linear and radial shaings here having type 2 and 3 respectively. We define shadings as square with a size % of 100bp times 100bp. Shadings are defined by functions. % In order to allow for rotation of shadings, we use the PGF approach of defining the shadings twice the % size of the path they should fill. Thus, we need to use multiple functions to define the shading, because % the outer part of the shading object will be clipped away by the path. We do this by defining the % functions in a nested way. The outer function is a type 3 function, which defines the inner functions. % The inner functions depend on the type of the shading and the number of colors used. % Every shading defined by its type, the used colors and whether or not it has some offset (for radial % shadings) is defined only once and a PDF XObject is created for it. In the PDF, two XObjects are created, % one that defines the shading using functions and one that represents a box referring to the shading. Upon % use, the latter XObject is (re-)used by placing it in a box which is then scaled to twice the size of the % path bounding box, rotated and placed at the center of the relevant path, then clipped by this path. % === \msg_new:nnn { hawkdraw } { shading-unknown } { Shading ~ `#1` ~ unknown. } \box_new:N \l_hawkdraw_shading_box \clist_new:N \l_hawkdraw_shading_colors_clist \fp_new:N \l_hawkdraw_shading_rotate_fp \fp_new:N \l_hawkdraw_shading_offset_fp \bool_new:N \l_hawkdraw_shading_circular_bool \dim_new:N \l_hawkdraw_shading_bbox_xmin_dim \dim_new:N \l_hawkdraw_shading_bbox_xmax_dim \dim_new:N \l_hawkdraw_shading_bbox_ymin_dim \dim_new:N \l_hawkdraw_shading_bbox_ymax_dim \exp_args_generate:n { NVVVV } \cs_set:Npn \hawkdraw_scope_reset_bb_begin: { \draw_scope_begin: \__draw_scope_bb_begin: } \cs_set:Npn \hawkdraw_scope_reset_bb_end: { \__draw_scope_bb_end: \draw_scope_end: } \keys_define:nn { hawkdraw / path } { shading .code:n = { \__hawkdraw_error_unsupported:n { Shading } \tl_put_right:Nn \l_hawkdraw_path_preactions_tl { \hawkdraw_scope_reset_bb_begin: \tl_trim_spaces_apply:nN { \g_hawkdraw_softpath_original_tl } \__hawkdraw_path_process:o \tl_use:N \g_hawkdraw_softpath_original_tl \draw_path_use_clear:n { clip } \dim_set_eq:NN \l_hawkdraw_shading_bbox_xmin_dim \g_draw_bb_xmin_dim \dim_set_eq:NN \l_hawkdraw_shading_bbox_xmax_dim \g_draw_bb_xmax_dim \dim_set_eq:NN \l_hawkdraw_shading_bbox_ymin_dim \g_draw_bb_ymin_dim \dim_set_eq:NN \l_hawkdraw_shading_bbox_ymax_dim \g_draw_bb_ymax_dim \hawkdraw_shading_fill:n {#1} \bool_gset_false:N \g__hawkdraw_path_use_clip_bool \hawkdraw_scope_reset_bb_end: } } , shading ~ colors .clist_set:N = \l_hawkdraw_shading_colors_clist , shading ~ rotate .fp_set:N = \l_hawkdraw_shading_rotate_fp , shading ~ rotate .initial:n = { 0.0 } , shading ~ offset .fp_set:N = \l_hawkdraw_shading_offset_fp , shading ~ offset .initial:n = { 0.0 } , shading ~ circular .bool_set:N = \l_hawkdraw_shading_circular_bool , shading ~ circular .default:n = { true } , shading ~ circular .initial:n = { false } , } \tl_new:N \l__hawkdraw_shading_color_value_tmp_tl \seq_new:N \l__hawkdraw_shading_color_values_seq \box_new:N \l__hawkdraw_shading_object_box \cs_generate_variant:Nn \color_export:nnN { e } \cs_new_protected:Npn \hawkdraw_shading_set:nnn #1#2#3 { \hbox_set_to_wd:Nnn \l__hawkdraw_shading_object_box { 100bp } { \vbox_to_ht:nn { 100bp } { \skip_vertical:n { 0pt plus 1fil } \hawkdraw_support_pdfliteral:n { /Sh ~ sh } } \skip_horizontal:n { 0pt plus 1fil } } \pdf_object_new:n { hawkdraw_shading_ #1 } \tl_if_empty:nTF {#3} { \pdf_object_write:nne { hawkdraw_shading_ #1 } { dict } { #2 } } { \pdf_object_write:nne { hawkdraw_shading_ #1 } { stream } { {#2} {#3} } } \hawkdraw_support_pdfxform:nnN { } { % not need to set up a pattern dictionary % because shadings are directly used via the sh operator /Shading ~ << ~ /Sh ~ \pdf_object_ref:n { hawkdraw_shading_ #1 } ~ >> } \l__hawkdraw_shading_object_box \int_const:cn { c__hawkdraw_shading_ #1 _int } { \hawkdraw_support_pdflastxform: } } \cs_new_protected:Npn \hawkdraw_shading_use:n #1 { \hawkdraw_support_pdfrefxform:c { c__hawkdraw_shading_ #1 _int } } \cs_new_protected:Npn \__hawkdraw_shading_color_set_value:Nnnn #1#2#3#4 { \hawkdraw_case_color_space:nnn { \tl_set:Ne \l__hawkdraw_shading_color_value_tmp_tl {#2} \seq_put_right:NV #1 \l__hawkdraw_shading_color_value_tmp_tl } { \color_export:enN {#3} { space-sep-rgb } \l__hawkdraw_shading_color_value_tmp_tl \seq_put_right:NV #1 \l__hawkdraw_shading_color_value_tmp_tl } { \color_export:enN {#4} { space-sep-cmyk } \l__hawkdraw_shading_color_value_tmp_tl \seq_put_right:NV #1 \l__hawkdraw_shading_color_value_tmp_tl } } \cs_new_protected:Npn \hawkdraw_shading_color_set_values:Nn #1#2 { \seq_clear:N #1 \clist_map_inline:nn {#2} { \__hawkdraw_shading_color_set_value:Nnnn #1 {##1} {##1} {##1} } } \cs_generate_variant:Nn \hawkdraw_shading_color_set_values:Nn { NV } \cs_new_protected:Npn \hawkdraw_shading_fill:n #1 { \hawkdraw_shading_create:nV {#1} \l_hawkdraw_shading_colors_clist \hbox_set:Nn \l_hawkdraw_shading_box { \hawkdraw_shading_use:n { #1 . \clist_use:N \l_hawkdraw_shading_colors_clist \str_if_eq:nnT {#1} { radial } { . \fp_to_decimal:n { \l_hawkdraw_shading_offset_fp } } } } % scale to 2 * width of current bbox, 2 * height of current bbox % translate to center of current bbox \draw_transform_shift:n { ( \l_hawkdraw_shading_bbox_xmin_dim + ( \l_hawkdraw_shading_bbox_xmax_dim - \l_hawkdraw_shading_bbox_xmin_dim ) / 2 , \l_hawkdraw_shading_bbox_ymin_dim + ( \l_hawkdraw_shading_bbox_ymax_dim - \l_hawkdraw_shading_bbox_ymin_dim ) / 2 ) } \draw_transform_rotate:n { \l_hawkdraw_shading_rotate_fp } \bool_lazy_and:nnT { \l_hawkdraw_shading_circular_bool } { \str_if_eq_p:nn {#1} { radial } } { \dim_set:Nn \l_hawkdraw_shading_bbox_xmax_dim { \dim_max:nn { \l_hawkdraw_shading_bbox_xmax_dim } { \l_hawkdraw_shading_bbox_ymax_dim } } \dim_set:Nn \l_hawkdraw_shading_bbox_xmin_dim { \dim_min:nn { \l_hawkdraw_shading_bbox_xmin_dim } { \l_hawkdraw_shading_bbox_ymin_dim } } \dim_set_eq:NN \l_hawkdraw_shading_bbox_ymax_dim \l_hawkdraw_shading_bbox_xmax_dim \dim_set_eq:NN \l_hawkdraw_shading_bbox_ymin_dim \l_hawkdraw_shading_bbox_xmin_dim } \box_resize_to_wd_and_ht:Nnn \l_hawkdraw_shading_box { \fp_to_dim:n { ( \l_hawkdraw_shading_bbox_xmax_dim - \l_hawkdraw_shading_bbox_xmin_dim ) * 2 } } { \fp_to_dim:n { ( \l_hawkdraw_shading_bbox_ymax_dim - \l_hawkdraw_shading_bbox_ymin_dim ) * 2 } } \draw_box_use:Nn \l_hawkdraw_shading_box { ( \l_hawkdraw_shading_bbox_xmin_dim - \l_hawkdraw_shading_bbox_xmax_dim , \l_hawkdraw_shading_bbox_ymin_dim - \l_hawkdraw_shading_bbox_ymax_dim ) } } \cs_new_protected:Npn \hawkdraw_shading_create:nn #1#2 { \cs_if_exist_use:cTF { hawkdraw_shading_ #1 :n } { {#2} } { \msg_warning:nnn { hawkdraw } { shading-unknown } {#1} } } \cs_generate_variant:Nn \hawkdraw_shading_create:nn { nV } % === \cs_set:Npn \__hawkdraw_shading_linear_bounds:n #1 { \fp_format:nn { 25 } { .5 } ~ \int_step_tokens:nnn { 2 } { \clist_count:n {#1} - 1 } { \__hawkdraw_shading_linear_bounds_aux:nn { \clist_count:n {#1} } } \fp_format:nn { 75 } { .5 } ~ } \cs_set:Npn \__hawkdraw_shading_linear_bounds_aux:nn #1#2 { \fp_format:nn { ( 50 / ( #1 - 1 ) ) * ( #2 - 1 ) + 25 } { .5 } ~ } \cs_new:Npn \__hawkdraw_shading_linear_functions:n #1 { << ~ /FunctionType ~ 2 ~ /Domain ~ [ 0.0 ~ 100.0 ] ~ /C0 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { 1 } ] ~ /C1 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { 1 } ] ~ /N ~ 1 ~ >> ~ \int_step_function:nnN { 2 } { \seq_count:N \l__hawkdraw_shading_color_values_seq } \__hawkdraw_shading_linear_functions_aux:n << ~ /FunctionType ~ 2 ~ /Domain ~ [ 0.0 ~ 100.0 ] ~ /C0 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { -1 } ] ~ /C1 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { -1 } ] ~ /N ~ 1 ~ >> ~ } \cs_generate_variant:Nn \__hawkdraw_shading_linear_functions:n { V } \cs_new:Npn \__hawkdraw_shading_linear_functions_aux:n #1 { << ~ /FunctionType ~ 2 ~ /Domain ~ [ 0.0 ~ 100.0 ] ~ /C0 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { #1 - 1 } ] ~ /C1 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq {#1} ] ~ /N ~ 1 ~ >> ~ } \cs_new_protected:Npn \hawkdraw_shading_linear:n #1 { \int_if_exist:cF { c__hawkdraw_shading_ linear . #1 _int } { \hawkdraw_shading_color_set_values:Nn \l__hawkdraw_shading_color_values_seq {#1} \hawkdraw_shading_set:nnn { linear . #1 } { /ShadingType ~ 2 ~ \hawkdraw_case_color_space:nnn { /ColorSpace ~ /DeviceGray ~ } { /ColorSpace ~ /DeviceRGB ~ } { /ColorSpace ~ /DeviceCMYK ~ } /Domain ~ [ 0.0 ~ 100.0 ] ~ /Coords ~ [ 0.0 ~ 0.0 ~ 0.0 ~ 100.0 ] ~ /Extend ~ [ false ~ false ] ~ /Function ~ << ~ /FunctionType ~ 3 ~ /Domain ~ [ 0.0 ~ 100.0 ] ~ /Functions ~ [ ~ \__hawkdraw_shading_linear_functions:V \l__hawkdraw_shading_color_values_seq ] ~ /Bounds ~ [ \__hawkdraw_shading_linear_bounds:n {#1} ] ~ /Encode ~ [ \prg_replicate:nn { \clist_count:n {#1} + 1 } { 0 ~ 1 ~ } ] ~ >> ~ } { } } } % === \cs_new:Npn \__hawkdraw_shading_radial_bounds:n #1 { \int_step_tokens:nn { \clist_count:n {#1} - 1 } { \__hawkdraw_shading_radial_bounds_aux:nn { \clist_count:n {#1} } } } \cs_new:Npn \__hawkdraw_shading_radial_bounds_aux:nn #1#2 { \fp_format:nn { ( 50 / ( #1 + 1 ) ) * ( #2 ) } { .3 } ~ } \cs_new:Npn \__hawkdraw_shading_radial_functions:n #1 { \int_step_function:nN { \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 } \__hawkdraw_shading_radial_functions_aux:n << ~ /FunctionType ~ 2 ~ /Domain ~ [ 0.0 ~ 50.0 ] ~ /C0 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { -1 } ] ~ /C1 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { -1 } ] ~ /N ~ 1 ~ >> ~ } \cs_generate_variant:Nn \__hawkdraw_shading_radial_functions:n { V } \cs_new:Npn \__hawkdraw_shading_radial_functions_aux:n #1 { << ~ /FunctionType ~ 2 ~ /Domain ~ [ 0.0 ~ 50.0 ] ~ /C0 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq {#1} ] ~ /C1 ~ [ \seq_item:Nn \l__hawkdraw_shading_color_values_seq { #1 + 1 } ] ~ /N ~ 1 ~ >> ~ } \cs_new:Npn \hawkdraw_shading_radial_offset:n #1 { \fp_format:nn { 50 + ( #1 * 25 ) } { .5 } ~ } \cs_new_protected:Npn \hawkdraw_shading_radial:n #1 { \int_if_exist:cF { c__hawkdraw_shading_ radial . #1 . \fp_to_decimal:n { \l_hawkdraw_shading_offset_fp } _int } { \hawkdraw_shading_color_set_values:Nn \l__hawkdraw_shading_color_values_seq {#1} \hawkdraw_shading_set:nnn { radial . #1 . \fp_to_decimal:n { \l_hawkdraw_shading_offset_fp } } { /ShadingType ~ 3 ~ \hawkdraw_case_color_space:nnn { /ColorSpace ~ /DeviceGray ~ } { /ColorSpace ~ /DeviceRGB ~ } { /ColorSpace ~ /DeviceCMYK ~ } /Domain ~ [ 0.0 ~ 50.0 ] ~ /Coords ~ [ \hawkdraw_shading_radial_offset:n { \l_hawkdraw_shading_offset_fp } 50.0 ~ 0.0 ~ 50.0 ~ 50.0 ~ 50.0 ] ~ /Extend ~ [ true ~ false ] ~ /Function ~ << ~ /FunctionType ~ 3 ~ /Domain ~ [ 0.0 ~ 50.0 ] ~ /Functions ~ [ ~ \__hawkdraw_shading_radial_functions:V \l__hawkdraw_shading_color_values_seq ] ~ /Bounds ~ [ \__hawkdraw_shading_radial_bounds:n {#1} ] ~ /Encode ~ [ \prg_replicate:nn { \clist_count:n {#1} } { 0 ~ 1 ~ } ] ~ >> ~ } { } } } % === \cs_new_protected:Npn \hawkdraw_shading_conic_stream:N #1 { \tl_set:Ne #1 { \seq_map_indexed_function:NN \l__hawkdraw_shading_color_values_seq \__hawkdraw_shading_conic_stream_aux:nn } \exp_args:Ne \tl_analysis_log:n { \seq_use:Nn \l__hawkdraw_shading_color_values_seq { , } } } \cs_new:Npn \__hawkdraw_shading_conic_stream_aux:nn #1#2 { % skip first entry in seq which is the start color \int_compare:nNnF {#1} = { 1 } { % flag (4 bits) \hawkdraw_hex_to_binary:n { 00 } % patch is pie segment going from 0 to 360 / ( n * 4 ) % points (12 points, 2 * 16 bits each) \prg_replicate:nn { 2 } { \__hawkdraw_shading_conic_stream_point_polar:nn { 0 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 2 ) } } \prg_replicate:nn { 2 } { \__hawkdraw_shading_conic_stream_point_polar:nn { 1 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 2 ) } } \__hawkdraw_shading_conic_stream_point_polar:nn { 1 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 1.75 ) } \__hawkdraw_shading_conic_stream_point_polar:nn { 1 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 1.25 ) } \prg_replicate:nn { 2 } { \__hawkdraw_shading_conic_stream_point_polar:nn { 1 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 1 ) } } \prg_replicate:nn { 3 } { \__hawkdraw_shading_conic_stream_point_polar:nn { 0 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 1 ) } } \__hawkdraw_shading_conic_stream_point_polar:nn { 0 } { 360 / ( \seq_count:N \l__hawkdraw_shading_color_values_seq - 1 ) * ( #1 - 2 ) } % colors (4 colors, 3 * 8 bits each) \hawkdraw_hex_to_binary:e { \hawkdraw_color_pdf_to_hex:e { \seq_item:Nn \l__hawkdraw_shading_color_values_seq { #1 - 1 } } } \hawkdraw_hex_to_binary:e { \hawkdraw_color_pdf_to_hex:e { \seq_item:Nn \l__hawkdraw_shading_color_values_seq { #1 - 1 } } } \hawkdraw_hex_to_binary:e { \hawkdraw_color_pdf_to_hex:n {#2} } \hawkdraw_hex_to_binary:e { \hawkdraw_color_pdf_to_hex:n {#2} } } } \cs_new:Npn \__hawkdraw_shading_conic_stream_point_polar:nn #1#2 { % get coordinates from shifted point polar and normalize to FFFF \hawkdraw_hex_to_binary:e { \int_format:nn { \fp_to_int:n { \hawkdraw_tuple_use_i:n { ( 50bp , 50bp ) + ( \draw_point_polar:nn { ( #1 ) * 50bp } {#2} ) } / 100bp * 65535 } } { 0>4X } } \hawkdraw_hex_to_binary:e { \int_format:nn { \fp_to_int:n { \hawkdraw_tuple_use_ii:n { ( 50bp , 50bp ) + ( \draw_point_polar:nn { ( #1 ) * 50bp } {#2} ) } / 100bp * 65535 } } { 0>4X } } } \seq_new:N \l__hawkdraw_shading_color_values_tmp_seq \cs_new_protected:Npn \hawkdraw_shading_conic_color_set_values:Nn #1#2 { \seq_clear:N #1 \seq_set_from_clist:Nn \l__hawkdraw_shading_color_values_tmp_seq {#2} \seq_map_indexed_inline:Nn \l__hawkdraw_shading_color_values_tmp_seq { \int_compare:nNnTF {##1} = { 1 } { % first entry is the start color \__hawkdraw_shading_color_set_value:Nnnn #1 {##2} {##2} {##2} } { \__hawkdraw_shading_color_set_value:Nnnn #1 { \fp_to_decimal:n { 0.75 * \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } + 0.25 * ##2 } } { \seq_item:Nn \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } ! 75 ! ##2 } { \seq_item:Nn \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } ! 75 ! ##2 } \__hawkdraw_shading_color_set_value:Nnnn #1 { \fp_to_decimal:n { 0.5 * \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } + 0.5 * ##2 } } { \seq_item:Nn \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } ! 50 ! ##2 } { \seq_item:Nn \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } ! 50 ! ##2 } \__hawkdraw_shading_color_set_value:Nnnn #1 { \fp_to_decimal:n { 0.25 * \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } + 0.75 * ##2 } } { \seq_item:Nn \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } ! 25 ! ##2 } { \seq_item:Nn \l__hawkdraw_shading_color_values_tmp_seq { ##1 - 1 } ! 25 ! ##2 } \__hawkdraw_shading_color_set_value:Nnnn #1 {##2} {##2} {##2} } } } \cs_new_protected:Npn \hawkdraw_shading_conic:n #1 { \int_if_exist:cF { c__hawkdraw_shading_ conic . #1 _int } { \hawkdraw_shading_conic_color_set_values:Nn \l__hawkdraw_shading_color_values_seq {#1} \hawkdraw_shading_conic_stream:N \l_tmpa_tl \hawkdraw_shading_set:nnn { conic . #1 } { /ShadingType ~ 6 ~ \hawkdraw_case_color_space:nnn { /ColorSpace ~ /DeviceGray ~ } { /ColorSpace ~ /DeviceRGB ~ } { /ColorSpace ~ /DeviceCMYK ~ } /BitsPerCoordinate ~ 16 ~ /BitsPerComponent ~ 8 ~ /BitsPerFlag ~ 8 ~ /Decode ~ [ ~ 0 ~ 100 ~ 0 ~ 100 ~ \hawkdraw_case_color_space:nnn { 0 ~ 1 ~ } { 0 ~ 1 ~ 0 ~ 1 ~ 0 ~ 1 ~ } { 0 ~ 1 ~ 0 ~ 1 ~ 0 ~ 1 ~ 0 ~ 1 ~ } ] ~ } { \tl_use:N \l_tmpa_tl } } } %EOF