From 982ab08406ab7b0850b4eaa9cf2c0098dce96b78 Mon Sep 17 00:00:00 2001 From: zongpingding <98604286+zongpingding@users.noreply.github.com> Date: Fri, 24 Nov 2023 03:04:41 +0800 Subject: [PATCH] Add files via upload --- .../TikZ_Coordinate/2d_plot/2d_plot.sty" | 144 ++ .../2d_plot/Scripts/data_gen.gp" | 9 + .../2d_plot/Scripts/param_data_gen.gp" | 9 + .../gnuplot_output_data/data_gen_1.table" | 1505 +++++++++++++++++ .../gnuplot_output_data/data_gen_2.table" | 505 ++++++ .../gnuplot_output_data/data_gen_4.table" | 505 ++++++ .../param_data_gen_1.table" | 1005 +++++++++++ .../param_data_gen_2.table" | 505 ++++++ .../param_data_gen_3.table" | 505 ++++++ .../param_data_gen_4.table" | 1005 +++++++++++ .../BugOfexpl3/Test/test_2.log" | 0 .../TikZ_Coordinate/BugOfexpl3/main.pdf" | Bin 0 -> 10179 bytes .../TikZ_Coordinate/BugOfexpl3/main.tex" | 18 + .../TikZ_Coordinate/KeyVal/latex3_2.pdf" | Bin 0 -> 16359 bytes .../TikZ_Coordinate/KeyVal/latex3_2.tex" | 126 ++ .../TikZ_Coordinate/String_Equal/test.pdf" | Bin 0 -> 2492 bytes .../TikZ_Coordinate/String_Equal/test.tex" | 24 + .../TikZ_Coordinate/clist_iter/iter_list.pdf" | Bin 0 -> 7272 bytes .../TikZ_Coordinate/clist_iter/iter_list.tex" | 65 + .../TikZ_Coordinate/shoots.png" | Bin 0 -> 216636 bytes .../TikZ_Coordinate/tikz_coor.pdf" | Bin 0 -> 496855 bytes .../tikz_coor.pgf-plot.gnuplot" | 2 + .../TikZ_Coordinate/tikz_coor.pgf-plot.table" | 30 + .../TikZ_Coordinate/tikz_coor.tex" | 602 +++++++ 24 files changed, 6564 insertions(+) create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/2d_plot.sty" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/data_gen.gp" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/param_data_gen.gp" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/data_gen_1.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/data_gen_2.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/data_gen_4.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/param_data_gen_1.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/param_data_gen_2.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/param_data_gen_3.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/param_data_gen_4.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/BugOfexpl3/Test/test_2.log" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/BugOfexpl3/main.pdf" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/BugOfexpl3/main.tex" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/KeyVal/latex3_2.pdf" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/KeyVal/latex3_2.tex" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/String_Equal/test.pdf" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/String_Equal/test.tex" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/clist_iter/iter_list.pdf" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/clist_iter/iter_list.tex" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/shoots.png" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pdf" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.gnuplot" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.table" create mode 100644 "LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.tex" diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/2d_plot.sty" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/2d_plot.sty" new file mode 100644 index 0000000..b54d3b0 --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/2d_plot.sty" @@ -0,0 +1,144 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{2d_plot/2d_plot} +\RequirePackage{expl3, l3sys-shell} +\RequirePackage{xparse} + + + +\ExplSyntaxOn +% plot data's id(counter) +\newcounter{gnu@plot@data@counter} +\newcommand{\gnu@data@fullname}{} +\bool_new:N \Change@Precise@Once + + +%%%%% the relative path there = path of '.tex' source file +%%%%% Bug: \file_if_exist can't check if a dir is exsits +\sys_shell_now:n {mkdir~ ./2d_plot/gnuplot_output_data} + + + +% ---------------------------------------------------------------------- +% 1.precision of plot +% ---------------------------------------------------------------------- +\NewDocumentCommand\NormalPlotPrecise{O{once}m}{ + \str_if_eq:nnTF {#1}{once}{ + \bool_set_true:N \Change@Precise@Once + }{\relax} + \sys_shell_now:n {sed~ -i~ "3s|set~ samples~ .*|set~ samples~ #2|"~ ./2d_plot/Scripts/data_gen.gp} +} +\NewDocumentCommand\ParamPlotPrecise{O{once}m}{ + \str_if_eq:nnTF {#1}{once}{ + \bool_set_true:N \Change@Precise@Once + }{\relax} + \sys_shell_now:n {sed~ -i~ "3s|set~ samples~ .*|set~ samples~ #2|"~ ./2d_plot/Scripts/param_data_gen.gp} +} + + + + + +% ---------------------------------------------------------------------- +% 2.coordinate basic components +% ---------------------------------------------------------------------- +% Example: \ShowPoint[radius=3pt, color=blue, opacity=.5] {(1, 1); (2, 2)}[text1; text2; text3][text style]; +\keys_define:nn { __Point__ }{ + type .tl_set:N = \l__Point_type, + type .initial:n = { circle }, + radius .dim_set:N = \l__Point_radius, + radius .initial:n = { 1pt }, + color .tl_set:N = \l__Point_color, + color .initial:n = { black }, + opacity .tl_set:N = \l__Point_opacity, + opacity .initial:n = { 1 } +} +\NewDocumentCommand\ShowPoint{ O{}mO{}O{} }{ + % use the following to initial options each times if not in local group + % \keys_set:nn { __Point__ } {color=black, opacity=1, type=circle, radius=1pt} + \group_begin: + \keys_set:nn { __Point__ } { #1 } + \seq_set_split:Nnn \l__point_param_ii_seq { ; }{#2} + \seq_set_split:Nnn \l__point_param_iii_seq { ; }{#3} + % ==> previous showpoint code without annotate=ion + % \seq_map_inline:Nn \l__point_param_ii_seq{ + % \fill[color=\l__Point_color, opacity=\l__Point_opacity] + % ##1 \l__Point_type(\dim_use:N \l__Point_radius); + % } + \int_step_inline:nnnn {1}{1}{\seq_count:N \l__point_param_ii_seq}{ + \fill[color=\l__Point_color, opacity=\l__Point_opacity] + \seq_item:Nn \l__point_param_ii_seq{##1} \l__Point_type(\dim_use:N \l__Point_radius) + node[#4]{\seq_item:Nn \l__point_param_iii_seq{##1}}; + } + \group_end: +} + +% Example: \ShowGrid[color=red, thick]{(-5, -5); (5, 5)} +\NewDocumentCommand\ShowGrid{ O{color=gray, very~ thin, step=1}m }{ + \seq_set_split:Nnn \l__grid_param_ii_seq { ; }{#2} + \draw[#1] \seq_item:Nn \l__grid_param_ii_seq{1} grid \seq_item:Nn \l__grid_param_ii_seq{2}; +} + +% Example: \ShowAxis {(0, -8); (0, 8)} +\NewDocumentCommand\ShowAxis{ O{color=black}m }{ + \seq_set_split:Nnn \l__axis_param_ii_seq { ; }{#2} + \draw[->, #1] \seq_item:Nn \l__axis_param_ii_seq{1} -- \seq_item:Nn \l__axis_param_ii_seq{2}; +} + +% Example:\ShowIntersecions{exp; ellipse}{2} +\NewDocumentCommand\ShowIntersecions{ omm }{ + \seq_set_split:Nnn \l__intersection_num_seq { ; }{#2} + % get all intersections + \path[name~ intersections={of=\seq_item:Nn \l__intersection_num_seq{1}~ and~ \seq_item:Nn \l__intersection_num_seq{2}}]; + % show all intersections by \ShowPoint + \int_step_inline:nnnn {1}{1}{#3}{ + \ShowPoint[#1]{(intersection-##1)} + } +} + + + + + +% ---------------------------------------------------------------------- +% 3.2d function plot +% ---------------------------------------------------------------------- +% normal 2d function +\NewDocumentCommand\NormalPlot{O{color=black}O{-5:5}m}{ + % step id of data + \stepcounter{gnu@plot@data@counter} + % sed gnuplot scripts + \sys_shell_now:n {sed~ -i~ "8s|set~ xr~ .*|set~ xr~ [#2]|"~ ./2d_plot/Scripts/data_gen.gp} + \sys_shell_now:n {sed~ -i~ "7s|f(x)~ =~ .*|f(x)~ =~ #3|"~ ./2d_plot/Scripts/data_gen.gp} + \sys_shell_now:n {gnuplot~ ./2d_plot/Scripts/data_gen.gp} + % data file rename + \renewcommand{\gnu@data@fullname}{data_gen_\the\value{gnu@plot@data@counter}.table} + \cs_generate_variant:Nn \sys_shell_mv:nn {nx} + \sys_shell_mv:nx {./2d_plot/gnuplot_output_data/data_gen.table}{./2d_plot/gnuplot_output_data/\gnu@data@fullname} + % draw function graph according to data in file + \draw[#1] plot[smooth] file {./2d_plot/gnuplot_output_data/\gnu@data@fullname}; + % reset boolean and set to default precise + \bool_if:NTF \Change@Precise@Once{ + \NormalPlotPrecise{500} + }{\relax} +} + +% parametric 2d function +\NewDocumentCommand\ParamPlot{O{color=black}O{-5:5}m}{ + % step id of data + \stepcounter{gnu@plot@data@counter} + % sed gnuplot scripts + \sys_shell_now:n {sed~ -i~ "8s|set~ trange~ .*|set~ trange~ [#2]|"~ ./2d_plot/Scripts/param_data_gen.gp} + \sys_shell_now:n {sed~ -i~ "9s|plot~ .*|plot~ #3|"~ ./2d_plot/Scripts/param_data_gen.gp} + \sys_shell_now:n {gnuplot~ ./2d_plot/Scripts/param_data_gen.gp} + % data file rename + \renewcommand{\gnu@data@fullname}{param_data_gen_\the\value{gnu@plot@data@counter}.table} + \cs_generate_variant:Nn \sys_shell_mv:nn {nx} + \sys_shell_mv:nx {./2d_plot/gnuplot_output_data/param_data_gen.table}{./2d_plot/gnuplot_output_data/\gnu@data@fullname} + % draw function graph according to data in file + \draw[#1] plot[smooth] file {./2d_plot/gnuplot_output_data/\gnu@data@fullname}; + % reset boolean and set to default + \bool_if:NTF \Change@Precise@Once{ + \ParamPlotPrecise{500} + }{\relax} +} +\ExplSyntaxOff \ No newline at end of file diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/data_gen.gp" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/data_gen.gp" new file mode 100644 index 0000000..205b137 --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/data_gen.gp" @@ -0,0 +1,9 @@ +set table "./2d_plot/gnuplot_output_data/data_gen.table" +set format "%.5f" +set samples 500 + + +# specific a 2d function +f(x) = 3*sin(1/x) +set xr [-6:-1] +plot f(x) diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/param_data_gen.gp" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/param_data_gen.gp" new file mode 100644 index 0000000..3532631 --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/Scripts/param_data_gen.gp" @@ -0,0 +1,9 @@ +set table "./2d_plot/gnuplot_output_data/param_data_gen.table" +set format "%.5f" +set samples 500 +set parametric + + +# specific a parametric function +set trange [0:2*pi] +plot 7*sin(t), 4*cos(t) \ No newline at end of file diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/data_gen_1.table" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/data_gen_1.table" new file mode 100644 index 0000000..3b3c2c3 --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/2d_plot/gnuplot_output_data/data_gen_1.table" @@ -0,0 +1,1505 @@ + +# Curve 0 of 1, 1500 points +# Curve title: "f(x)" +# x y type +-7.00000 -0.42712 i +-6.99013 -0.42771 i +-6.98025 -0.42832 i +-6.97038 -0.42892 i +-6.96051 -0.42952 i +-6.95063 -0.43013 i +-6.94076 -0.43074 i +-6.93089 -0.43134 i +-6.92101 -0.43196 i +-6.91114 -0.43257 i +-6.90127 -0.43318 i +-6.89139 -0.43380 i +-6.88152 -0.43442 i +-6.87165 -0.43504 i +-6.86177 -0.43566 i +-6.85190 -0.43628 i +-6.84203 -0.43691 i +-6.83215 -0.43753 i +-6.82228 -0.43816 i +-6.81241 -0.43879 i +-6.80254 -0.43943 i +-6.79266 -0.44006 i +-6.78279 -0.44070 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gBw^qFdvRRdj9uKkT>h4Wn~ReT@adDdq6FYS0MvO*I{*Lx literal 0 HcmV?d00001 diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/BugOfexpl3/main.tex" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/BugOfexpl3/main.tex" new file mode 100644 index 0000000..79bc578 --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/BugOfexpl3/main.tex" @@ -0,0 +1,18 @@ +\documentclass[12pt]{article} +% \usepackage{2d_plot/2d_plot} +\usepackage{tikz} + + +\begin{document} + % \begin{tikzpicture} + % \NormalPlot{cos(x)} + % \end{tikzpicture} + + % \begin{tikzpicture} + % \ParamPlot[red][0:pi]{6*sin(t), cos(t)} + % \end{tikzpicture} + \ExplSyntaxOn + \file_if_exist:nTF{./Test}{ + exists + }{don't~ exists} +\end{document} \ No newline at end of file diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/KeyVal/latex3_2.pdf" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/KeyVal/latex3_2.pdf" new file mode 100644 index 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+\clist_set:Nn \lisa {(1, 1); (2, 2); (3, 3)} +\clist_item:Nn \lisa{-1} + +% using seq_set_split +\par +\seq_set_split:Nnn \lisb { ; } { (1, 1); (2, 2); (3, 3); (4, 4) } +% \seq_item:Nn \lisb{1}, \seq_item:Nn \lisb{-1} +\int_step_inline:nnnn {1}{1}{4}{ + \seq_item:Nn \lisb{#1} +} +% use map_inline is convenient +\par\seq_map_inline:Nn \lisb{ + % \seq_item:Nn \lisb{#1} + #1 +} +\par\seq_use:Nnnn \lisb{;}{;}{;} + + +\newcommand{\test}[1]{ + \seq_set_split:Nnn \lisc { ; }{#1} + The~ First~ is:\seq_item:Nn \lisc{1},The Second~ is:\seq_item:Nn \lisc{2}. +} +\par\test{(1, 1); (2, 2); (3, 3); (4, 4)} + + +\section{storage intersections} +\begin{center} + \begin{tikzpicture} + \draw[orange, name~ path=line] (-2, -2) -- (1.8, 2) -- (1.8, -2.2); + \draw[green, name~ path=circle] (0, 0) circle (2); + % get the intersections(by don't get it by return value) + \path[name~ intersections={of=line~ and~ circle}]; + \fill[red] (intersection-1) circle (1pt); + \fill[blue] (intersection-2) circle (1pt); + + % get all intersections + % \path[name~ intersections={of=line1~ and~ line2}]; + % put each intersection to seq + \seq_set_split:Nnn \l__all_intersections_seq{;}{} + \int_step_inline:nnnn {1}{1}{5}{ + \seq_put_right:Nn \l__all_intersections_seq{(intersection-#1)} + } + % show all intersections by \ShowPoint + % \node at (0, -3) {\seq_use:Nnnn \l__all_intersections_seq{}{;}{;}}; + % \node at (0, -4) {\cs_meaning:N \l__all_intersections_seq}; + % \node at (0, -1.5) {\seq_item:Nn \l__all_intersections_seq{1}}; + \fill[blue] \seq_item:Nn \l__all_intersections_seq{2} circle(5pt); + % \ShowPoint[#1]{\seq_use:Nnnn \l__all_intersections_seq{;}{;}{;}} +\end{tikzpicture} +\end{center} + + +\ExplSyntaxOff +\end{document} \ No newline at end of file diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/shoots.png" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/shoots.png" new file mode 100644 index 0000000000000000000000000000000000000000..83dbf2294bbfbcc3774d77b8a9301e37a7aef2b9 GIT 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zqKsBx=~WYTa(nDs>KDUze&fLN#6XJRCB!My#g*u(^@WGt65!nFRN-P#|J3*5Oz$-K z;s@ai{l%FnQY>Yg@qU!D^}t<^ng}ZzZwV^z23pdm>{=epxWQ{0HjVk8$B9Ba_@MoL U;Lapc5U@B{l7xpxO<$elU(AIxvj6}9 literal 0 HcmV?d00001 diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.gnuplot" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.gnuplot" new file mode 100644 index 0000000..382616f --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.gnuplot" @@ -0,0 +1,2 @@ +set table "tikz_coor.pgf-plot.table"; set format "%.5f" +set format "%.7e";; set samples 25; set dummy x; plot [x=3:7] -(36/25) + (336*x)/125 - (6*x**2)/5 + (24*x**3)/125 - (x**4)/100; diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.table" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.table" new file mode 100644 index 0000000..be62be1 --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.pgf-plot.table" @@ -0,0 +1,30 @@ + +# Curve 0 of 1, 25 points +# Curve title: "-(36/25) + (336*x)/125 - (6*x**2)/5 + (24*x**3)/125 - (x**4)/100" +# x y type +3.0000000e+00 6.3800000e-01 i +3.1666667e+00 5.6999228e-01 i +3.3333333e+00 5.0320988e-01 i +3.5000000e+00 4.3937500e-01 i +3.6666667e+00 3.8002469e-01 i +3.8333333e+00 3.2651080e-01 i +4.0000000e+00 2.8000000e-01 i +4.1666667e+00 2.4147377e-01 i +4.3333333e+00 2.1172840e-01 i +4.5000000e+00 1.9137500e-01 i +4.6666667e+00 1.8083951e-01 i +4.8333333e+00 1.8036265e-01 i +5.0000000e+00 1.9000000e-01 i +5.1666667e+00 2.0962191e-01 i +5.3333333e+00 2.3891358e-01 i +5.5000000e+00 2.7737500e-01 i +5.6666667e+00 3.2432099e-01 i +5.8333333e+00 3.7888117e-01 i +6.0000000e+00 4.4000000e-01 i +6.1666667e+00 5.0643673e-01 i +6.3333333e+00 5.7676543e-01 i +6.5000000e+00 6.4937500e-01 i +6.6666667e+00 7.2246914e-01 i +6.8333333e+00 7.9406636e-01 i +7.0000000e+00 8.6200000e-01 i + diff --git "a/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.tex" "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.tex" new file mode 100644 index 0000000..7139e3a --- /dev/null +++ "b/LaTeX \350\277\233\351\230\266/TikZ_Coordinate/tikz_coor.tex" @@ -0,0 +1,602 @@ +\documentclass[12pt]{article} +\usepackage[a4paper, total={6.5in, 10in}]{geometry} +\PassOptionsToPackage{quiet}{fontspec} +\usepackage{ctex} +\usepackage{float} +\usepackage{tikz, pgfplots} +\usepackage{2d_plot/2d_plot} +\pgfplotsset{compat=1.18} +\usetikzlibrary{arrows.meta} +\usetikzlibrary{intersections} +\usetikzlibrary{patterns} +\usetikzlibrary{positioning} + + +% code print environment +\usepackage{listings} +\lstset{ + aboveskip=3mm, + belowskip=3mm, + showstringspaces=false, + columns=flexible, + rulecolor=\color{gray}, + backgroundcolor=\color{white}, + numbers=left, + numbersep=5pt, + numberstyle=\fontsize{8pt}{8pt}\selectfont\color{gray}\ttfamily, + breaklines=true, + postbreak=\raisebox{0ex}[0ex][0ex]{\ensuremath{\hookrightarrow\space}}, + breakatwhitespace=true, + tabsize=4, +} +\lstnewenvironment{codeprint}[1][10] % setting default code fontsize = \normalsize +{ + \lstset{% + frame=tlb, + frameround=fftt, + aboveskip=1em, + basicstyle=\fontsize{#1pt}{#1pt}\selectfont\ttfamily, + } +}{} + +\title{TikZ 坐标系统} +\author{Eureka} +\date{\today} + + +% \newcommand{\ddt}[2][]{\fill[#1] (#2) circle(1pt);} +\newcommand{\lrl}{~\ensuremath{\Longleftrightarrow}~} + + +\begin{document} +\maketitle +\tableofcontents +\clearpage + + +\section{基础知识} +常用的\verb|\draw,\fill,\shade|和\verb|\filldraw|命令,实际上 +都是带某些选项的\verb|\path|命令的简写,详情可以参见pgfmanual的p172的\verb|actions on paths|内容. +\begin{itemize} + \item \verb|\draw| \lrl\verb|\path[draw]| + \item \verb|\fill| \lrl\verb|\path[fill]| + \item \verb|\clip| \lrl\verb|\path[clip]| + \item \verb|\shade| \lrl\verb|\path[shade]| + \item \verb|\filldraw| \lrl\verb|\path[fill, draw]| + \item \verb|\node| \lrl \verb|\path node| +\end{itemize} + + +\subsection{draw命令} +\begin{itemize} + \item \textbf{tikz中坐标系的默认单位,通常是cm; 但是在scope中指定偏移时一定要带上cm单位,默认单位不对} + \item 相对坐标: \verb|+, ++|的区别, \verb|+|始终以第一个点为偏移参考点,这里每次的便宜参考点均为 $(0, 1)$;但是 + 在\verb|++|中,第二次的参考点即为 $(0, 1)+(1, -1)$. 以下分别为两幅图的代码: + \begin{verbatim} + \draw (0,1) -- +(1,-1) -- +(1,1); + \draw (0,1) -- ++(1,-1) -- +(1,1); + \end{verbatim} + \begin{center} + \begin{tikzpicture} + \draw[red] (0,1)node[left]{$(0, 1)$} -- +(1,-1) -- +(1,1); + \ShowPoint[color=red] {(0, 1)} + \end{tikzpicture} + \hspace*{8em} + \begin{tikzpicture} + \draw[blue] (0,1)node[left]{$(0, 1)$} -- ++(1,-1) -- +(1,1); + \ShowPoint[color=blue] {(0, 1)} + \end{tikzpicture} + \end{center} + \item 极坐标: \verb|(angle:distance)| + \item 坐标运算:需要导入\verb|calu|库: \verb|\usetikzlibrary{calc}|,使用格式为:\par + \verb|\draw (0,1) -- ($(0,1)-2*(-1,1)$);| + \item draw命令的复用:在一个\verb|\draw|中可以同时绘制多条线段,用法如下\par + \verb|\draw (0,0) -- (1,1) (0,1) -- (1,0);| + \item draw绘制闭合曲线:一定要加上 \verb|-- cycle;| + \item 绘制过两点的直角折线: \verb!\draw (0,0) |- (1,1);! 与 \verb!\draw (0,0) -| (1,1);! + \begin{center} + \begin{tikzpicture} + \draw (0,0)node[left]{$(0, 0)$} |- (1,1)node[right]{$(1, 1)$}; + \ShowPoint[color=gray] {(0, 0); (1, 1)} + \end{tikzpicture} + \hspace*{8em} + \begin{tikzpicture} + \draw (0,0)node[left]{$(0, 0)$} -| (1,1)node[right]{$(1, 1)$}; + \ShowPoint[color=gray] {(0, 0); (1, 1)} + \end{tikzpicture} + \end{center} + \item 网格线绘制: \verb|\draw[step=0.5] (0,0) grid (3,2);|x + \item draw绘制描点折线: \verb|\draw plot coordinates {(0,0) (1,2) (2,1) (4,2)};| +\end{itemize} + + +\subsection{node 命令} +\begin{itemize} + \item node 形状: \verb|\node[shape=rectangle]| + \item node 填充: \verb|\node[fill=red]|, 预先定义好的节点形状有三种:矩形(rectangle), 圆形(circle), 和点形(coordinate) + \item node 描边: \verb|\node[draw=red]|, 默认不描边,使用draw=none可以取消描边 + \item node 文本: \verb|\node[text=red]| + \item node 的anchor:默认为文本中心.% + \begin{tikzpicture} + \draw[fill=blue, draw=none] (0,0) circle (2pt); + \node[anchor=center] at (0,0) {CENTER}; + \end{tikzpicture} + \item node 文本位置: 需\verb|positioning|库,语法:\verb|\node[below right=8mm and 4mm] ...;| + \item node 连接点设置: 给定节点名称\verb|\node (a) at (x, y) {};|之后,\par + \verb|a.east, a.west, a.south, a.north, a.south|\par + \verb|east, a.south west, a.north east, a.north west| + 均可使用. + \item coordinate:和node的突然标注类似,我们也可以使用coordinate进行临时标记,语法如下: + \verb|\draw (1, 1)node[]{} -- (2, 2)coordinate(c);| + 然后我们在之后便可以使用\verb|(c)|这个点,甚至可以这样:\par + \verb|\draw (1, 1) -- (2, 2)coordinate(c)node[left]{node $c$};| +\end{itemize} + + +\subsection{Curvels} +\begin{itemize} + \item arc:arc命令有时是极为方便的,基本的参数中 + \item Bessel curvel\par + 此时需要将\verb|\draw|中的\verb|--|操作改为\verb|..|操作, 添加曲线切线公共点, + 即\verb|control|命令,于是完整的命令为: + \begin{verbatim} + \draw (0,0) .. controls (1,1) .. (4,0); + \end{verbatim} + \begin{center} + \begin{tikzpicture} + \draw[blue] (0,0) .. controls (1,1) .. (4,0); + \ShowPoint[color=red] {(1, 1)} + \end{tikzpicture} + \end{center} + + \begin{verbatim} + \draw (0,0) .. controls (1,1) and (2,1) .. (4,0); + \end{verbatim} + \begin{center} + \begin{tikzpicture} + \draw[blue] (0,0) .. controls (1,1) and (2,1) .. (4,0); + \ShowPoint[color=red] {(1, 1); (2, 1)} + \end{tikzpicture} + \end{center} + + \item in 和 out \par + 使用另外一种方式,使用 \verb|in, out|两参数设置初值和结束角度: + \begin{verbatim} + \draw[green] (-6, -4) to[out=60, in=-120] (-2, -4); + \end{verbatim} + \begin{center} + \begin{tikzpicture} + \draw[green] (-2, 0) to[out=60, in=-120] (2, 0); + \draw (-3, 0) -- (3, 0); + \draw[dashed] (-2, 0) -- +(60:.5) -- +(-120:.5); + \draw[dashed] (2, 0) -- +(60:.5) -- +(-120:.5); + \ShowPoint[color=red] {(-2, 0); (2, 0)} + \end{tikzpicture} + \end{center} + \item 描点曲线\par + 给 plot 操作加上 smooth 选项将用光滑曲线连接各点.而 tension + 选项描述该光滑曲线的绷紧度,取值范围为从 0 到 1,默认值为 0.55.\par + \verb|\draw[color=red] plot[smooth, tension=.9] coordinates ...;| + \begin{center} + \begin{tikzpicture}[>=Latex] + \draw[->] (0,0) -- (4,0); + \draw[->] (0,0) -- (0,2); + \draw[color=red] plot[smooth] coordinates {(0,0) (1,2) (2,1) (4,2)}; + \draw[color=green] plot[smooth, tension=.9] coordinates {(0,0) (1,2) (2,1) (4,2)}; + \ShowPoint[color=blue] {(0, 0); (1, 2); (2, 1); (4, 2)} + \end{tikzpicture} + \end{center} + \item smooth cycle\par + 如果将选项 smooth 改为 smooth cycle,将绘制一条闭合曲线.\par +\begin{codeprint} +\begin{tikzpicture}[smooth cycle] + \draw plot[tension=0] + coordinates {(0,1) (1,0) (2,1) (1,2)}; + \draw[xshift=3cm] plot[tension=0.3] + coordinates{(0,1) (1,0) (2,1) (1,2)}; + \draw[xshift=6cm] plot[tension=0.7] + coordinates{(0,1) (1,0) (2,1) (1,2)}; + \draw[xshift=9cm] plot[tension=1] + coordinates{(0,1) (1,0) (2,1) (1,2)}; +\end{tikzpicture} +\end{codeprint} + \begin{center} + \begin{tikzpicture}[smooth cycle] + \draw plot[tension=0, draw=red] + coordinates {(0,1) (1,0) (2,1) (1,2)}; + \draw[xshift=3cm, draw=blue] plot[tension=0.3] + coordinates{(0,1) (1,0) (2,1) (1,2)}; + \draw[xshift=6cm, draw=orange] plot[tension=0.7] + coordinates{(0,1) (1,0) (2,1) (1,2)}; + \draw[xshift=9cm, draw=cyan] plot[tension=1] + coordinates{(0,1) (1,0) (2,1) (1,2)}; + \end{tikzpicture} + \end{center} +\end{itemize} + +\subsection{positioning库} +\begin{itemize} + \item node文本同时指定多方向偏移量: \verb|\node[below right=8mm and 4mm] ...;| + \item node文本偏移量可为数学表达式: \verb|\node[below=8mm/2+4pt*2] ...;| + \item node节点之间的相对位置:\verb|\node[fill=gray,right=1cm of a] (b) {B};| +\end{itemize} + + + + +\subsection{路径交点} +此时你需要使用intersections库, \verb|\usetikzlibrary{intersections}|,使用语法为: +\begin{codeprint} +% Name the coordinates, but do not draw anything: +\path [name intersections={of= and }]; +\coordinate (C) at (intersection-1); +\end{codeprint} + +\begin{itemize} + \item 示例 1:在循环中使用 +\begin{codeprint} +\begin{tikzpicture}[ + every node/.style={black,above right}, + smooth cycle, scale=3 + ] + \draw[draw=orange, name path=line 1] plot[tension=0.3] + coordinates{(0, 0) (0,1) (1,1) (1,0)}; + \draw[draw=green, name path=line 2] + (.25, -.25) rectangle (.75,1.25); + \fill[red,name intersections={of=line 1 and line 2,total=\t}] + \foreach \s in {1,...,\t} + {(intersection-\s) circle (1pt) node {\footnotesize\s}}; +\end{tikzpicture} +\end{codeprint} + \begin{center} + \begin{tikzpicture}[every node/.style={black,above right}, smooth cycle, >=Latex] + % coordinate + \draw[help lines] (-1.5, -1.5) grid (1.5, 1.5); + \draw[->] (-1.5, 0) -- (1.5, 0); + \draw[->] (-1, -1.5) -- (-1, 1.5); + \begin{scope}[scale=1] + % two paths + \draw[draw=orange, name path=line 1] plot[tension=0.3] + coordinates{(0, 0) (0,1) (1,1) (1,0)}; + \draw[draw=green, name path=line 2] (.25, -.25) rectangle (.75,1.25); + \fill[red,name intersections={of=line 1 and line 2,total=\t}] + \foreach \s in {1,...,\t}{(intersection-\s) circle (1pt) node {\footnotesize\s}}; + \end{scope} + + \end{tikzpicture} + \end{center} + + + \item 示例 2:不显式调用(不用设置变量来接受返回值),使用\verb|intersection-| + 表示第\verb||个交点. +\begin{codeprint} +\begin{tikzpicture} + \draw[orange, name path=line 1] (-2, -2) -- (2, 2); + \draw[green, name path=circle 1] (0, 0) circle (2); + % get the intersections(by don't get it by return value) + \path[name intersections={of=line 1 and circle 1}]; + \fill[red] (intersection-1) circle (1pt); + \fill[blue] (intersection-2) circle (1pt); +\end{tikzpicture} +\end{codeprint} + \begin{center} + \begin{tikzpicture}[>=Latex] + % coordinate + \draw[help lines] (-3, -3) grid (3, 3); + \draw[->] (-3, 0) -- (3, 0); + \draw[->] (0, -3) -- (0, 3); + % two paths + \draw[orange, name path=line 1] (-2, -2) -- (2, 2); + \draw[green, name path=circle 1] (0, 0) circle (2); + % get the intersections(by don't get it by return value) + \path[name intersections={of=line 1 and circle 1}]; + \fill[red] (intersection-1) circle (1pt); + \fill[blue] (intersection-2) circle (1pt); + \end{tikzpicture} + \end{center} + \item 示例 3:不同scope之间共享, 此时需要把原始的 \par + \verb|name path=| $\longrightarrow$ \verb|name path global=|, + 下面及一个最小示例: +\begin{codeprint} +\begin{tikzpicture}[>=Latex] + \draw[help lines] (-4, -4) grid (4, 4); + \draw[->] (-4, 0) -- (4, 0); + \draw[->] (0, -4) -- (0, 4); + \begin{scope} + \draw[green, name path global=line 1] (-2, -2) -- (3, 3); + \end{scope} + \begin{scope}[xshift=2cm] + \draw[green, name path global=line 2] (-1, 2) -- (1, -2); + \end{scope} + % out of scope to get the intersections + \path[name intersections={of=line 1 and line 2}]; + \fill[red] (intersection-1) circle (1pt); +\end{tikzpicture} +\end{codeprint} + \begin{center} + \begin{tikzpicture}[>=Latex] + \draw[help lines] (-4, -4) grid (4, 4); + \draw[->] (-4, 0) -- (4, 0); + \draw[->] (0, -4) -- (0, 4); + \begin{scope} + \draw[green, name path global=line 1] (-2, -2) -- (3, 3); + \end{scope} + \begin{scope}[xshift=2cm] + \draw[green, name path global=line 2] (-1, 2) -- (1, -2); + \end{scope} + % out of scope to get the intersections + \path[name intersections={of=line 1 and line 2}]; + \fill[red] (intersection-1) circle (1pt); + \end{tikzpicture} + \end{center} +\end{itemize} + + +\subsection{路径剪裁} +对于要使用填充功能的用户来说,路径剪裁是必须知道的,最起码得知道 +\verb|\clip|命令。不要认为这个命令很复杂,实际上你把这个clip裁剪的区域 +看作\textbf{定义域}即可,之后所有的绘图,或者是填充均只会出现在定义域,也即clip区域, +也就是和clip做交集得到的区域. + + + +\clearpage +\subsection{支持函数} +这里有一个关于函数写法注意事项: +\textbf{只要你的函数表达式含有(),那么你的怎么函数表达式就需要使用}\verb|{}|\textbf{来包围.} + +比如下面的正确示例: +\begin{codeprint} +\draw[smooth, purple, domain=-6.927:6.927] plot (\x, {sqrt(16 - pow(\x, 2)/3)}); +\end{codeprint} + +加入你写作下面这样就是错误的: +\begin{codeprint} +\draw[smooth, purple, domain=-6.927:6.927] plot (\x, sqrt(16 - pow(\x, 2)/3)); +\end{codeprint} + +PGF(TiKZ) 的数学引擎支持下面这些数学函数: +\begin{center} + \begin{tabular}{ccccc} + \hline + abs & cot & hex & neg & rnd \\ + acos & deg & Hex & not & round \\ + add & depth & int & notequal & sec \\ + and & div & ifthenelse & notgreater & sin \\ + array & divide & less & notless & sinh \\ + asin & e & ln & oct & sqrt \\ + atan & equal & log10 & or & subtract \\ + atan2 & factorial & log2 & pi & tan \\ + bin & false & max & pow & tanh \\ + ceil & floor & min & rad & true \\ + cos & frac & mod & rand & veclen \\ + cosec & greater & Mod & random & width \\ + cosh & height & multiply & real & \\ + \hline + \end{tabular} +\end{center} + + + +\clearpage +\section{绘图库\texttt{2d\_plot}} +\subsection{基础命令} +这里主要是依靠Geogebra来估计交点的坐标,当然前面已经提到,我们可以使用自带的intersection库进行交点的求解. +本库的基本命令有以下函数提供: +\begin{itemize} + \item \verb|\NormalPlot| + \item \verb|\ParamPlot| + \item \verb|\ShowPoint| + \item \verb|\ShowIntersections| + \item \verb|\ShowGrid| + \item \verb|\NormalPlotPrecise| + \item \verb|\ParamPlotPrecise| +\end{itemize} + +由于pgfplots包太过于底层,且个人感觉没有tikz方便,于是本人没有对pgfplots宏包下 +太大的功夫. + +\subsection{函数绘制} +同时这里为了解决tikz自身的计算能力不足问题,我自定义了两个命令: +\begin{codeprint} +\NormalPlot[<\draw cmd's option>][]{<2d function>} +\ParamPlot[<\draw cmd's option>][]{<2d param function>} +\end{codeprint} + + +\subsection{阴影描绘} +同样的也是基于上面的两个命令\verb|\NormalPlot, \ParamPlot|进行阴影的绘制。此时我们有了两个新的命令 +\begin{verbatim} + \NormalFill[][] {a set of function} + \ParamFill[][] {a set of param function} +\end{verbatim} + + +\subsection{绘制精度} +并且有如下的备用选项命令\verb|\ParamPlotPrecise|, \verb|\NormalPlotPrecise|, 用于设置 +绘图的采样精度,默认在给定区间内平均采样1000个点,可以使用如下命令进行这个参数的更改 +\begin{codeprint} +\NormalPlotPrecise{10} % 更改NarmalPlot采样精度为10个点 +\ParamPlotPrecise{10} % 更改ParamlPlot采样精度为10个点 +\end{codeprint} + +注意:改变精度命令仅对当前绘图函数的紧邻的第一个绘图命令有影响,不会影响之后的所有绘图命令的 +采样精度。如果想要更改之后所有绘图的采样率可以设置默认的影响范围参数\verb|once|为\verb|after|. +但是目前的话,只要你可选参数填的不是once,那么它都是会改变之后的所有采样精度的. +两命令并没有用到pgfplots宏包\verb|axis|环境. + + +\subsection{点的标注} +使用自定义的\verb|2d_plot|库,可以避免自己进行如下的繁杂代码书写: +\begin{codeprint} +% 1.original plot method for parametric function +\draw[smooth, purple, domain=-6.927:6.927] plot (\x, {sqrt(16 - pow(\x, 2)/3)}); +\draw[smooth, purple, domain=-6.927:6.927] plot (\x, -{sqrt(16 - pow(\x, 2)/3)}); + +% 2.use gnuplot gnerate data +\draw plot[smooth] file {./data.table}; +\draw[red] plot[smooth] file {./param_data.table}; + +% 3.use pgfplots --> ticks is not the same +\begin{axis} + \addplot gnuplot[domain=-6:6] {-sqrt(16 - x^2/3)}; +\end{axis} +\end{codeprint} + +同时本绘图库还包含了基本的点的标注功能函数\verb|\ShowPoint|,使用参数如下: +\begin{codeprint} + \ShowPoint[radius=3pt, color=blue, opacity=.5, style=circle] + {(1, 1); (2, 2)}[text1; text2; text3][above left]; +\end{codeprint} + +其中的每一个点的标注文本\verb|text_i|是可以省略或者是多于欲标注的点的个数的。最后的 +\verb|

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