☰

生成 Delaunay 三角剖分

tag-icon • tag-icon tikz-pgf asymptote
生成 Delaunay 三角剖分

有人知道我如何通过输入随机生成的点列表在 tikz 中生成 2D Delaunay 三角剖分吗？或者至少有一个程序可以获取该列表并生成 tikz 输出。

答案1

其中一种方法是按照这个路线：asy=> svg=> TikZ。

文档中的这段d.asy代码Asymptote创建了随机点并建立了三角测量：

size(200);
int np=12;
pair[] points;
real r() {return 1.2*(rand()/randMax*2-1);}

srand(1234321);
for(int i=0; i < np; ++i) points.push((r(),r()));

int[][] trn=triangulate(points);
for(int i=0; i < trn.length; ++i) {
  draw(points[trn[i][0]]--points[trn[i][1]]);
  draw(points[trn[i][2]]--points[trn[i][2]]);
  draw(points[trn[i][2]]--points[trn[i][0]]);
}
for(int i=0; i < np; ++i) dot(points[i],red);

d.svg使用命令生成输出：

asy -f svg d.asy

然后将其转换TikZ为svg2tikz：

svg2tikz --standalone d.svg > d.tex

生成的d.tex文件如下所示：

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}

\begin{document}
\definecolor{cff0000}{RGB}{255,0,0}


\begin{tikzpicture}[y=0.80pt,x=0.80pt,yscale=-1, inner sep=0pt, outer sep=0pt]
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (39.9691,-90.7908) -- (43.3652,-100.6640);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (43.3652,-100.6640) -- (98.7641,-39.0366);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (98.7641,-39.0366) -- (39.9691,-90.7908);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (80.9286,65.0406) -- (-16.1836,36.7579);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-16.1836,36.7579) -- (98.7641,-39.0366);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (98.7641,-39.0366) -- (80.9286,65.0406);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-16.1836,36.7579) -- (39.9691,-90.7908);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (39.9691,-90.7908) -- (98.7641,-39.0366);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (98.7641,-39.0366) -- (-16.1836,36.7579);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-43.1652,96.4547) -- (-16.1836,36.7579);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-16.1836,36.7579) -- (35.5692,80.1023);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (35.5692,80.1023) -- (-43.1652,96.4547);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-98.9747,37.4920) -- (-48.7898,13.8156);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-48.7898,13.8156) -- (-43.1652,96.4547);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-43.1652,96.4547) -- (-98.9747,37.4920);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-78.9290,-89.2327) -- (-49.1180,-92.8069);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-49.1180,-92.8069) -- (-48.7898,13.8156);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-48.7898,13.8156) -- (-78.9290,-89.2327);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-98.9747,37.4920) -- (-78.9290,-89.2327);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-78.9290,-89.2327) -- (-48.7898,13.8156);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-48.7898,13.8156) -- (-98.9747,37.4920);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (77.7164,83.1456) -- (35.5692,80.1023);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (35.5692,80.1023) -- (80.9286,65.0406);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (80.9286,65.0406) -- (77.7164,83.1456);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (35.5692,80.1023) -- (-16.1836,36.7579);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-16.1836,36.7579) -- (80.9286,65.0406);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (80.9286,65.0406) -- (35.5692,80.1023);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-43.1652,96.4547) -- (-48.7898,13.8156);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-48.7898,13.8156) -- (-16.1836,36.7579);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-16.1836,36.7579) -- (-43.1652,96.4547);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (39.9691,-90.7908) -- (-49.1180,-92.8069);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-49.1180,-92.8069) -- (43.3652,-100.6640);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (43.3652,-100.6640) -- (39.9691,-90.7908);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-43.1652,96.4547) -- (35.5692,80.1023);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (35.5692,80.1023) -- (77.7164,83.1456);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (77.7164,83.1456) -- (-43.1652,96.4547);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-16.1836,36.7579) -- (-48.7898,13.8156);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-48.7898,13.8156) -- (39.9691,-90.7908);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (39.9691,-90.7908) -- (-16.1836,36.7579);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-48.7898,13.8156) -- (-49.1180,-92.8069);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (-49.1180,-92.8069) -- (39.9691,-90.7908);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[draw=black,line join=round,line cap=round,miter limit=10.04,line
      width=0.401pt] (39.9691,-90.7908) -- (-48.7898,13.8156);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (43.3652,-100.6640) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (35.5692,80.1023) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (80.9286,65.0406) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (-49.1180,-92.8069) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (77.7164,83.1456) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (-78.9290,-89.2327) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (39.9691,-90.7908) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (-48.7898,13.8156) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (98.7641,-39.0366) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (-43.1652,96.4547) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (-98.9747,37.4920) circle (0.0425cm);
  \end{scope}
  \begin{scope}[cm={{1.0,0.0,0.0,1.0,(157.101,156.23)}}]
    \path[fill=cff0000] (-16.1836,36.7579) circle (0.0425cm);
  \end{scope}

\end{tikzpicture}
\end{document}

照常处理：pdflatex d.tex给出输出：

在此处输入图片描述

相关内容