所以我有一個腳本可以產生代表離散半球的點圖和三角形元素：
請參閱下面的程式碼。現在我想知道是否有一些好的方法來繪製這個半球並根據透視區分可見線和隱藏線？正如您所看到的，它幾乎可以工作，但這只是因為解析三角形的順序。
編輯：現在所有點和單元格都包含在內。
\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{60}{125}
%
\pgfmathsetmacro{\rvec}{1.5}
\pgfmathsetmacro{\thetavec}{30}
\pgfmathsetmacro{\phivec}{45}
%
\begin{tikzpicture}[scale=3,tdplot_main_coords]
% Coordinate axes
\draw[thick,->] (0,0,0) -- (-1,0,0) node[anchor=south]{$z$};
\draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$x$};
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$y$};
% Points
\coordinate (p0) at (0,1,0);
\coordinate (p1) at (0,0,-1);
\coordinate (p2) at (-1,0,0);
\coordinate (p3) at (0,0,1);
\coordinate (p4) at (1,0,0);
\coordinate (p5) at (0,0.707107,-0.707107);
\coordinate (p6) at (0.707107,0,-0.707107);
\coordinate (p7) at (0.707107,0.707107,0);
\coordinate (p8) at (-0.707107,0,-0.707107);
\coordinate (p9) at (-0.707107,0.707107,0);
\coordinate (p10) at (-0.707107,0,0.707107);
\coordinate (p11) at (0,0.707107,0.707107);
\coordinate (p12) at (0.707107,0,0.707107);
\coordinate (p13) at (0,0.92388,-0.382683);
\coordinate (p14) at (0.408248,0.816497,-0.408248);
\coordinate (p15) at (0.382683,0.92388,0);
\coordinate (p16) at (0,0.382683,-0.92388);
\coordinate (p17) at (0.408248,0.408248,-0.816497);
\coordinate (p18) at (0.382683,0,-0.92388);
\coordinate (p19) at (0.816497,0.408248,-0.408248);
\coordinate (p20) at (0.92388,0,-0.382683);
\coordinate (p21) at (0.92388,0.382683,0);
\coordinate (p22) at (-0.408248,0.816497,-0.408248);
\coordinate (p23) at (-0.382683,0.92388,0);
\coordinate (p24) at (-0.408248,0.408248,-0.816497);
\coordinate (p25) at (-0.382683,0,-0.92388);
\coordinate (p26) at (-0.816497,0.408248,-0.408248);
\coordinate (p27) at (-0.92388,0,-0.382683);
\coordinate (p28) at (-0.92388,0.382683,0);
\coordinate (p29) at (-0.408248,0.816497,0.408248);
\coordinate (p30) at (0,0.92388,0.382683);
\coordinate (p31) at (-0.816497,0.408248,0.408248);
\coordinate (p32) at (-0.92388,0,0.382683);
\coordinate (p33) at (-0.408248,0.408248,0.816497);
\coordinate (p34) at (-0.382683,0,0.92388);
\coordinate (p35) at (0,0.382683,0.92388);
\coordinate (p36) at (0.408248,0.816497,0.408248);
\coordinate (p37) at (0.408248,0.408248,0.816497);
\coordinate (p38) at (0.382683,0,0.92388);
\coordinate (p39) at (0.816497,0.408248,0.408248);
\coordinate (p40) at (0.92388,0,0.382683);
% Triangular cells
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p0) -- (p13) -- (p15) -- (p0);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p5) -- (p13) -- (p14) -- (p5);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p13) -- (p14) -- (p15) -- (p13);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p7) -- (p14) -- (p15) -- (p7);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p1) -- (p16) -- (p18) -- (p1);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p5) -- (p16) -- (p17) -- (p5);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p16) -- (p17) -- (p18) -- (p16);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p6) -- (p17) -- (p18) -- (p6);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p5) -- (p17) -- (p14) -- (p5);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p6) -- (p17) -- (p19) -- (p6);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p17) -- (p19) -- (p14) -- (p17);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p7) -- (p19) -- (p14) -- (p7);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p4) -- (p20) -- (p21) -- (p4);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p6) -- (p20) -- (p19) -- (p6);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p20) -- (p19) -- (p21) -- (p20);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p7) -- (p19) -- (p21) -- (p7);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p0) -- (p13) -- (p23) -- (p0);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p5) -- (p13) -- (p22) -- (p5);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p13) -- (p22) -- (p23) -- (p13);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p9) -- (p22) -- (p23) -- (p9);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p1) -- (p16) -- (p25) -- (p1);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p5) -- (p16) -- (p24) -- (p5);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p16) -- (p24) -- (p25) -- (p16);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p8) -- (p24) -- (p25) -- (p8);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p5) -- (p24) -- (p22) -- (p5);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p8) -- (p24) -- (p26) -- (p8);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p24) -- (p26) -- (p22) -- (p24);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p9) -- (p26) -- (p22) -- (p9);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p2) -- (p27) -- (p28) -- (p2);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p8) -- (p27) -- (p26) -- (p8);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p27) -- (p26) -- (p28) -- (p27);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p9) -- (p26) -- (p28) -- (p9);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p0) -- (p23) -- (p30) -- (p0);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p9) -- (p23) -- (p29) -- (p9);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p23) -- (p29) -- (p30) -- (p23);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p11) -- (p29) -- (p30) -- (p11);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p2) -- (p28) -- (p32) -- (p2);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p9) -- (p28) -- (p31) -- (p9);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p28) -- (p31) -- (p32) -- (p28);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p10) -- (p31) -- (p32) -- (p10);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p9) -- (p31) -- (p29) -- (p9);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p10) -- (p31) -- (p33) -- (p10);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p31) -- (p33) -- (p29) -- (p31);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p11) -- (p33) -- (p29) -- (p11);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p3) -- (p34) -- (p35) -- (p3);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p10) -- (p34) -- (p33) -- (p10);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p34) -- (p33) -- (p35) -- (p34);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p11) -- (p33) -- (p35) -- (p11);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p0) -- (p30) -- (p15) -- (p0);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p11) -- (p30) -- (p36) -- (p11);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p30) -- (p36) -- (p15) -- (p30);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p7) -- (p36) -- (p15) -- (p7);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p3) -- (p35) -- (p38) -- (p3);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p11) -- (p35) -- (p37) -- (p11);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p35) -- (p37) -- (p38) -- (p35);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p12) -- (p37) -- (p38) -- (p12);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p11) -- (p37) -- (p36) -- (p11);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p12) -- (p37) -- (p39) -- (p12);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p37) -- (p39) -- (p36) -- (p37);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p7) -- (p39) -- (p36) -- (p7);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p4) -- (p40) -- (p21) -- (p4);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p12) -- (p40) -- (p39) -- (p12);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p40) -- (p39) -- (p21) -- (p40);
\draw[fill=green,draw=black,opacity=.8,very thin,line join=round] (p7) -- (p39) -- (p21) -- (p7);
\end{tikzpicture}
\end{document}
答案1
歡迎來到 TeX-SE！您必須根據點在可見線上的投影對點進行排序。好消息是它可以pgfplots為您做到這一點。您提供的資料格式幾乎可以完全適應。我所做的只是進行正規表示式搜尋和替換，以去除資料的重複元素，將它們放入表格中並繪製它們。上表對應於繪圖的下半部分，您可以在其中指定要連接的頂點，下表定義這些頂點。
\documentclass[tikz,border=3.14pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[view={135}{45},axis equal image,scale=4,
xmin=-1,xmax=1,ymin=-1,ymax=1,zmin=-1,zmax=1,
colormap={greenblue}{color=(green) color=(blue)}]
\addplot3 [patch,table/row sep=\\,patch table={
0 13 15 \\
5 13 14 \\
13 14 15 \\
7 14 15 \\
1 16 18 \\
5 16 17 \\
16 17 18 \\
6 17 18 \\
5 17 14 \\
6 17 19 \\
17 19 14 \\
7 19 14 \\
4 20 21 \\
6 20 19 \\
20 19 21 \\
7 19 21 \\
0 13 23 \\
5 13 22 \\
13 22 23 \\
9 22 23 \\
1 16 25 \\
5 16 24 \\
16 24 25 \\
8 24 25 \\
5 24 22 \\
8 24 26 \\
24 26 22 \\
9 26 22 \\
2 27 28 \\
8 27 26 \\
27 26 28 \\
9 26 28 \\
0 23 30 \\
9 23 29 \\
23 29 30 \\
11 29 30 \\
2 28 32 \\
9 28 31 \\
28 31 32 \\
10 31 32 \\
9 31 29 \\
10 31 33 \\
31 33 29 \\
11 33 29 \\
3 34 35 \\
10 34 33 \\
34 33 35 \\
11 33 35 \\
0 30 15 \\
11 30 36 \\
30 36 15 \\
7 36 15 \\
3 35 38 \\
11 35 37 \\
35 37 38 \\
12 37 38 \\
11 37 36 \\
12 37 39 \\
37 39 36 \\
7 39 36 \\
4 40 21 \\
12 40 39 \\
40 39 21 \\
7 39 21 \\
}] table [row sep=\\,point meta=\thisrow{c}] {
x y z c\\
0 1 0 0\\
0 0 -1 0\\
-1 0 0 0\\
0 0 1 0\\
1 0 0 0\\
0 0.707107 -0.707107 0\\
0.707107 0 -0.707107 0\\
0.707107 0.707107 0 0\\
-0.707107 0 -0.707107 0\\
-0.707107 0.707107 0 0\\
-0.707107 0 0.707107 0\\
0 0.707107 0.707107 0\\
0.707107 0 0.707107 0\\
0 0.92388 -0.382683 0\\
0.408248 0.816497 -0.408248 0\\
0.382683 0.92388 0 0\\
0 0.382683 -0.92388 0\\
0.408248 0.408248 -0.816497 0\\
0.382683 0 -0.92388 0\\
0.816497 0.408248 -0.408248 0\\
0.92388 0 -0.382683 0\\
0.92388 0.382683 0 0\\
-0.408248 0.816497 -0.408248 0\\
-0.382683 0.92388 0 0\\
-0.408248 0.408248 -0.816497 0\\
-0.382683 0 -0.92388 0\\
-0.816497 0.408248 -0.408248 0\\
-0.92388 0 -0.382683 0\\
-0.92388 0.382683 0 0\\
-0.408248 0.816497 0.408248 0\\
0 0.92388 0.382683 0\\
-0.816497 0.408248 0.408248 0\\
-0.92388 0 0.382683 0\\
-0.408248 0.408248 0.816497 0\\
-0.382683 0 0.92388 0\\
0 0.382683 0.92388 0\\
0.408248 0.816497 0.408248 0\\
0.408248 0.408248 0.816497 0\\
0.382683 0 0.92388 0\\
0.816497 0.408248 0.408248 0\\
0.92388 0 0.382683 0\\
};
\end{axis}
\end{tikzpicture}
\end{document}
如果您將視圖更改為view={45}{45}，您將獲得
也就是說，您保留調整您所了解的視圖的自由tikz-3dplot，但排序是自動完成的。