行进立方体 - 获得倾斜的表面
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【中文标题】行进立方体 - 获得倾斜的表面【英文标题】：Marching Cubes - Getting Skewed Surfaces 【发布时间】：2021-06-01 16:13:58 【问题描述】：我尝试绘制 Paul Brouke (http://paulbourke.net/geometry/polygonise/) 的 Marching cube LUT 生成的所有等值面。我通过 triTable LUT 选择了顶点作为边缘的中点。我得到了这些高度倾斜的表面，我试图弄清楚我是否犯了任何错误。这是 matlab 代码。
我得到的结果似乎不是 MC 应该提供的 14 种独特配置的对称性。我想知道我哪里出错了。我确信 LUT 是正确的，因为来源有被广泛使用..
function visualize
clear all
close all
clc
for id =1:256
fig = figure('color',[1 1 1]);
[vertices,faces] = mc(id);
[rows,cols]=size(vertices);
patch('vertices',vertices,'faces',faces,'edgecolor',[0 0 0],...
'facecolor',[1 0 0],'facelighting','phong')
box on
ax = gca;
ax.BoxStyle = 'full';
axis([0 1 0 1 0 1])
set(gca,'linewidth',2)
title(strcat(num2str(id),'(',num2str(round(rows/3)),' Triangles)'));
xlabel('X')
ylabel('Y')
zlabel('Z')
view(3)
camup([0 0 1])
fname = strcat('outputs/',num2str(id),'.png');
saveas(gcf,fname)
pause()
close(fig)
end
end
%id can be from 0-256 configuration
function [vertices,faces] = mc(id)
triTable = [
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1;
3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1;
3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1;
3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1;
9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1;
1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1;
9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1;
2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1;
8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1;
9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1;
4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1;
3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1;
1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1;
4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1;
4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1;
9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1;
1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1;
5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1;
2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1;
9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1;
0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1;
2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1;
10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1;
4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1;
5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1;
5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1;
9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1;
0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1;
1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1;
10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1;
8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1;
2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1;
7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1;
9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1;
2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1;
11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1;
9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1;
5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1;
11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1;
11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1;
1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1;
9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1;
5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1;
2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1;
0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1;
5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1;
6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1;
0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1;
3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1;
6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1;
5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1;
1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1;
10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1;
6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1;
1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1;
8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1;
7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1;
3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1;
5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1;
0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1;
9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1;
8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1;
5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1;
0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1;
6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1;
10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1;
10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1;
8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1;
1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1;
3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1;
0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1;
10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1;
0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1;
3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1;
6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1;
9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1;
8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1;
3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1;
6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1;
0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1;
10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1;
10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1;
1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1;
2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1;
7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1;
7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1;
2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1;
1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1;
11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1;
8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1;
0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1;
7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1;
10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1;
2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1;
6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1;
7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1;
2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1;
1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1;
10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1;
10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1;
0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1;
7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1;
6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1;
8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1;
9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1;
6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1;
1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1;
4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1;
10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1;
8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1;
0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1;
1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1;
8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1;
10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1;
4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1;
10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1;
5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1;
11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1;
9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1;
6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1;
7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1;
3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1;
7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1;
9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1;
3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1;
6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1;
9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1;
1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1;
4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1;
7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1;
6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1;
3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1;
0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1;
6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1;
1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1;
0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1;
11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1;
6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1;
5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1;
9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1;
1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1;
1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1;
10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1;
0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1;
5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1;
10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1;
11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1;
0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1;
9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1;
7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1;
2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1;
8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1;
9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1;
9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1;
1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1;
9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1;
9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1;
5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1;
0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1;
10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1;
2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1;
0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1;
0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1;
9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1;
5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1;
3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1;
5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1;
8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1;
0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1;
9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1;
0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1;
1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1;
3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1;
4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1;
9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1;
11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1;
11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1;
2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1;
9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1;
3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1;
1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1;
4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1;
4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1;
0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1;
3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1;
3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1;
0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1;
9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1;
1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1;
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
]+1;
edgeConnection = [
0,1;
1,3;
2,3;
0,2;
4,5;
5,7;
6,7;
4,6;
0,4;
1,5;
3,7;
2,6]+1;
vertexList = [
0,0,0;
1,0,0;
0,1,0;
1,1,0;
0,0,1;
1,0,1;
0,1,1;
1,1,1];
edgeDim = [
0;
1;
0;
1;
0;
1;
0;
1;
2;
2;
2;
2;
]+1;
dummy = triTable(id,:);
vertices = [];
faces = [];
for i=0:4
if dummy(3*i+1)==0
break;
end
for k=1:3 %3verticies for triangle
vertex = [0,0,0];
for j=1:3 %3 Dim
if edgeDim(dummy(3*i+k))==j
vertex(j) = 0.5*(vertexList(edgeConnection(dummy(3*i+k),1),j)+vertexList(edgeConnection(dummy(3*i+k),2),j));
else
vertex(j) = vertexList(edgeConnection(dummy(3*i+k),1),j);
end
end
vertices = [vertices;vertex];
end
faces = [faces;[3*i+1,3*i+2,3*i+3]];
end
end
【问题讨论】：
问题是什么？ 这是MC的工作方式还是我做错了什么 通常为 3D MC 显示的 14 种独特的表面配置中没有一个显示出这种偏斜度 1) 有没有什么暗示你这不是它的工作方式？你带来了代码，有一个最小的假设是你编写了这个代码来使 MC 工作。 2）有什么暗示你做错了什么吗？ 你能定义偏度吗？你不只是被立方体的形状弄糊涂了吗 (axis square?) 为什么你不将你的东西与大量已经存在的代码进行适当的比较（即它们是相同的表面）而不是使用模糊的术语？
【参考方案1】：
我犯了一个愚蠢的错误，即用不同的编号符号定义 EdgeConnection 和 vertexList...我现在已经编辑了问题中的代码，它现在可以工作了
非常感谢@Ander Biguri 在调试期间为我指明了正确的方向
【讨论】：
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