一个正十二面体的基本顶点集合

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1. #include <cmath>
2. #include <vector>
4. struct Point3D {
5.     double x, y, z;
6. };
8. // 初始十二个顶点坐标，它们是单位半径球面上正十二面体的顶点
9. std::vector<Point3D> initialVertices = {
10.     { 0.0, 0.0, 1.0 }, // North pole
11.     { 0.8944271909999159, 0.0, -0.4472135954999579 }, // Equatorial vertices
12.     {-0.8944271909999159, 0.0, -0.4472135954999579 },
13.     { 0.2763932022500212, 0.8506508083520399, -0.4472135954999579 },
14.     { 0.2763932022500212, -0.8506508083520399, -0.4472135954999579 },
15.     {-0.7236067977499788, 0.5257311121191336, -0.4472135954999579 },
16.     {-0.7236067977499788, -0.5257311121191336, -0.4472135954999579 },
17.     { 0.7236067977499788, 0.5257311121191336, 0.4472135954999579 },
18.     { 0.7236067977499788, -0.5257311121191336, 0.4472135954999579 },
19.     {-0.2763932022500212, 0.8506508083520399, 0.4472135954999579 },
20.     {-0.2763932022500212, -0.8506508083520399, 0.4472135954999579 }
21. };
23. void subdivide(std::vector<Point3D>& vertices, std::vector<std::array<int, 3>>& faces) {
24.     std::vector<Point3D> newVertices;
25.     std::vector<std::array<int, 3>> newFaces;
27.     for (const auto& face : faces) {
28.         // 中心点索引
29.         int centerIndex = vertices.size();
31.         // 计算三角形中心点
32.         Point3D center = {
33.             (vertices[face[0]].x + vertices[face[1]].x + vertices[face[2]].x) / 3.0,
34.             (vertices[face[0]].y + vertices[face[1]].y + vertices[face[2]].y) / 3.0,
35.             (vertices[face[0]].z + vertices[face[1]].z + vertices[face[2]].z) / 3.0
36.         };
37.         // 投影到单位球面上
38.         double length = std::sqrt(center.x * center.x + center.y * center.y + center.z * center.z);
39.         if (length > 1e-6) {
40.             center.x /= length;
41.             center.y /= length;
42.             center.z /= length;
43.         }
45.         // 添加新的顶点
46.         vertices.push采用back(center);
48.         // 创建四个新的面
49.         newFaces.push采用back({ face[0], centerIndex, face[2] });
50.         newFaces.push采用back({ face[1], centerIndex, face[0] });
51.         newFaces.push采用back({ face[2], centerIndex, face[1] });
52.         newFaces.push采用back({ centerIndex, face[1], face[2] });
54.         // 移除旧的面
55.     }
56.    
57.     // 替换旧的面和顶点数据
58.     faces.swap(newFaces);
59. }
61. int main() {
62.     // 初始化基本的正十二面体顶点和面片
63.     std::vector<Point3D> vertices(initialVertices.begin(), initialVertices.end());
64.     std::vector<std::array<int, 3>> faces; // 填充正十二面体的各个面
66.     // 对初始网格进行多次细分以得到更细密的网格
67.     for (int i = 0; i < desiredSubdivisionLevels; ++i) {
68.         subdivide(vertices, faces);
69.     }
71.     // 输出最终的网格顶点和面信息
72.     // ...
74.     return 0;
75. }

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