一个正十二面体的基本顶点集合
#include <cmath>#include <vector>
struct Point3D {
double x, y, z;
};
// 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
std::vector<Point3D> initialVertices = {
{ 0.0, 0.0, 1.0 }, // North pole
{ 0.8944271909999159, 0.0, -0.4472135954999579 }, // Equatorial vertices
{-0.8944271909999159, 0.0, -0.4472135954999579 },
{ 0.2763932022500212, 0.8506508083520399, -0.4472135954999579 },
{ 0.2763932022500212, -0.8506508083520399, -0.4472135954999579 },
{-0.7236067977499788, 0.5257311121191336, -0.4472135954999579 },
{-0.7236067977499788, -0.5257311121191336, -0.4472135954999579 },
{ 0.7236067977499788, 0.5257311121191336, 0.4472135954999579 },
{ 0.7236067977499788, -0.5257311121191336, 0.4472135954999579 },
{-0.2763932022500212, 0.8506508083520399, 0.4472135954999579 },
{-0.2763932022500212, -0.8506508083520399, 0.4472135954999579 }
};
void subdivide(std::vector<Point3D>& vertices, std::vector<std::array<int, 3>>& faces) {
std::vector<Point3D> newVertices;
std::vector<std::array<int, 3>> newFaces;
for (const auto& face : faces) {
// 中心点索引
int centerIndex = vertices.size();
// 计算三角形中心点
Point3D center = {
(vertices].x + vertices].x + vertices].x) / 3.0,
(vertices].y + vertices].y + vertices].y) / 3.0,
(vertices].z + vertices].z + vertices].z) / 3.0
};
// 投影到单位球面上
double length = std::sqrt(center.x * center.x + center.y * center.y + center.z * center.z);
if (length > 1e-6) {
center.x /= length;
center.y /= length;
center.z /= length;
}
// 添加新的顶点
vertices.push采用back(center);
// 创建四个新的面
newFaces.push采用back({ face, centerIndex, face });
newFaces.push采用back({ face, centerIndex, face });
newFaces.push采用back({ face, centerIndex, face });
newFaces.push采用back({ centerIndex, face, face });
// 移除旧的面
}
// 替换旧的面和顶点数据
faces.swap(newFaces);
}
int main() {
// 初始化基本的正十二面体顶点和面片
std::vector<Point3D> vertices(initialVertices.begin(), initialVertices.end());
std::vector<std::array<int, 3>> faces; // 填充正十二面体的各个面
// 对初始网格进行多次细分以得到更细密的网格
for (int i = 0; i < desiredSubdivisionLevels; ++i) {
subdivide(vertices, faces);
}
// 输出最终的网格顶点和面信息
// ...
return 0;
}
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