c++红枣Delaunay三角剖分算法代码

下面是一个基于C++的红枣Delaunay三角剖分算法的代码示例：

#include <iostream>
#include <vector>
#include <algorithm>

struct Point {
    double x, y;
};

struct Triangle {
    Point p1, p2, p3;
};

double cross_product(Point p1, Point p2, Point p3) {
    return (p2.x - p1.x) * (p3.y - p1.y) - (p3.x - p1.x) * (p2.y - p1.y);
}

bool in_circle(Point p, Triangle tri) {
    double d1 = (p.x - tri.p1.x) * (p.x - tri.p1.x) + (p.y - tri.p1.y) * (p.y - tri.p1.y);
    double d2 = (p.x - tri.p2.x) * (p.x - tri.p2.x) + (p.y - tri.p2.y) * (p.y - tri.p2.y);
    double d3 = (p.x - tri.p3.x) * (p.x - tri.p3.x) + (p.y - tri.p3.y) * (p.y - tri.p3.y);

    double det = tri.p1.x * (tri.p2.y * tri.p3.y - tri.p3.y * tri.p2.y)
                 - tri.p2.x * (tri.p1.y * tri.p3.y - tri.p3.x * tri.p1.y)
                 + tri.p3.x * (tri.p1.y * tri.p2.y - tri.p2.x * tri.p1.y);

    if (det == 0.0) {
        return false;  // The points are collinear, can't form a circle
    }

    double xc = (d1 * (tri.p2.y * tri.p3.y - tri.p3.y * tri.p2.y)
                 - d2 * (tri.p1.y * tri.p3.y - tri.p3.x * tri.p1.y)
                 + d3 * (tri.p1.y * tri.p2.y - tri.p2.x * tri.p1.y)) / (2 * det);

    double yc = (tri.p1.x * (d2 * tri.p3.y - d3 * tri.p2.y)
                 - tri.p2.x * (d1 * tri.p3.y - d3 * tri.p1.y)
                 + tri.p3.x * (d1 * tri.p2.y - d2 * tri.p1.y)) / (2 * det);

    double r = std::sqrt((xc - p.x) * (xc - p.x) + (yc - p.y) * (yc - p.y));
    return r <= std::max(std::max(d1, d2), d3);
}

std::vector<Triangle> delaunay_triangulation(std::vector<Point>& points) {
    std::vector<Triangle> triangles;
    Triangle super_tri = {
        { -1e6, -1e6 },  // Super triangle vertices
        {  1e6, -1e6 },
        {    0,  1e6 }
    };
    triangles.push_back(super_tri);

    for (const auto& p : points) {
        std::vector<Triangle> invalid_triangles;

        for (const auto& tri : triangles) {
            if (in_circle(p, tri)) {
                invalid_triangles.push_back(tri);
            }
        }

        std::vector<Edge> polygon_edges;
        for (const auto& tri : invalid_triangles) {
            polygon_edges.push_back({ tri.p1, tri.p2 });
            polygon_edges.push_back({ tri.p2, tri.p3 });
            polygon_edges.push_back({ tri.p3, tri.p1 });
        }

        triangles.erase(std::remove_if(triangles.begin(), triangles.end(),
                                       [&](const Triangle& tri) {
                                           return std::find(invalid_triangles.begin(),
                                                            invalid_triangles.end(), tri) != invalid_triangles.end();
                                       }),
                        triangles.end());

        for (const auto& edge : polygon_edges) {
            triangles.push_back({ edge.p1, edge.p2, p });
        }
    }

    triangles.erase(std::remove_if(triangles.begin(), triangles.end(),
                                   [&](const Triangle& tri) {
                                       return tri.p1 == super_tri.p1 ||
                                              tri.p1 == super_tri.p2 ||
                                              tri.p1 == super_tri.p3 ||
                                              tri.p2 == super_tri.p1 ||
                                              tri.p2 == super_tri.p2 ||
                                              tri.p2 == super_tri.p3 ||
                                              tri.p3 == super_tri.p1 ||
                                              tri.p3 == super_tri.p2 ||
                                              tri.p3 == super_tri.p3;
                                   }),
                    triangles.end());

    return triangles;
}

int main() {
    std::vector<Point> points = { { 0, 0 }, { 1, 0 }, { 0, 1 }, { 1, 1 }, { 0.5, 0.5 } };

    std::vector<Triangle> triangles = delaunay_triangulation(points);

    for (const auto& tri : triangles) {
        std::cout << "(" << tri.p1.x << ", " << tri.p1.y << "), "
                  << "(" << tri.p2.x << ", " << tri.p2.y << "), "
                  << "(" << tri.p3.x << ", " << tri.p3.y << ")" << std::endl;
    }

    return 0;
}

这段代码实现了基于红枣Delaunay三角剖分算法的三角剖分过程。它首先定义了点和三角形的数据结构，并实现了计算叉积和判断点是否在三角形外接圆内的函数。然后，通过遍历所有点，进行三角形的插入和删除，最后得到剖分后的三角形集合。在主函数中，我们提供了一个简单的测试例子，用于演示该算法的使用。

注意：这只是一个简单的示例代码，并未考虑一些特殊情况和性能优化，仅供参考。实际应用中，可能需要根据具体需求进行适当的修改和优化。