c++判断两条三维线段是否相交的函数

以下是一个简单的 C++ 函数，用于判断两条三维线段是否相交：

#include <iostream>
#include <cmath>
using namespace std;

struct Point3D {
    double x, y, z;
};

bool isIntersected(Point3D p1, Point3D p2, Point3D p3, Point3D p4) {
    Point3D p13, p43, p21;
    double d1343, d4321, d1321, d4343, d2121;
    double numer, denom;
    const double EPSILON = 0.0000001;

    p13.x = p1.x - p3.x;
    p13.y = p1.y - p3.y;
    p13.z = p1.z - p3.z;
    p43.x = p4.x - p3.x;
    p43.y = p4.y - p3.y;
    p43.z = p4.z - p3.z;
    if (fabs(p43.x) < EPSILON && fabs(p43.y) < EPSILON && fabs(p43.z) < EPSILON)
        return false;
    p21.x = p2.x - p1.x;
    p21.y = p2.y - p1.y;
    p21.z = p2.z - p1.z;
    if (fabs(p21.x) < EPSILON && fabs(p21.y) < EPSILON && fabs(p21.z) < EPSILON)
        return false;

    d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
    d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
    d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
    d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
    d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;

    denom = d2121 * d4343 - d4321 * d4321;
    if (fabs(denom) < EPSILON)
        return false;
    numer = d1343 * d4321 - d1321 * d4343;

    double mua = numer / denom;
    double mub = (d1343 + d4321 * mua) / d4343;

    Point3D pa, pb;
    pa.x = p1.x + mua * p21.x;
    pa.y = p1.y + mua * p21.y;
    pa.z = p1.z + mua * p21.z;
    pb.x = p3.x + mub * p43.x;
    pb.y = p3.y + mub * p43.y;
    pb.z = p3.z + mub * p43.z;

    double dist = sqrt((pa.x - pb.x) * (pa.x - pb.x) + (pa.y - pb.y) * (pa.y - pb.y) + (pa.z - pb.z) * (pa.z - pb.z));
    if (dist < EPSILON)
        return true;
    else
        return false;
}

int main() {
    Point3D p1 = {0, 0, 0};
    Point3D p2 = {1, 1, 1};
    Point3D p3 = {0, 1, 0};
    Point3D p4 = {1, 0, 1};
    if (isIntersected(p1, p2, p3, p4)) {
        cout << "The two line segments intersect." << endl;
    } else {
        cout << "The two line segments do not intersect." << endl;
    }
    return 0;
}

该函数的输入是两个三维线段的端点坐标，输出是一个布尔值，表示它们是否相交。如果相交，返回 `true`，否则返回 `false`。

该函数使用了两条线段的参数方程，通过求解它们的交点来判断它们是否相交。如果交点在两条线段之间，则它们相交，否则它们不相交。

该函数还考虑了一些特殊情况，例如两条线段重合、平行、退化为点或直线等。