c++写一个判断三维空间中判断射线与平面是否相交

下面是一个简单的 C++ 代码实现：

#include <iostream>
#include <cmath>

using namespace std;

struct Vector3
{
    double x, y, z;

    Vector3() {}
    Vector3(double x, double y, double z) : x(x), y(y), z(z) {}

    Vector3 operator+(const Vector3& other) const
    {
        return Vector3(x + other.x, y + other.y, z + other.z);
    }

    Vector3 operator-(const Vector3& other) const
    {
        return Vector3(x - other.x, y - other.y, z - other.z);
    }

    Vector3 operator*(double scalar) const
    {
        return Vector3(x * scalar, y * scalar, z * scalar);
    }

    double dot(const Vector3& other) const
    {
        return x * other.x + y * other.y + z * other.z;
    }

    Vector3 cross(const Vector3& other) const
    {
        return Vector3(y * other.z - z * other.y, z * other.x - x * other.z, x * other.y - y * other.x);
    }

    double length() const
    {
        return sqrt(x * x + y * y + z * z);
    }
};

struct Ray
{
    Vector3 origin, direction;

    Ray() {}
    Ray(const Vector3& origin, const Vector3& direction) : origin(origin), direction(direction) {}
};

struct Plane
{
    Vector3 point, normal;

    Plane() {}
    Plane(const Vector3& point, const Vector3& normal) : point(point), normal(normal) {}
};

bool intersect(const Ray& ray, const Plane& plane, double& t)
{
    double denom = plane.normal.dot(ray.direction);
    if (abs(denom) < 1e-6) // 判断是否平行
        return false;

    t = plane.normal.dot(plane.point - ray.origin) / denom;

    return t >= 0;
}

int main()
{
    // 示例：射线由点(0, 0, 0)出发，方向为(1, 1, 1)；平面上的一点为(0, 0, 1)，法向量为(0, 0, 1)
    Ray ray(Vector3(0, 0, 0), Vector3(1, 1, 1));
    Plane plane(Vector3(0, 0, 1), Vector3(0, 0, 1));

    double t;
    if (intersect(ray, plane, t))
    {
        Vector3 intersection = ray.origin + ray.direction * t;
        cout << "Intersection point: (" << intersection.x << ", " << intersection.y << ", " << intersection.z << ")" << endl;
    }
    else
    {
        cout << "No intersection." << endl;
    }

    return 0;
}

这里我们定义了三个结构体：`Vector3` 表示三维向量，`Ray` 表示射线，`Plane` 表示平面。`intersect` 函数判断射线与平面是否相交，并返回相交参数t。在主函数中，我们给出了一个示例并输出相交点的坐标。