需求：

对于给定的三角形面片3个顶点，和一条直线的2个点，求三角面和直线的交点，若无交点，输出-1。

思路：

利用海伦公式，可以得到三角形的面积，然后用3个点的2个向量，进行叉乘，得到面的法向量。ax+by+cz=d可以表示面，求出常数d，联力面的方程和直线方程，求解交点。

代码：

class CVector
{
public:
    union
    {
        float vec[3];
        struct { float x, y, z; };
    };
};

class CrossPoint
{
public:
    CrossPoint();
    virtual ~CrossPoint();
public:
    static bool ValidPoint(CVector &LinePoint, CVector &LineV,
        CVector &TrianglePoint1, CVector &TrianglePoint2, CVector &TrianglePoint3, CVector &result);
    static float Area(float a, float b, float c);
    static float Distance(CVector &p1, CVector &p2);
};

///

CrossPoint::CrossPoint()
{

}

CrossPoint::~CrossPoint()
{

}
//计算p1到p2的距离的平方
float CrossPoint::Distance(CVector &p1, CVector &p2)
{
    float dist;
    dist = ((p2.x - p1.x)*(p2.x - p1.x)
        + (p2.y - p1.y)*(p2.y - p1.y)
        + (p2.z - p1.z)*(p2.z - p1.z));
    return (float)sqrt(dist);
}
//利用海伦公式求变成为a,b,c的三角形的面积
float CrossPoint::Area(float a, float b, float c)
{
    float s = (a + b + c) / 2;
    return (float)sqrt(s*(s - a)*(s - b)*(s - c));
}


bool CrossPoint::ValidPoint(CVector &LinePoint1, CVector &LinePoint2, CVector &TrianglePoint1, CVector

    &TrianglePoint2, CVector &TrianglePoint3, CVector &result)
{
    //三角形所在平面的法向量
    CVector TriangleV;
    //三角形的边方向向量
    CVector VP12, VP13;
    //直线与平面的交点
    CVector CrossPoint;
    //平面方程常数项
    float TriD;
    //CVector LineV = LinePoint2 - LinePoint1;
    CVector LineV;
    LineV.x = 0, LineV.y = 0, LineV.z = 100;
    /*-------计算平面的法向量及常数项-------*/
    //point1->point2
    VP12.x = TrianglePoint2.x - TrianglePoint1.x;
    VP12.y = TrianglePoint2.y - TrianglePoint1.y;
    VP12.z = TrianglePoint2.z - TrianglePoint1.z;
    //point1->point3
    VP13.x = TrianglePoint3.x - TrianglePoint1.x;
    VP13.y = TrianglePoint3.y - TrianglePoint1.y;
    VP13.z = TrianglePoint3.z - TrianglePoint1.z;
    //VP12xVP13
    TriangleV.x = VP12.y*VP13.z - VP12.z*VP13.y;
    TriangleV.y = -(VP12.x*VP13.z - VP12.z*VP13.x);
    TriangleV.z = VP12.x*VP13.y - VP12.y*VP13.x;
    //计算常数项
    TriD = -(TriangleV.x*TrianglePoint1.x
        + TriangleV.y*TrianglePoint1.y
        + TriangleV.z*TrianglePoint1.z);
    /*-------求解直线与平面的交点坐标---------*/
    /* 思路：
    * 首先将直线方程转换为参数方程形式，然后代入平面方程，求得参数t，
    * 将t代入直线的参数方程即可求出交点坐标
    */
    float tempU, tempD; //临时变量
    tempU = TriangleV.x*LinePoint1.x + TriangleV.y*LinePoint1.y
        + TriangleV.z*LinePoint1.z + TriD;
    tempD = TriangleV.x*LineV.x + TriangleV.y*LineV.y + TriangleV.z*LineV.z;
    //直线与平面平行或在平面上
    if (tempD == 0.0)
    {
        //printf("The line is parallel with the plane.\n");
        return false;
    }
    //计算参数t
    float t = -tempU / tempD;
    //计算交点坐标
    CrossPoint.x = LineV.x*t + LinePoint1.x;
    CrossPoint.y = LineV.y*t + LinePoint1.y;
    CrossPoint.z = LineV.z*t + LinePoint1.z;
    /*----------判断交点是否在三角形内部---*/

    //计算三角形三条边的长度
    float d12 = Distance(TrianglePoint1, TrianglePoint2);
    float d13 = Distance(TrianglePoint1, TrianglePoint3);
    float d23 = Distance(TrianglePoint2, TrianglePoint3);
    //计算交点到三个顶点的长度
    float c1 = Distance(CrossPoint, TrianglePoint1);
    float c2 = Distance(CrossPoint, TrianglePoint2);
    float c3 = Distance(CrossPoint, TrianglePoint3);
    //求三角形及子三角形的面积
    float areaD = Area(d12, d13, d23); //三角形面积
    float area1 = Area(c1, c2, d12); //子三角形1
    float area2 = Area(c1, c3, d13); //子三角形2
    float area3 = Area(c2, c3, d23); //子三角形3
                                     //根据面积判断点是否在三角形内部
    if (fabs(area1 + area2 + area3 - areaD) > 0.001)
    {
        return false;
    }

    result = CrossPoint;
    return true;
}

转载于:https://www.cnblogs.com/SeekHit/p/7061451.html