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->point2VP12.x = TrianglePoint2.x - TrianglePoint1.x;VP12.y = TrianglePoint2.y - TrianglePoint1.y;VP12.z = TrianglePoint2.z - TrianglePoint1.z;//point1->point3VP13.x = TrianglePoint3.x - TrianglePoint1.x;VP13.y = TrianglePoint3.y - TrianglePoint1.y;VP13.z = TrianglePoint3.z - TrianglePoint1.z;//VP12xVP13TriangleV.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tfloat 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1float area2 = Area(c1, c3, d13); //子三角形2float 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;
}