#include<string>#include<sstream>#include<fstream>#include<cstdio>#include<cstring>#include<iostream>#include<vector>#include<stack>#include<queue>#include<list>#include<algorithm>#include<ctime>#include<unordered_map>#include<map>#include<typeinfo>#include<cmath>#include<ctime>#include<climits>using namespace std;//类定义：二维向量
class Vector2d
{
public:double x_;double y_;public:Vector2d(double x, double y):x_(x), y_(y){}Vector2d():x_(0), y_(0){}//二维向量叉乘, 叉乘的结果其实是向量，方向垂直于两个向量组成的平面，这里我们只需要其大小和方向double CrossProduct(const Vector2d vec){return x_*vec.y_ - y_*vec.x_;}//二维向量点积double DotProduct(const Vector2d vec){return x_ * vec.x_ + y_ * vec.y_;}//二维向量减法Vector2d Minus(const Vector2d vec) const{return Vector2d(x_ - vec.x_, y_ - vec.y_);}//判断点M,N是否在直线AB的同一侧static bool IsPointAtSameSideOfLine(const Vector2d &pointM, const Vector2d &pointN, const Vector2d &pointA, const Vector2d &pointB){Vector2d AB = pointB.Minus(pointA);Vector2d AM = pointM.Minus(pointA);Vector2d AN = pointN.Minus(pointA);//等于0时表示某个点在直线上return AB.CrossProduct(AM) * AB.CrossProduct(AN) >= 0;}
};//三角形类
class Triangle
{
private:Vector2d pointA_, pointB_, pointC_;public:Triangle(Vector2d point1, Vector2d point2, Vector2d point3):pointA_(point1), pointB_(point2), pointC_(point3){//todo 判断三点是否共线
    }//计算三角形面积double ComputeTriangleArea(){//依据两个向量的叉乘来计算，可参考http://blog.csdn.net/zxj1988/article/details/6260576Vector2d AB = pointB_.Minus(pointA_);Vector2d BC = pointC_.Minus(pointB_);return fabs(AB.CrossProduct(BC) / 2.0);}bool IsPointInTriangle1(const Vector2d pointP){double area_ABC = ComputeTriangleArea();double area_PAB = Triangle(pointP, pointA_, pointB_).ComputeTriangleArea();double area_PAC = Triangle(pointP, pointA_, pointC_).ComputeTriangleArea();double area_PBC = Triangle(pointP, pointB_, pointC_).ComputeTriangleArea();if(fabs(area_PAB + area_PBC + area_PAC - area_ABC) < 0.000001)return true;else return false;}bool IsPointInTriangle2(const Vector2d pointP){return Vector2d::IsPointAtSameSideOfLine(pointP, pointA_, pointB_, pointC_) &&Vector2d::IsPointAtSameSideOfLine(pointP, pointB_, pointA_, pointC_) &&Vector2d::IsPointAtSameSideOfLine(pointP, pointC_, pointA_, pointB_);}bool IsPointInTriangle3(const Vector2d pointP){Vector2d AB = pointB_.Minus(pointA_);Vector2d AC = pointC_.Minus(pointA_);Vector2d AP = pointP.Minus(pointA_);double dot_ac_ac = AC.DotProduct(AC);double dot_ac_ab = AC.DotProduct(AB);double dot_ac_ap = AC.DotProduct(AP);double dot_ab_ab = AB.DotProduct(AB);double dot_ab_ap = AB.DotProduct(AP);double tmp = 1.0 / (dot_ac_ac * dot_ab_ab - dot_ac_ab * dot_ac_ab);double u = (dot_ab_ab * dot_ac_ap - dot_ac_ab * dot_ab_ap) * tmp;if(u < 0 || u > 1)return false;double v = (dot_ac_ac * dot_ab_ap - dot_ac_ab * dot_ac_ap) * tmp;if(v < 0 || v > 1)return false;return u + v <= 1;}bool IsPointInTriangle4(const Vector2d pointP){Vector2d PA = pointA_.Minus(pointP);Vector2d PB = pointB_.Minus(pointP);Vector2d PC = pointC_.Minus(pointP);double t1 = PA.CrossProduct(PB);double t2 = PB.CrossProduct(PC);double t3 = PC.CrossProduct(PA);return t1*t2 >= 0 && t1*t3 >= 0;}
};int main()
{Triangle tri(Vector2d(0,0), Vector2d(6,6), Vector2d(12,0));srand(time(0));for(int i = 0; i < 20; ++i){Vector2d point((rand()*1.0 / RAND_MAX) * 12, (rand()*1.0 / RAND_MAX) * 6);cout<<point.x_<<" "<<point.y_<<":     ";cout<<tri.IsPointInTriangle1(point)<<" ";cout<<tri.IsPointInTriangle2(point)<<" ";cout<<tri.IsPointInTriangle3(point)<<" ";cout<<tri.IsPointInTriangle4(point)<<endl;}
}