#include<iostream>#include<cstdio>#include<cmath>#include<algorithm>using namespace std;struct Point {double x,y;Point(double x,double y):x(x),y(y){}Point(){}};//点类和构造函数，方便编写代码typedef Point Vector;Vector operator - ( Vector a,Vector b){return Vector(a.x-b.x,a.y-b.y);}//点的减法等于点的各个坐标相减Vector operator + (Vector a,Vector b){return Vector(a.x+b.x,a.y+b.y);}//点的加法等于点的各个坐标相加Vector operator * (Vector a,double p){return Vector(a.x*p,a.y*p);}//点的乘法等于两点乘以同一值Vector operator / (Vector a,double p){return Vector(a.x/p,a.x/p);}//点的除法等于两点除以同一值bool operator<(const Point &a, const Point & b){return a.x < b.x || (a.x == b.x && a.y < b.y);}//方便坐标比较大小，const double eps = 1e-10;int dcmp(double x){if(fabs(x) < eps) return 0;else return x < 0 ? -1 : 1;}//精度比较，当不等于精度的时候，返回x是正还是负bool operator== (const Point & a, const Point & b){return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0;}//精度比较大小，含精度epsdouble Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}//点的点乘double Length(Vector a){return sqrt(Dot(a,a));}//向量的模长double Angle(Vector a ,Vector b){return acos(Dot(a,b) / Length(a)/Length(b));}//两向量的夹角，两向量的点积 = 两向量的模长 * 向量的夹角的余弦，返回的弧度Vector Rotate(Vector a, double rad){return Vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));}//向量的旋转，向量绕着起点旋转，旋转后的坐标公式 x =a.x*cos(rad)-a.y*sin(rad) , y =a.x*sin(rad)+a.y*cos(rad),rad都为弧度double Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}//向量的叉乘，意义组成平行四边形的面积，可判断点的顺逆时针double Area2(Point a,Point b,Point c){return Cross(b-a,c-a);}//a,b,c组成面积的二倍Vector Normal(Vector a){double l = Length(a);return Vector(-a.y/l,a.x/l);}//向量的单位法向量，左转90度，长度归一化，单位向量即该向量除以自己的模长double DistanceToLine(Point p,Point a,Point b){Vector v = b-a;double a = Cross(v,p-a);return fabs(a) / Length(v);}//点到直线的距离，面积/低double DistanceToSegment(Point p,Point a,Point b){if(a == b) return Length(p-a);Vector v1 = p-a,v2 = b - a,v3 = p-b;if(dcmp(Dot(v1,v2)) < 0) return Length(v1);else if(dcmp(v1,v3) > 0) return Length(v3);else return Cross(v2,v1) / Length(v2);}//点到线段的距离，如果不在延长线上，在是点到直线的距离，如果点在ab延长线，那么距离为点到b的距离，反之，点到a的距离Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){Vector u = P - Q;double t = Cross(w,u) / Cross(v,w);return P+v*t;}//两直线相交求交点
