二维几何模板（刘汝佳）

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <complex>#include <cstdlib>#include <vector> using namespace std;const double PI=acos(0)*2;struct Point{    double x,y;    Point(double x=0,double y=0):x(x),y(y){}  //构造函数};typedef Point Vector;  //从程序的实现上，Vector只是Point的别名Vector operator +(Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}Vector operator -(Point A,Point B){ return Vector(A.x-B.x,A.y-B.y); }Vector operator *(Vector A,double p){return Vector(A.x*p,A.y*p);}Vector operator /(Vector A,double p){return Vector(A.x/p,A.y/p);}bool operator< (const Point& a ,const Point& b){    return a.x<b.x||(a.x==b.x&&a.y<b.y);}const double eps=1e-10;int dcmp(double x){    if(fabs(x)<eps)return 0;else return x<0?-1:1;}bool operator == (const Point& a,const Point &b){    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}double Dot(Vector A,Vector B){  return A.x*B.x+A.y*B.y;}double Dist2(const Point& A, const Point& B) {    return (A.x-B.x)*(A.x-B.x) + (A.y-B.y)*(A.y-B.y);  } double Length(Vector A){return sqrt(Dot(A,A));}double Angle(Vector A,Vector B) { return acos(Dot(A,B)/Length(A)/Length(B)); }double Cross(Vector A,Vector B){ return A.x*B.y-A.y*B.x;}double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}Vector Rotate(Vector A,double rad){   return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}Vector Normal(Vector A){   double L=Length(A);   return Vector(-A.y/L,A.x/L);}double torad(double deg){   return deg/180*acos(-1);}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;}double DistanceToLine(Point P,Point A,Point B){   Vector v1=B-A,v2=P-A;   return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(Point P,Point A,Point B){   if(A==B)return Length(P-A);   Vector v1=B-A,v2=P-A,v3=P-B;   if(dcmp(Dot(v1,v2))<0) return Length(v2);   else if(dcmp(Dot(v1,v3))>0) return Length(v3);   else return fabs(Cross(v1,v2))/Length(v1);}Point GetLineProjection(Point P,Point A,Point B){   Vector v=B-A;   return A+v*(Dot(v,P-A)/Dot(v,v));}bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){   double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),          c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);   return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;}bool OnSegment(Point P,Point a1,Point a2){   return dcmp(Cross(a1-P,a2-P))==0&&dcmp(Dot(a1-P,a2-P))<0;}double PolygonArea(Point *p,int n){    double area=0;    for(int i=1;i<n-1;i++)        area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;}int isPointInPolygon(Point p,Point poly[],int n){  //点是否在多边形内    int wn=0;    for(int i=0;i<n;i++){        if(OnSegment(p,poly[i],poly[(i+1)%n])) return -1;  //在边界上        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1=dcmp(poly[i].y-p.y);        int d2=dcmp(poly[(i+1)%n].y-p.y);        if(k>0&&d1<=0&&d2>0)wn++;        if(k<0&&d2<=0&&d1>0)wn--;    }    if(wn!=0) return 1;  //点在内部    return 0;  //点在外部}Point Gravity(Point *p, int n) {  //返回多边形的重心    double area = 0;    Point center;    center.x = 0;    center.y = 0;    for (int i = 0; i < n-1; i++) {        area += (p[i].x*p[i+1].y - p[i+1].x*p[i].y)/2;        center.x += (p[i].x*p[i+1].y - p[i+1].x*p[i].y) * (p[i].x + p[i+1].x);        center.y += (p[i].x*p[i+1].y - p[i+1].x*p[i].y) * (p[i].y + p[i+1].y);    }    area += (p[n-1].x*p[0].y - p[0].x*p[n-1].y)/2;    center.x += (p[n-1].x*p[0].y - p[0].x*p[n-1].y) * (p[n-1].x + p[0].x);    center.y += (p[n-1].x*p[0].y - p[0].x*p[n-1].y) * (p[n-1].y + p[0].y);    center.x /= 6*area;    center.y /= 6*area;    return center;}