计算几何模板

#include<bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const double inf = 1e100;
const double eps = 1e-6;
struct Point{
    double x, y;
    Point(double x = 0, double y = 0):x(x),y(y){} //构造函数 方便代码编写 
};
typedef Point Vector; //点的别名 
Vector operator + (Vector A, Vector B){
    return Vector(A.x+B.x, A.y+B.y);
}
//向量+向量=向量 
Vector operator - (Point A, Point B){
    return Vector(A.x-B.x, A.y-B.y);
}
//点-点=向量 
Vector operator * (Vector A, double p){
    return Vector(A.x*p,A.y*p);
}
//向量*数=向量 
Vector operator / (Vector A,double p){
    return Vector(A.x/p,A.y/p);
}
//向量/数=向量 
bool operator < (const Point &a, const Point &b){
    return a.x<b.x || (a.x==b.x && a.y<b.y);
}
//用于排序 
int dcmp(double x){
    if(fabs(x)<eps) return 0;
    else return x<0?-1:1;
}
//正数 1 负数 -1 零 0
bool operator == (const Point &a, const Point &b){
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
//判断两向量是否相等
double Dot(Vector A, Vector B){
    return A.x*B.x+A.y*B.y;
}
//点积
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));
}
//弧度表示的角度
double Cross(Vector A, Vector B){
    return A.x*B.y-A.y*B.x;
}
//叉积 可用来判断两个向量的位置关系 如果B在A的逆时针方向 叉积为正 反之 叉积为正
//若两向量共线则叉积为0
double Area2(Point A,Point B,Point C){
    return Cross(B-A,C-A);
}
//向量B-A和向量C-A的叉积 就是平行四边形的面积
Vector Rotate(Vector A, double rad){
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
//向量旋转公式 rad为弧度
Vector Normal(Vector A){
    double L=Length(A);
    return Vector(-A.y/L,A.x/L);
}
//求向量的法线 向量不能是零向量
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;
}
//计算两直线的交点 两直线不能平行
double DistanceToLine(Point P,Point A,Point B){
    Vector v1=B-A; Vector v2=P-A;
    return fabs(Cross(v1,v2))/Length(v1);
}
//求点p到直线ab的距离
double DistanceToSegment(Point P,Point A,Point B){
    if(A==B) return Length(P-A);
    Vector v1=B-A; Vector v2=P-A; Vector 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);
}
//求点p到线段ab的距离
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;
} 
//判断两线段规范相交(即两线段恰好只有一个公共点，且不再任何一条线段的端点)
bool onSegment(Point p,Point a1,Point a2){
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}
//判断一个点是否在线段a1a2上 
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;
}
//求多边形的面积