计算几何基本模板

#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
struct Point{
double x, y;
Point(double x = 0, double y = 0);
};
typedef Point Vector;
Point::Point(double x, double y){
this->x = x;    this->y = y;
}
//向量与向量的+ - 点积 叉积
Vector operator +(const Vector &A, const Vector &B){//向量的加
return Vector(A.x + B.x, A.y + B.y);
}
Vector operator -(const Vector &A, const Vector &B){//向量的减
return Vector(A.x - B.x, A.y - B.y);
}
double dot(const Vector &A, const Vector &B){//向量点积
return (A.x * B.x + A.y * B.y);
}
double cross(const Vector &A, const Vector &B){//向量叉乘
return (A.x * B.y - B.x * A.y);
}
//向量关系运算符
bool operator <(const Vector &A, const Vector &B){
return (A.x < B.x || (A.x == B.x && A.y < B.y));
}
int dcmp(double x){//处理double数据i，减少精度问题
if(fabs(x) < 1e-7)  return 0;
if(x < 0)   return 0;
else   return 1;
}
bool operator == (const Vector &A,const Vector &B){
return (dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0) ;
}
//向量与数字的乘除
Vector operator *(const Vector &A,double p){
return Vector(A.x * p, A.y * p);
}
Vector operator /(const Vector &A,double p){
if(fabs(p-0) < 1e-7) return A;
return Vector(A.x / p, A.y / p);
}
//向量的模
double length(const Vector &A){
return sqrt(dot(A,A));
}
double angle (const Vector &A,const Vector &B){//两向量夹角，弧度表示
return acos(dot(A,B) / length(A) / length(B));
}
Point GetLineIntrersection(Point P, Vector v, Point Q, Vector w){ //直线交点
Vector u = P - Q;
double t = Cross(w, u) / Cross(v, w);
return P + v * t;
}
double DistanceToLine(Point P, Point A, Point B){//点到直线距离，这里是P到AB的距离，等于向量AB X 向量AP 再除以 |向量AB|
Vector v1 = B - A, v2 = P - A;
return fabs(Cross(v1, v2) / length(v1));
}
double DistanceToSegment(Point P, Point A, Point B){//点到线段距离，其中可以看两向量点积的正负，来判断点相对于线段的位置
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);
}
double DistanceMaxToSegment(Point P, Point A, Point B){//点到线段最远距离
Vector v2 = P - A,v3 = P - B;
return max(length(v2), length(v3));
}
//线段是否“正规相交”，即交点不在四个端点上
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){ //点是否在线段上
return dcmp(cross(a1 - p, a2 - p)) == 0 && dcmp(dot(a1 - p, a2 - p) < 0) ;
}