计算几何模板

白书上部分代码

#include <iostream>
#include <stdio.h>
#include <math.h>
#include <string.h>
using namespace std;
const double esp = 1e-10;
struct Point{
    double x,y;
    Point(double x = 0,double y = 0):x(x),y(y){}
};
typedef Point Vector;
Vector operator + (Vector A ,Vector B) {return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Vector A ,Vector 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);
}
int dcmp(double x){
    if(fabs(x)<esp) 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 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){//向量旋转
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
//单位方向向量
Vector Normal(Vector A)
{
    double L = Length(A);
    return Vector(-A.y/L,A.x/L);
}
//直线相交
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;
}
/*点到直线距离*/
double DistanceToLine(Point P,Point A, Point B){
    Vector v1 = B-A,v2 = P-A;
    return fabs(Cross(v1,v2)/Length(v1));
}
/*点到线段距离*/
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);
}
/*点在线段上投影*/
Point GetLineProjection(Point P,Point A,Point B){
    Vector v = B - A;
    return A+v*(Dot(v,P-A)/Dot(v,v));
}
/*线段相交*/
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;
}
/*端点相交*/
bool OnSegment(Point p,Point a1, Point a2){
    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;
}