2D几何

#include<cstdio>  
#include<cstring>  
#include<iostream>  
#include<algorithm>  
#include<cmath>  
#include<vector>  
#include<queue>  
#include<map>  
#include<set>  
using namespace std;  
#define INF 1 << 30  
#define eps 1e-10  
#define  Vector Point  
#define MAXD 310  
/*=============================================*/  
int dcmp(double x){  
    if(fabs(x) < eps)  
        return 0;  
    else  
        return x < 0 ? -1 : 1;  
}  
struct Point{  
    double x;  
    double y;  
    Point(double a = 0,double b = 0): x(a),y(b) {};  
    friend bool operator < (Point p,Point q){  
        if(p.x == q.x)  
            return p.y < q.y;  
        else  
            return p.x < q.x;  
    }  
friend Vector operator + (Point p,Point q){  
        return Vector(p.x + q.x , p.y + q.y);  
}  
friend Vector operator - (Point p,Point q){  
        return Vector(p.x - q.x ,  p.y - q.y);  
}  
friend Vector operator * (Point p,double t){  
        return Vector(p.x * t , p.y * t);  
}  
friend Vector operator / (Point p,double t){  
        return Vector(p.x / t , p.y / t);  
}  
friend bool operator == (Point p,Point q){  
        return dcmp(p.x - q.x) == 0 && dcmp(p.y - q.y) == 0;  
}  
};  
double Dot(Vector p, Vector q){  //向量点积  
    return p.x * q.x + p.y * q.y;  
}  
double Length(Vector p){        //向量长度  
    return sqrt(p.x * p.x + p.y * p.y);  
}  
double Angle(Vector p ,Vector q){  
    return acos( Dot(p, q) /( Length(p) * Length(q) ) );  
}  
double Cross(Vector p,Vector q){  
    return p.x * q.y - p.y * q.x;  
}  
double Area2(Point a,Point b,Point c){  
    return Cross(a - b , c - b);  
}  
Vector Rotate(Vector p,double angle){  
    return Vector(p.x * cos(angle) - p.y * sin(angle), p.x * sin(angle) + p.y * cos(angle));  
}  
Vector Normal(Vector p){  //求法向量  
    double L = Length(p);  
    return Vector( - p.y / L , p.x / L);  
}  
Point GetLineCross(Point p,Vector v,Point q,Vector w){ //交点  
    Vector u = p - q;  
    double t = Cross(w,u) / Cross(v,w);  
    return p + v * t;  
}  
double Distance(Point p,Point a,Point b){  //点到射线的距离  
    Vector v1 = b - a;  
    Vector v2 = p - a;  
    return fabs(Cross(v1,v2)) / Length(v1);  
}  
double Distance2(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 GetLinePoint(Point p,Point a,Point b){ //点在线上的投影  
    Vector v = b - a;  
    return a + v *  (Dot(v, p -a ) / Dot(v,v));  
}  
bool If_Cross(Point a1,Point a2,Point b1,Point b2){  //是否相交  
    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 If_InLine(Point p,Point a1,Point a2){  
    return dcmp(Cross(a1 - p , a2 - p)) == 0 && dcmp(Dot(a1 - p , a2 - p)) < 0;  
}