【计算几何】全代码

const double eps=1e-7;
const double pi=acos(-1);
int dcmp(double x){
    return (fabs(x)<=eps)?0:(x<0?-1:1);
}
struct Point{
    double x,y;
    Point(double X=0,double Y=0){x=X,y=Y;}
};
struct Vector{
    double x,y;
    Vector(double X=0,double Y=0){x=X,y=Y;}
};
inline Vector operator+(Vector x,Vector y){// 向量+向量=向量
    return Vector(x.x+y.x,x.y+y.y);
}
inline Point operator+(Point x,Vector y){// 点+向量=点
    return Point(x.x+y.x,x.y+y.y);
}
inline Point operator+(Vector y,Point x){// 向量+点=点
    return Point(x.x+y.x,x.y+y.y);
}
inline Vector operator-(Vector x,Vector y){// 向量-向量=向量
    return Vector(x.x-y.x,x.y-y.y);
}
inline Point operator-(Point x,Vector y){// 点-向量=点
    return Point(x.x-y.x,x.y-y.y);
}
inline Vector operator-(Point x,Point y){// 点-点=向量
    return Vector(x.x-y.x,x.y-y.y);
}
inline Vector operator*(Vector x,double y){ // 向量*数=向量
    return Vector(x.x*y,x.y*y);
}
inline Vector operator/(Vector x,double y){ // 向量/数=向量
    return Vector(x.x/y,x.y/y);
}
inline double polar(Vector x){ // 向量极角
    return atan2(x.y,x.x);
}
inline double len(Vector x){ // 向量模长
    return sqrt(x.x*x.x+x.y*x.y);
}
inline double dot(Vector x,Vector y){ // 向量点积
    return x.x*y.x+x.y*y.y;
}
inline double cross(Vector x,Vector y){ // 向量叉积
    return x.x*y.y-x.y*y.x;
}
inline double operator*(Vector x,Vector y){ // 向量叉积
    return cross(x,y);
}
inline double theta(Vector x,Vector y){// 向量夹角
    return acos(dot(x,y)/len(x)/len(y));
}
inline Vector rotate(Vector A, double rad){ // 向量旋转，rad 是顺时针弧度制
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
struct Line{
    Point x;Vector y;
    Line(Point X,Vector Y){x=X,y=Y;}
    Line(Point X,Point Y){x=X,y=Y-X;}
};
inline Point GetLineIntersection(Line x,Line y){// 两直线交点
    Vector u=x.y-y.y;
    double t=cross(y.y,u)/cross(x.y,y.y);
    return x.x+x.y*t;
}
inline double DistanceToLine(Point P,Line x){// 点到直线的距离
    Vector v1=x.y, v2=P-x.x;
    return fabs(cross(v1,v2))/len(v1);
}
inline Point GetLineProjection(Point P, Line x){// 点到直线的投影
    return x.x+x.y*(dot(x.y,P-x.x)/dot(x.y,x.y));
}
double PolygonSignedArea(vector<Point> poly){// 多边形有向面积
    double area=0;
    for(int i=1;i<(poly.size()-1);i++){
        area+=(poly[i]-poly[0])*(poly[i+1]-poly[0]);
    }
    return area/2;
}
double PolygonArea(vector<Point> poly){ // 多边形无向面积
    double area=0;
    for(int i=1;i<(poly.size()-1);i++){
        area+=fabs((poly[i]-poly[0])*(poly[i+1]-poly[0]));
    }
    return area/2;
}