计算几何模板《算法竞赛入门经典训练指南》

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 - (Piont A,Point 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);
}

Voctor 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);
}

const double eps=1e-10;

int dcmp(double x)
{
    if(fabs(x)<eps) 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)
{
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}

Vector Normal(Vector A)//计算向量的单位法线
{
    double L=Length(A);
    return Vector(-A.y/L,A.x/L);
}

//P+tv  Q+tw u=QP
Piont GetLineIntersection(Piont P,Vector v,Point Q,Vector w)
{
    Vector k=P-Q;
    double t=Cross(w,k)/Cross(v,w);
    return p+v*t;
}

double DistanceToLine(Piont P,Piont A,Piont B)
{
    Vector v1=B-A,v2=P-A;
    return fabs(Cross(v1,v2)/Length(v1));
}

double DistanceToSegment(Piont P,Piont A,Piont 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));
}

double GetLineProjection(Piont P,Piont A,Piont B)
{
    Vector v=B-A;
    return A+v*(Dot(v,P-A)/Dot(v,v));
}

bool SegmentProperIntersection(Piont a1,Piont a2,Piont b1,Piont b2)
{
    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);
    double 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)
{
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}

double ConvexPolgonArea(Piont *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;
}