计算几何模板

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>

#define eps 1e-7

using namespace std;

struct Point{
    double x,y;
    Point(){}
    Point(double x,double y):x(x),y(y){}
    void input()
    {
        scanf("%lf %lf",&x,&y);
    }
};

typedef Point Vector;//从程序上，Vector只是Point的别名


int dcmp(double x)//控制精度
{
    if(fabs(x)<eps) return 0;
    else return x<0?-1:1;
}

double toRad(double deg)//角度变为弧度
{
    return deg/180.0*acos(-1.0);
}

Vector operator+(Vector A,Vector B)//向量加
{
    return Vector(A.x+B.x, A.y+B.y);
}

Vector operator-(Vector A,Vector B)//向量减
{
    return Vector(A.x-B.x,A.y-B.y);
}

Vector operator*(Vector A,double p)//向量数乘
{
    return Vector(A.x*p,A.y*p);
}

Vector operator/(Vector A,double p)//向量数除
{
    return Vector(A.x/p,A.y/p);
}

bool operator<(const Point &A,const Point &B)//两点比较
{
    return dcmp(A.x-B.x)<0 || (dcmp(A.x-B.x) == 0 && dcmp(A.y-B.y) < 0);
}

bool operator==(const Point &A, const Point &B)//两点相等
{
    return dcmp(A.x-B.x) == 0 && dcmp(A.y-B.y) == 0;
}

struct Line
{
    Point s,e;
    Vector v;
    Line(){}
    Line(Point s, Point v, int type)://法向量式
       s(s),v(v){}
    Line(Point s, Point e):s(s),e(e)//两点式
    {
        v=e-s;
    }
};


double Dot(Vector A,Vector B)//向量点乘,|A|*|B|*cos<A,B>
{
    return A.x*B.x+A.y*B.y;
}

double Length(Vector A)//向量模
{
    return sqrt(Dot(A,A));
}

double Angle(Vector A,Vector B)//向量夹角
{
    return acos(Dot(A,B)/Length(A)/Length(B));
}

double Cross(Vector A,Vector B)//向量叉积
{
    return A.x*B.y-B.x*A.y;
}

double Area2(Point A,Point B,Point C)//向量的有向面积，三角形面积的2倍
{
    return Cross(B-A,C-A);
}

double Dist(Point A,Point B)//两点之间的距离
{
    return Length(A-B);
}

Vector Rotate(Vector A, double rad)//向量逆时针旋转
{
    return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
}

Vector Normal(Vector A)//向量单位法向量，前提不是零向量，即左转90度
{
    double L=Length(A);
    return Vector(-A.y/L,A.x/L);
}

Point GetLineIntersection(Line l1,Line l2)//两直线的交点，调用前确保两条直线有唯一交点
{
    Point P=l1.s;
    Vector v=l1.v;
    Point Q=l2.s;
    Vector w=l2.v;
    Vector u=P-Q;
    double t=Cross(w,u)/Cross(v,w);//注意分母不能为0
    return P+v*t;
}

double DistanceToLine(Point P,Line L)//点到直线的距离
{
    Point A,B;
    A=L.s,B=L.e;
    Vector v1=B-A,v2=P-A;
    return fabs(Cross(v1,v2)/Length(v1));
}

double DistanceToSegment(Point P,Line L)//点到线段的距离
{
    Point A,B;
    A=L.s,B=L.e;
    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 GetLineProjection(Point P,Line L)//点在直线上的投影
{
    Point A,B;
    A=L.s,B=L.e;
    Vector v=B-A;
    return A+v*(Dot(v,P-A)/Dot(v,v));
}

bool OnSegment(Point p,Line l)//点在线段上包括端点
{
    Point a1=l.s;
    Point a2=l.e;
    return dcmp(Cross(a1-p,a2-p))==0 && dcmp(Dist(p,a1)+Dist(p,a2)-Dist(a1,a2))==0;
}

bool Paralled(Line l1,Line l2)//直线平行
{
    return dcmp(Cross(l1.e-l1.s,l2.e-l2.s))==0;
}

bool SegmentProperIntersection(Line l1,Line l2)//线段是否相交
{
    if(Paralled(l1,l2))
        return false;
    Point t=GetLineIntersection(l1,l2);
    if(OnSegment(t,l1))
        return true;
    return false;
}

double PolygonArea(Point *p, int n)//求多边形面积
{
    double area = 0;
    for(int i=1; i<n-1; i++)
      area += Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2.0;
}

int ConvexHull(Point *p,int n,Point *ch)    //求凸包
{
    sort(p,p+n);
    int m=0;
    for ( int i = 0; i < n; ++i )
    {
        while ( m > 1 && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;
        ch[m++] = p[i];
    }
    int k = m;
    for ( int i = n - 2; i >= 0; --i )
    {
        while ( m > k && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;
        ch[m++] = p[i];
    }
    if ( n > 1 ) --m;
    return m;
}


int main()
{
    
    return 0;
}