计算几何模板（有待更新）

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 - (Point 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); }
Vector operator / (Vector A, double p) { return Vector(A.x / p, A.y / p); }
Vector operator -(Vector A)  {return  Vector(-A.x,-A.y);}
const double eps = 1e-8;
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; }  //叉积
double Area2(Point A, Point B, Point C) { return Cross(B-A, C-A); }//有向面积的二倍

Vector Rotate(Vector A, double rad) //向量A逆时针旋转rad弧度
{
    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，用前要保证A不是零向量
{
    double L = Length(A);
    return Vector(-A.y/L, A.x/L);
}
//直线P+tv和Q+tw的交点， 使用前要保证Cross(v, w) != 0
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;
}

double distancee(Point p1,Point p2) //两点间距
{
    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}

double DistanceToLine(Point P, Point A, Point B) //点到直线距离
{
    Vector v1 = B - A, v2 = P - A;
    return fabs(Cross(v1, v2)) / Length(v1);
}

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

bool SegmentIns(Point a1, Point a2, Point b1, Point b2)//两线段是否相交( 不包括端点 )
{
    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 onSeg(Point p, Point a1, Point a2)//a1a2是否经过点p
{
    return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;
}

double cArea(Point* p, int n) //多边形的有向面积
{
    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;
}

bool cmp(const Point &x,const Point &y){return x.x==y.x?x.y<=y.y:x.x<y.x;}
//计算凸包，返回凸包顶点数， ch为各个顶点
//输入不能有重复点， 函数执行完后输入点的顺序被破坏
//如果不希望在凸包的边上有输入点， 把两个<=改成<
int ConvexHull(Point *p, int n, Point* ch)
{
    sort(p, p + n, cmp); //先比较x坐标，再比较y坐标
    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;
}