【模板】计几常用函数

struct Line{
    double a,b,c;
};
struct Point{
    double x,y;
    Point(){x=y=0;}

    Point(double a,double b){x=a,y=b;}

    Point operator - (const Point& b)const
    {return Point(x-b.x,y-b.y);}

    Point operator + (const Point& b)const
    {return Point(x+b.x,y+b.y);}

    Point operator * (const double& b)const
    {return Point(x*b,y*b);}

    //点看做向量，然后向量逆时针旋转 b （是弧度制）
    Point rotate(const double& b)const
    {return Point( x*cos(b) - y*sin(b) , x*sin(b) + y*cos(b) );}

    //求点关于直线l对称的点
    Point corPoint(Line l)const{
        Point p2;
        double d = l.a*l.a + l.b*l.b;
        p2.x = ( (l.b*l.b - l.a*l.a)*x - 2 * l.a * l.b * y - 2*l.a*l.c) /d;
        p2.y = ( (l.a*l.a - l.b*l.b)*y - 2 * l.a * l.b * x - 2*l.b*l.c) /d;
        return p2;
    }

    double dot (const Point& b)const
    {return x*b.x+y*b.y;}

    double cross (const Point& b,const Point& c)const
    {return (b.x - x)*(c.y - y) - (c.x - x)*(b.y - y);}

    double ToPdis (const Point& b)const
    {return sqrt( (x-b.x)*(x-b.x) + (y-b.y)*(y-b.y) );}

    //点到直线距离
    double ToLdis (Line l)const{
        return fabs(l.a * x + l.b * y + l.c) / sqrt(l.a*l.a + l.b*l.b);
    }

    bool OnLine (const Point& st,Point& ed)const
    {return !sgn(cross(st,ed));}

    bool OnSeg (const Point& st,Point& ed)const
    {return OnLine(st,ed) && (*this - ed).dot(*this - st) < eps;}
};

//两线段是否相交
bool insert(Line l1,Line l2){
    return 
        max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&
        max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&
        max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&
        max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&
        sgn((l2.s-l1.s)^(l1.e-l1.s))*sgn((l2.e-l1.s)^(l1.e-l1.s))<=0 &&
        sgn((l1.s-l2.s)^(l2.e-l2.s))*sgn((l1.e-l2.s)^(l2.e-l2.s))<=0;
}
//两点求出直线
Line twoPoLine(Point p1,Point p2){
    Line l;
    l.a = p2.y - p1.y;
    l.b = p1.x - p2.x;
    l.c = p2.x * p1.y - p1.x * p2.y;
    return l;
}

Point LineCross(Point a,Point b,Point c,Point d){
    double u = a.cross(b,c), v = b.cross(a,d);
    return Point( (c.x*v + d.x*u)/(u+v) , (c.y*v + d.y*u)/(u+v) );
}
//求垂足
Point footOfPerpendicular(const Line& l, const Point& p)
{
    double t = (l.a * p.x + l.b * p.y + l.c) / (l.a * l.a + l.b * l.b);
    return p + Point(l.a, l.b) * t;
}

 

 

 

Point GetLineIntersection(Point a, Point va, Point b, Point vb) {
    Point u = a - b;
    double t = (vb ^  u) / (va ^ vb);
    return a + va * t;
}

 极角排序

int Quadrant(Point b)//象限排序
{
    Point a = b - p0;
    if(a.x>=0&&a.y>=0)  return 1;
    if(a.x<=0&&a.y>=0)  return 2;
    if(a.x<=0&&a.y<=0)  return 3;
    return 4;
}
 
 
bool cmp(Point a,Point b)  //先按象限从小到大排序 再按极角从小到大排序
{
    if(Quadrant(a)==Quadrant(b)){
        if( p0.cross(a,b) == 0) return p0.dis(a) < p0.dis(b);
        return p0.cross(a,b) > 0;
    }
    else return Quadrant(a)<Quadrant(b);
}