简单的点与直线的几何模板

<span style="font-size:18px;">点到直线距离，直线相交交点，线段相交，向量点乘，向量叉乘，三角形有向面积，点到直线距离。</span>

struct point{
double x,y;
point(double x=0,double y=0):x(x),y(y) { }
};
typedef point V;
struct circle{
point c;
double r;
circle(point c,double r):c(c),r(r){}
point Point(double a){
return point(c.x+cos(a)*r,+c.y+sin(a)*r);
}
};
struct line{
point c;
V v;
};
V operator + (V a,V b){ return V(a.x+b.x,a.y+b.y);}
V operator - (V a,V b){ return V(a.x-b.x,a.y-b.y);}
V operator * (V a,double p){return V(a.x*p,a.y*p);}
V operator / (V a,double p){return V(a.x/p,a.y/p);}
bool operator < (const V& a,const V& 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(V a,V b){return a.x*b.x+a.y*b.y; }
double length(V a){return sqrt(dot(a,a));}
double angle(V a,V b){return acos(dot(a,b)/length(a)/length(b)); }
double cross(V a,V b){return a.x*b.y-a.y*b.x; }
double area2(point a,point b,point c){return cross(b-a,c-a); }

/*two line change point返回两线交点(保证有唯一交点)*/
point twolineispoint(point p,V v,point q,V w){
    V u=p-q;
    double t=cross(w,u)/cross(v,w);
    return p+v*t;
}
/*线段是否相交*/
bool segmentmeet(point a1,point a2,point b1,point b2){
    double c1=cross(a2-a1,b1-a1),c2=cross(a2-a1,b2-a1),
           c3=cross(b2-b1,a1-b1),c4=cross(b2-b1,a1-b1);
    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
/*点到直线距离*/
point pointtoline(point p,point a,point b){
    V v1=b-a,v2=p-a;
    return fabs(cross(v1,v2))/length(v1);
}