bool linesIntersection
(complex<T> p1,complex<T> p2,complex<T> p3,
complex<T> p4,complex<double>& p)
{
if(fabs(dcross(p1-p2,p3-p4))<EPS)return false;
double t=dcross(p3-p1,p3-p4)/dcross(p2-p1,p3-p4);
p.x()=1.0*p1.x()+1.0*(p2.x()-p1.x())*t;
p.y()=1.0*p1.y()+1.0*(p2.y()-p1.y())*t;
return true;
}
bool circlesIntersection
( complex<T> p1,T r1,complex<T> p2,T r2,complex<double>& inter)
{
double dx = p2.x() - p1.x();
double dy = p2.y() - p1.y();
double d = mysqrt(dx*dx + dy*dy);
if(d>r1+r2+EPS||d+EPS<fabs(r1-r2))return false;
//circle overlap
if(d<EPS)return false;
double e = (r1*r1 - r2*r2 + d*d)/(2*d);
double f = mysqrt(r1*r1 - e*e);
inter=complex<double>(1.0*p1.x() + (e*dx - f*dy)/d,1.0*p1.y() + (f*dx + e*dy)/d);
return true;
}
int segmentsIntersection
(complex<T> p1,complex<T> p2,complex<T> p3,complex<T> p4,complex<double>& inter)
{
if(sigcross(p3-p1,p2-p1)*sigcross(p2-p1,p4-p1)<0)return 0;
if(sigcross(p1-p3,p4-p3)*sigcross(p4-p3,p2-p3)<0)return 0;
if(sigcross(p2-p1,p3-p1)==0&&sigcross(p2-p1,p4-p1)==0)
{
if(p1.x()==p2.x())
{
if(p1.y()>p2.y())swap(p1,p2);
if(p3.y()>p4.y())swap(p3,p4);
int ly=max(p1.y(),p3.y());
int hy=min(p2.y(),p4.y());
if(ly>hy)return 0;
if(ly<hy)return 2;
inter=p2;
return 1;
}
else
{
if(p1.x()>p2.x())swap(p1,p2);
if(p3.x()>p4.x())swap(p3,p4);
int lx=max(p1.x(),p3.x());
int hx=min(p2.x(),p4.x());
if(lx>hx)return 0;
if(lx<hx)return 2;
inter=p2;
return 1;
}
}
linesIntersection(p1,p2,p3,p4,inter);
return 1;
}
double length(complex<T> p)
{
return sqrt(1.0*p.x()*p.x()+1.0*p.y()*p.y());
}
double dcross(complex<T> p1,complex<T> p2)
{
return 1.0*p1.x()*p2.y()-p2.x()*p1.y();
}
llint llcross(complex<T> p1,complex<T> p2)
{
return (llint)p1.x()*(llint)p2.y()-(llint)p2.x()*(llint)p1.y();
}