//Construct the line with two points on it
line::line(point a, point b){
complex u = a.conj()*b - a*b.conj();
double v = ( (a - b) * (1 - a.conj()*b) ).abs();
complex w = a.conj() * (1 + b.abs2()) - b.conj() * (1 + a.abs2());
left = (u + v)/w;
right = (u - v)/w;
}
line::line(point a, ideal b){
left = -b*(1 + a.abs2() - 2*b.conj()*a)/(1 + a.abs2() - 2*b*a.conj());
right = b;
}
line::line(ideal a, point b){
left = a;
right = -a*(1 + b.abs2() - 2*a.conj()*b)/(1 + b.abs2() - 2*a*b.conj());
}
