static DoublePt lineIntersectionPt(LineThroughPoint l1, LineThroughPoint l2) {
  DoublePt p1 = doublePt(l1.x, l1.y), p2 = l1.pointOnLine(1);
  DoublePt p3 = doublePt(l2.x, l2.y), p4 = l2.pointOnLine(1);
  double d = (p1.x-p2.x)*(p3.y-p4.y)-(p1.y-p2.y)*(p3.x-p4.x);
  double x = ((p1.x*p2.y-p1.y*p2.x)*(p3.x-p4.x)
    -(p1.x-p2.x)*(p3.x*p4.y-p3.y*p4.x))/d;
  double y = ((p1.x*p2.y-p1.y*p2.x)*(p3.y-p4.y)
    -(p1.y-p2.y)*(p3.x*p4.y-p3.y*p4.x))/d;
  ret doublePt(x, y);
}