static double distancePointToLineSegment(Pt a, Pt b, Pt p) {
  int x1 = a.x, y1 = a.y, x2 = b.x, y2 = b.y, x3 = p.x, y3 = p.y;
  
  float px=x2-x1;
  float py=y2-y1;
  float temp=(px*px)+(py*py);
  float u=((x3 - x1) * px + (y3 - y1) * py) / (temp);
  if (u>1) u=1; else if(u<0) u=0;
  float x = x1 + u * px;
  float y = y1 + u * py;
  float dx = x - x3;
  float dy = y - y3;
  ret sqrt(dx*dx + dy*dy);
}