// from https://stackoverflow.com/questions/4103405/what-is-the-algorithm-for-finding-the-center-of-a-circle-from-three-points
// (by Adam Gawne-Cain)

static DoublePt circleCenterFrom3Points(DoublePt p1, DoublePt p2, DoublePt p3) {
  double ax = (p1.x + p2.x) / 2;
  double ay = (p1.y + p2.y) / 2;
  double ux = (p1.y - p2.y);
  double uy = (p2.x - p1.x);
  double bx = (p2.x + p3.x) / 2;
  double by = (p2.y + p3.y) / 2;
  double vx = (p2.y - p3.y);
  double vy = (p3.x - p2.x);
  double dx = ax - bx;
  double dy = ay - by;
  double vu = vx * uy - vy * ux;
  if (vu == 0)
      null; // Points are collinear, so no unique solution
  double g = (dx * uy - dy * ux) / vu;
  ret DoublePt(bx + g * vx, by + g * vy);
}