// returns null if unknown
static DoublePt bwCentroid2(BWImage img, bool dark) {
  int w = img.getWidth(), h = img.getHeight();
  double sumX = 0, sumY = 0, sum = 0;
  for y to h: for x to w: {
    float weight = img.getPixel(x, y);
    if (dark) weight = 1-weight;
    sumX += weight*x;
    sumY += weight*y;
    sum += weight;
  }
  if (sum == 0) null;
  ret DoublePt(sumX/sum, sumY/sum);
}