private final void flat_ellipse_symmetry(int centerX, int centerY,
                                           int ellipseX, int ellipseY,
                                           boolean filling) {
    if (filling) {
      for (int i = centerX - ellipseX + 1; i < centerX + ellipseX; i++) {
        thin_point(i, centerY - ellipseY, fillColor);
        thin_point(i, centerY + ellipseY, fillColor);
      }
    } else {
      thin_point(centerX - ellipseX, centerY + ellipseY, strokeColor);
      thin_point(centerX + ellipseX, centerY + ellipseY, strokeColor);
      thin_point(centerX - ellipseX, centerY - ellipseY, strokeColor);
      thin_point(centerX + ellipseX, centerY - ellipseY, strokeColor);
    }
  }