/**
   * Transforms this circle by an affine transform. If the transformed shape is a circle (ellipse
   * with equal axis lengths), returns an instance of Circle2D. The resulting ellipse is direct if
   * this ellipse and the transform are either both direct or both indirect.
   */
  public EllipseShape2D transform(AffineTransform2D trans) {
    // When the transform is not a similarity, should switch to EllipseArc
    // computation
    if (!AffineTransform2D.isSimilarity(trans)) {
      return this.asEllipse().transform(trans);
    }

    // If transform is a similarity, the result is a circle
    Point2D center = this.center().transform(trans);
    Point2D p1 = this.firstPoint().transform(trans);

    boolean direct = !this.direct ^ trans.isDirect();
    Circle2D result = new Circle2D(center, center.distance(p1), direct);
    return result;
  }
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  /*
   * (non-Javadoc)
   *
   * @see math.geom2d.Shape2D#transform(math.geom2d.AffineTransform2D)
   */
  public EllipseArc2D transform(AffineTransform2D trans) {
    // transform supporting ellipse
    Ellipse2D ell = ellipse.transform(trans);

    // ensure ellipse is direct
    if (!ell.isDirect()) ell = ell.reverse();

    // Compute position of end points on the transformed ellipse
    double startPos = ell.project(this.firstPoint().transform(trans));
    double endPos = ell.project(this.lastPoint().transform(trans));

    // Compute the new arc
    boolean direct = !(angleExtent > 0 ^ trans.isDirect());
    return new EllipseArc2D(ell, startPos, endPos, direct);
  }