/** @deprecated replaced by circlesIntersections(Circle2D, Circle2D) (0.11.1) */
  @Deprecated
  public static Collection<Point2D> getIntersections(Circle2D circle1, Circle2D circle2) {
    ArrayList<Point2D> intersections = new ArrayList<Point2D>(2);

    // extract center and radius of each circle
    Point2D center1 = circle1.center();
    Point2D center2 = circle2.center();
    double r1 = circle1.radius();
    double r2 = circle2.radius();

    double d = Point2D.distance(center1, center2);

    // case of no intersection
    if (d < abs(r1 - r2) || d > (r1 + r2)) return intersections;

    // Angle of line from center1 to center2
    double angle = Angle2D.horizontalAngle(center1, center2);

    // position of intermediate point
    double d1 = d / 2 + (r1 * r1 - r2 * r2) / (2 * d);
    Point2D tmp = Point2D.createPolar(center1, d1, angle);

    // Add the 2 intersection points
    double h = sqrt(r1 * r1 - d1 * d1);
    intersections.add(Point2D.createPolar(tmp, h, angle + PI / 2));
    intersections.add(Point2D.createPolar(tmp, h, angle - PI / 2));

    return intersections;
  }
  /**
   * Computes intersections of a circle with a line. Returns an array of Point2D, of size 0, 1 or 2
   * depending on the distance between circle and line. If there are 2 intersections points, the
   * first one in the array is the first one on the line.
   *
   * @return a collection of intersection points
   * @since 0.11.1
   */
  public static Collection<Point2D> lineCircleIntersections(
      LinearShape2D line, CircularShape2D circle) {
    // initialize array of points (maximum 2 intersections)
    ArrayList<Point2D> intersections = new ArrayList<Point2D>(2);

    // extract parameters of the circle
    Circle2D parent = circle.supportingCircle();
    Point2D center = parent.center();
    double radius = parent.radius();

    // Compute line perpendicular to the test line, and going through the
    // circle center
    StraightLine2D perp = StraightLine2D.createPerpendicular(line, center);

    // Compute distance between line and circle center
    Point2D inter = perp.intersection(new StraightLine2D(line));
    if (inter == null) {
      throw new RuntimeException(
          "Could not compute intersection point when computing line-cicle intersection");
    }
    double dist = inter.distance(center);

    // if the distance is the radius of the circle, return the
    // intersection point
    if (abs(dist - radius) < Shape2D.ACCURACY) {
      if (line.contains(inter) && circle.contains(inter)) intersections.add(inter);
      return intersections;
    }

    // compute angle of the line, and distance between 'inter' point and
    // each intersection point
    double angle = line.horizontalAngle();
    double d2 = sqrt(radius * radius - dist * dist);

    // Compute position and angle of intersection points
    Point2D p1 = Point2D.createPolar(inter, d2, angle + Math.PI);
    Point2D p2 = Point2D.createPolar(inter, d2, angle);

    // add points to the array only if they belong to the line
    if (line.contains(p1) && circle.contains(p1)) intersections.add(p1);
    if (line.contains(p2) && circle.contains(p2)) intersections.add(p2);

    // return the result
    return intersections;
  }
  /**
   * Computes the intersections points between two circles or circular shapes.
   *
   * @param circle1 an instance of circle or circle arc
   * @param circle2 an instance of circle or circle arc
   * @return a collection of 0, 1 or 2 intersection points
   */
  public static Collection<Point2D> circlesIntersections(Circle2D circle1, Circle2D circle2) {
    // extract center and radius of each circle
    Point2D center1 = circle1.center();
    Point2D center2 = circle2.center();
    double r1 = circle1.radius();
    double r2 = circle2.radius();

    double d = Point2D.distance(center1, center2);

    // case of no intersection
    if (d < abs(r1 - r2) || d > (r1 + r2)) return new ArrayList<Point2D>(0);

    // Angle of line from center1 to center2
    double angle = Angle2D.horizontalAngle(center1, center2);

    if (d == abs(r1 - r2) || d == (r1 + r2)) {
      Collection<Point2D> r = new ArrayList<>(1);
      r.add(Point2D.createPolar(center1, r1, angle));
      return r;
    }

    // position of intermediate point
    double d1 = d / 2 + (r1 * r1 - r2 * r2) / (2 * d);
    Point2D tmp = Point2D.createPolar(center1, d1, angle);

    // distance between intermediate point and each intersection
    double h = sqrt(r1 * r1 - d1 * d1);

    // create empty array
    ArrayList<Point2D> intersections = new ArrayList<Point2D>(2);

    // Add the 2 intersection points
    Point2D p1 = Point2D.createPolar(tmp, h, angle + PI / 2);
    intersections.add(p1);
    Point2D p2 = Point2D.createPolar(tmp, h, angle - PI / 2);
    intersections.add(p2);

    return intersections;
  }