content: /**
   * Licensed to the Apache Software Foundation (ASF) under one or more
   * contributor license agreements.  See the NOTICE file distributed with
   * this work for additional information regarding copyright ownership.
   * The ASF licenses this file to You under the Apache License, Version 2.0
   * (the "License"); you may not use this file except in compliance with
   * the License.  You may obtain a copy of the License at
   *
   *     http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  
  package org.apache.lucene.spatial.geometry.shape;
  
  
  /**
   * Ellipse shape. From C++ gl.
   *
   * <p><font color="red"><b>NOTE:</b> This API is still in
   * flux and might change in incompatible ways in the next
   * release.</font>
   */
  public class Ellipse implements Geometry2D {
    private Point2D center;
  
    /**
     * Half length of major axis
     */
    private double a;
  
    /**
     * Half length of minor axis
     */
    private double b;
  
    private double k1, k2, k3;
  
    /**
     * sin of rotation angle
     */
    private double s;
  
    /**
     * cos of rotation angle
     */
    private double c;
  
    public Ellipse() {
      center = new Point2D(0, 0);
    }
  
    private double SQR(double d) {
      return d * d;
    }
  
    /**
     * Constructor given bounding rectangle and a rotation.
     */
    public Ellipse(Point2D p1, Point2D p2, double angle) {
      center = new Point2D();
  
      // Set the center
      center.x((p1.x() + p2.x()) * 0.5f);
      center.y((p1.y() + p2.y()) * 0.5f);
  
      // Find sin and cos of the angle
      double angleRad = Math.toRadians(angle);
      c = Math.cos(angleRad);
      s = Math.sin(angleRad);
  
      // Find the half lengths of the semi-major and semi-minor axes
      double dx = Math.abs(p2.x() - p1.x()) * 0.5;
      double dy = Math.abs(p2.y() - p1.y()) * 0.5;
      if (dx >= dy) {
        a = dx;
        b = dy;
      } else {
        a = dy;
        b = dx;
      }
  
      // Find k1, k2, k3 - define when a point x,y is on the ellipse
      k1 = SQR(c / a) + SQR(s / b);
      k2 = 2 * s * c * ((1 / SQR(a)) - (1 / SQR(b)));
      k3 = SQR(s / a) + SQR(c / b);
    }
  
    /**
     * Determines if a line segment intersects the ellipse and if so finds the
     * point(s) of intersection.
     * 
     * @param seg
     *            Line segment to test for intersection
     * @param pt0
     *            OUT - intersection point (if it exists)
     * @param pt1
     *            OUT - second intersection point (if it exists)
     * 
     * @return Returns the number of intersection points (0, 1, or 2).
     */
    public int intersect(LineSegment seg, Point2D pt0, Point2D pt1) {
      if (pt0 == null)
        pt0 = new Point2D();
      if (pt1 == null)
        pt1 = new Point2D();
  
      // Solution is found by parameterizing the line segment and
      // substituting those values into the ellipse equation.
      // Results in a quadratic equation.
      double x1 = center.x();
      double y1 = center.y();
      double u1 = seg.A.x();
      double v1 = seg.A.y();
      double u2 = seg.B.x();
      double v2 = seg.B.y();
      double dx = u2 - u1;
      double dy = v2 - v1;
      double q0 = k1 * SQR(u1 - x1) + k2 * (u1 - x1) * (v1 - y1) + k3
          * SQR(v1 - y1) - 1;
      double q1 = (2 * k1 * dx * (u1 - x1)) + (k2 * dx * (v1 - y1))
          + (k2 * dy * (u1 - x1)) + (2 * k3 * dy * (v1 - y1));
      double q2 = (k1 * SQR(dx)) + (k2 * dx * dy) + (k3 * SQR(dy));
  
      // Compare q1^2 to 4*q0*q2 to see how quadratic solves
      double d = SQR(q1) - (4 * q0 * q2);
      if (d < 0) {
        // Roots are complex valued. Line containing the segment does
        // not intersect the ellipse
        return 0;
      }
  
      if (d == 0) {
        // One real-valued root - line is tangent to the ellipse
        double t = -q1 / (2 * q2);
        if (0 <= t && t <= 1) {
          // Intersection occurs along line segment
          pt0.x(u1 + t * dx);
          pt0.y(v1 + t * dy);
          return 1;
        } else
          return 0;
      } else {
        // Two distinct real-valued roots. Solve for the roots and see if
        // they fall along the line segment
        int n = 0;
        double q = Math.sqrt(d);
        double t = (-q1 - q) / (2 * q2);
        if (0 <= t && t <= 1) {
          // Intersection occurs along line segment
          pt0.x(u1 + t * dx);
          pt0.y(v1 + t * dy);
          n++;
        }
  
        // 2nd root
        t = (-q1 + q) / (2 * q2);
        if (0 <= t && t <= 1) {
          if (n == 0) {
            pt0.x(u1 + t * dx);
            pt0.y(v1 + t * dy);
            n++;
          } else {
            pt1.x(u1 + t * dx);
            pt1.y(v1 + t * dy);
            n++;
          }
        }
        return n;
      }
    }
  
    public IntersectCase intersect(Rectangle r) {
      // Test if all 4 corners of the rectangle are inside the ellipse
      Point2D ul = new Point2D(r.MinPt().x(), r.MaxPt().y());
      Point2D ur = new Point2D(r.MaxPt().x(), r.MaxPt().y());
      Point2D ll = new Point2D(r.MinPt().x(), r.MinPt().y());
      Point2D lr = new Point2D(r.MaxPt().x(), r.MinPt().y());
      if (contains(ul) && contains(ur) && contains(ll) && contains(lr))
        return IntersectCase.CONTAINS;
  
      // Test if any of the rectangle edges intersect
      Point2D pt0 = new Point2D(), pt1 = new Point2D();
      LineSegment bottom = new LineSegment(ll, lr);
      if (intersect(bottom, pt0, pt1) > 0)
        return IntersectCase.INTERSECTS;
  
      LineSegment top = new LineSegment(ul, ur);
      if (intersect(top, pt0, pt1) > 0)
        return IntersectCase.INTERSECTS;
  
      LineSegment left = new LineSegment(ll, ul);
      if (intersect(left, pt0, pt1) > 0)
        return IntersectCase.INTERSECTS;
  
      LineSegment right = new LineSegment(lr, ur);
      if (intersect(right, pt0, pt1) > 0)
        return IntersectCase.INTERSECTS;
  
      // Ellipse does not intersect any edge : since the case for the ellipse
      // containing the rectangle was considered above then if the center
      // is inside the ellipse is fully inside and if center is outside
      // the ellipse is fully outside
      return (r.contains(center)) ? IntersectCase.WITHIN
          : IntersectCase.OUTSIDE;
    }
  
    public double area() {
      throw new UnsupportedOperationException();
    }
  
    public Point2D centroid() {
      throw new UnsupportedOperationException();
    }
  
    public boolean contains(Point2D pt) {
      // Plug in equation for ellipse, If evaluates to <= 0 then the
      // point is in or on the ellipse.
      double dx = pt.x() - center.x();
      double dy = pt.y() - center.y();
      double eq=(((k1 * SQR(dx)) + (k2 * dx * dy) + (k3 * SQR(dy)) - 1));
      
      return eq<=0;
    }
  
    public void translate(Vector2D v) {
      throw new UnsupportedOperationException();
    }
  
  }
  