--- /dev/null
+/**
+ * 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();
+ }
+
+}
fnp / pylucene.git / blobdiff