DiskGenerator.java

/*
 * 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
 *
 *      https://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.
 */

/*
 * This is not the original file distributed by the Apache Software Foundation
 * It has been modified by the Hipparchus project
 */
package org.hipparchus.geometry.euclidean.twod;

import java.util.List;

import org.hipparchus.fraction.BigFraction;
import org.hipparchus.geometry.enclosing.EnclosingBall;
import org.hipparchus.geometry.enclosing.SupportBallGenerator;
import org.hipparchus.util.FastMath;

/** Class generating an enclosing ball from its support points.
 */
public class DiskGenerator implements SupportBallGenerator<Euclidean2D, Vector2D> {

    /** Empty constructor.
     * <p>
     * This constructor is not strictly necessary, but it prevents spurious
     * javadoc warnings with JDK 18 and later.
     * </p>
     * @since 3.0
     */
    public DiskGenerator() { // NOPMD - unnecessary constructor added intentionally to make javadoc happy
        // nothing to do
    }

    /** {@inheritDoc} */
    @Override
    public EnclosingBall<Euclidean2D, Vector2D> ballOnSupport(final List<Vector2D> support) {

        if (support.isEmpty()) {
            return new EnclosingBall<>(Vector2D.ZERO, Double.NEGATIVE_INFINITY);
        } else {
            final Vector2D vA = support.get(0);
            if (support.size() < 2) {
                return new EnclosingBall<>(vA, 0, vA);
            } else {
                final Vector2D vB = support.get(1);
                if (support.size() < 3) {
                    final Vector2D center = new Vector2D(0.5, vA, 0.5, vB);

                    // we could have computed r directly from the vA and vB
                    // (it was done this way up to Hipparchus 1.0), but as center
                    // is approximated in the computation above, it is better to
                    // take the final value of center and compute r from the distances
                    // to center of all support points, using a max to ensure all support
                    // points belong to the ball
                    // see <https://github.com/Hipparchus-Math/hipparchus/issues/20>
                    final double r = FastMath.max(Vector2D.distance(vA, center),
                                                  Vector2D.distance(vB, center));
                    return new EnclosingBall<>(center, r, vA, vB);

                } else {
                    final Vector2D vC = support.get(2);
                    // a disk is 2D can be defined as:
                    // (1)   (x - x_0)^2 + (y - y_0)^2 = r^2
                    // which can be written:
                    // (2)   (x^2 + y^2) - 2 x_0 x - 2 y_0 y + (x_0^2 + y_0^2 - r^2) = 0
                    // or simply:
                    // (3)   (x^2 + y^2) + a x + b y + c = 0
                    // with disk center coordinates -a/2, -b/2
                    // If the disk exists, a, b and c are a non-zero solution to
                    // [ (x^2  + y^2 )   x    y   1 ]   [ 1 ]   [ 0 ]
                    // [ (xA^2 + yA^2)   xA   yA  1 ]   [ a ]   [ 0 ]
                    // [ (xB^2 + yB^2)   xB   yB  1 ] * [ b ] = [ 0 ]
                    // [ (xC^2 + yC^2)   xC   yC  1 ]   [ c ]   [ 0 ]
                    // So the determinant of the matrix is zero. Computing this determinant
                    // by expanding it using the minors m_ij of first row leads to
                    // (4)   m_11 (x^2 + y^2) - m_12 x + m_13 y - m_14 = 0
                    // So by identifying equations (2) and (4) we get the coordinates
                    // of center as:
                    //      x_0 = +m_12 / (2 m_11)
                    //      y_0 = -m_13 / (2 m_11)
                    // Note that the minors m_11, m_12 and m_13 all have the last column
                    // filled with 1.0, hence simplifying the computation
                    final BigFraction[] c2 = {
                        new BigFraction(vA.getX()), new BigFraction(vB.getX()), new BigFraction(vC.getX())
                    };
                    final BigFraction[] c3 = {
                        new BigFraction(vA.getY()), new BigFraction(vB.getY()), new BigFraction(vC.getY())
                    };
                    final BigFraction[] c1 = {
                        c2[0].multiply(c2[0]).add(c3[0].multiply(c3[0])),
                        c2[1].multiply(c2[1]).add(c3[1].multiply(c3[1])),
                        c2[2].multiply(c2[2]).add(c3[2].multiply(c3[2]))
                    };
                    final BigFraction twoM11 = minor(c2, c3).multiply(2);
                    final BigFraction m12    = minor(c1, c3);
                    final BigFraction m13    = minor(c1, c2);
                    final Vector2D center    = new Vector2D( m12.divide(twoM11).doubleValue(),
                                                            -m13.divide(twoM11).doubleValue());

                     // we could have computed r directly from the minors above
                     // (it was done this way up to Hipparchus 1.0), but as center
                     // is approximated in the computation above, it is better to
                     // take the final value of center and compute r from the distances
                     // to center of all support points, using a max to ensure all support
                     // points belong to the ball
                     // see <https://github.com/Hipparchus-Math/hipparchus/issues/20>
                     final double r = FastMath.max(Vector2D.distance(vA, center),
                                                   FastMath.max(Vector2D.distance(vB, center),
                                                                Vector2D.distance(vC, center)));
                    return new EnclosingBall<>(center, r, vA, vB, vC);

                }
            }
        }
    }

    /** Compute a dimension 3 minor, when 3<sup>d</sup> column is known to be filled with 1.0.
     * @param c1 first column
     * @param c2 second column
     * @return value of the minor computed has an exact fraction
     */
    private BigFraction minor(final BigFraction[] c1, final BigFraction[] c2) {
        return      c2[0].multiply(c1[2].subtract(c1[1])).
                add(c2[1].multiply(c1[0].subtract(c1[2]))).
                add(c2[2].multiply(c1[1].subtract(c1[0])));
    }

}