SphereGenerator.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.threed;

import java.util.Arrays;
import java.util.List;

import org.hipparchus.fraction.BigFraction;
import org.hipparchus.geometry.enclosing.EnclosingBall;
import org.hipparchus.geometry.enclosing.SupportBallGenerator;
import org.hipparchus.geometry.euclidean.twod.DiskGenerator;
import org.hipparchus.geometry.euclidean.twod.Euclidean2D;
import org.hipparchus.geometry.euclidean.twod.Vector2D;
import org.hipparchus.util.FastMath;

/** Class generating an enclosing ball from its support points.
 */
public class SphereGenerator implements SupportBallGenerator<Euclidean3D, Vector3D> {

    /** 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 SphereGenerator() { // NOPMD - unnecessary constructor added intentionally to make javadoc happy
        // nothing to do
    }

    /** {@inheritDoc} */
    @Override
    public EnclosingBall<Euclidean3D, Vector3D> ballOnSupport(final List<Vector3D> support) {

        if (support.isEmpty()) {
            return new EnclosingBall<>(Vector3D.ZERO, Double.NEGATIVE_INFINITY);
        } else {
            final Vector3D vA = support.get(0);
            if (support.size() < 2) {
                return new EnclosingBall<>(vA, 0, vA);
            } else {
                final Vector3D vB = support.get(1);
                if (support.size() < 3) {

                    final Vector3D center = new Vector3D(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(Vector3D.distance(vA, center),
                                                  Vector3D.distance(vB, center));
                    return new EnclosingBall<>(center, r, vA, vB);

                } else {
                    final Vector3D vC = support.get(2);
                    if (support.size() < 4) {

                        // delegate to 2D disk generator
                        final Plane p = new Plane(vA, vB, vC,
                                                  1.0e-10 * (vA.getNorm1() + vB.getNorm1() + vC.getNorm1()));
                        final EnclosingBall<Euclidean2D, Vector2D> disk =
                                new DiskGenerator().ballOnSupport(Arrays.asList(p.toSubSpace(vA),
                                                                                p.toSubSpace(vB),
                                                                                p.toSubSpace(vC)));

                        // convert back to 3D
                        final Vector3D center = p.toSpace(disk.getCenter());

                        // 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(Vector3D.distance(vA, center),
                                                      FastMath.max(Vector3D.distance(vB, center),
                                                                   Vector3D.distance(vC, center)));
                        return new EnclosingBall<>(center, r, vA, vB, vC);

                    } else {
                        final Vector3D vD = support.get(3);
                        // a sphere is 3D can be defined as:
                        // (1)   (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = r^2
                        // which can be written:
                        // (2)   (x^2 + y^2 + z^2) - 2 x_0 x - 2 y_0 y - 2 z_0 z + (x_0^2 + y_0^2 + z_0^2 - r^2) = 0
                        // or simply:
                        // (3)   (x^2 + y^2 + z^2) + a x + b y + c z + d = 0
                        // with sphere center coordinates -a/2, -b/2, -c/2
                        // If the sphere exists, a b, c and d are a non zero solution to
                        // [ (x^2  + y^2  + z^2)    x    y   z    1 ]   [ 1 ]   [ 0 ]
                        // [ (xA^2 + yA^2 + zA^2)   xA   yA  zA   1 ]   [ a ]   [ 0 ]
                        // [ (xB^2 + yB^2 + zB^2)   xB   yB  zB   1 ] * [ b ] = [ 0 ]
                        // [ (xC^2 + yC^2 + zC^2)   xC   yC  zC   1 ]   [ c ]   [ 0 ]
                        // [ (xD^2 + yD^2 + zD^2)   xD   yD  zD   1 ]   [ d ]   [ 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 + z^2) - m_12 x + m_13 y - m_14 z + m_15 = 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)
                        //      z_0 = +m_14 / (2 m_11)
                        // Note that the minors m_11, m_12, m_13 and m_14 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()), new BigFraction(vD.getX())
                        };
                        final BigFraction[] c3 = {
                            new BigFraction(vA.getY()), new BigFraction(vB.getY()),
                            new BigFraction(vC.getY()), new BigFraction(vD.getY())
                        };
                        final BigFraction[] c4 = {
                            new BigFraction(vA.getZ()), new BigFraction(vB.getZ()),
                            new BigFraction(vC.getZ()), new BigFraction(vD.getZ())
                        };
                        final BigFraction[] c1 = {
                            c2[0].multiply(c2[0]).add(c3[0].multiply(c3[0])).add(c4[0].multiply(c4[0])),
                            c2[1].multiply(c2[1]).add(c3[1].multiply(c3[1])).add(c4[1].multiply(c4[1])),
                            c2[2].multiply(c2[2]).add(c3[2].multiply(c3[2])).add(c4[2].multiply(c4[2])),
                            c2[3].multiply(c2[3]).add(c3[3].multiply(c3[3])).add(c4[3].multiply(c4[3]))
                        };
                        final BigFraction twoM11 = minor(c2, c3, c4).multiply(2);
                        final BigFraction m12    = minor(c1, c3, c4);
                        final BigFraction m13    = minor(c1, c2, c4);
                        final BigFraction m14    = minor(c1, c2, c3);
                        final Vector3D center    = new Vector3D( m12.divide(twoM11).doubleValue(),
                                                                -m13.divide(twoM11).doubleValue(),
                                                                 m14.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(Vector3D.distance(vA, center),
                                                      FastMath.max(Vector3D.distance(vB, center),
                                                                   FastMath.max(Vector3D.distance(vC, center),
                                                                                Vector3D.distance(vD, center))));
                        return new EnclosingBall<>(center, r, vA, vB, vC, vD);

                    }
                }
            }
        }
    }

    /** Compute a dimension 4 minor, when 4<sup>th</sup> column is known to be filled with 1.0.
     * @param c1 first column
     * @param c2 second column
     * @param c3 third column
     * @return value of the minor computed has an exact fraction
     */
    private BigFraction minor(final BigFraction[] c1, final BigFraction[] c2, final BigFraction[] c3) {
        return      c2[0].multiply(c3[1]).multiply(c1[2].subtract(c1[3])).
                add(c2[0].multiply(c3[2]).multiply(c1[3].subtract(c1[1]))).
                add(c2[0].multiply(c3[3]).multiply(c1[1].subtract(c1[2]))).
                add(c2[1].multiply(c3[0]).multiply(c1[3].subtract(c1[2]))).
                add(c2[1].multiply(c3[2]).multiply(c1[0].subtract(c1[3]))).
                add(c2[1].multiply(c3[3]).multiply(c1[2].subtract(c1[0]))).
                add(c2[2].multiply(c3[0]).multiply(c1[1].subtract(c1[3]))).
                add(c2[2].multiply(c3[1]).multiply(c1[3].subtract(c1[0]))).
                add(c2[2].multiply(c3[3]).multiply(c1[0].subtract(c1[1]))).
                add(c2[3].multiply(c3[0]).multiply(c1[2].subtract(c1[1]))).
                add(c2[3].multiply(c3[1]).multiply(c1[0].subtract(c1[2]))).
                add(c2[3].multiply(c3[2]).multiply(c1[1].subtract(c1[0])));
    }

}