/*
 * 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.commons.math3.geometry.euclidean.threed;

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

import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.geometry.enclosing.EnclosingBall;
import org.apache.commons.math3.geometry.enclosing.SupportBallGenerator;
import org.apache.commons.math3.geometry.euclidean.twod.DiskGenerator;
import org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D;
import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
import org.apache.commons.math3.util.FastMath;

Class generating an enclosing ball from its support points.
Since:3.3
/** Class generating an enclosing ball from its support points. * @since 3.3 */
public class SphereGenerator implements SupportBallGenerator<Euclidean3D, Vector3D> {
{@inheritDoc}
/** {@inheritDoc} */
public EnclosingBall<Euclidean3D, Vector3D> ballOnSupport(final List<Vector3D> support) { if (support.size() < 1) { return new EnclosingBall<Euclidean3D, Vector3D>(Vector3D.ZERO, Double.NEGATIVE_INFINITY); } else { final Vector3D vA = support.get(0); if (support.size() < 2) { return new EnclosingBall<Euclidean3D, Vector3D>(vA, 0, vA); } else { final Vector3D vB = support.get(1); if (support.size() < 3) { return new EnclosingBall<Euclidean3D, Vector3D>(new Vector3D(0.5, vA, 0.5, vB), 0.5 * vA.distance(vB), 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 return new EnclosingBall<Euclidean3D, Vector3D>(p.toSpace(disk.getCenter()), disk.getRadius(), 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[] { new BigFraction(vA.getX()), new BigFraction(vB.getX()), new BigFraction(vC.getX()), new BigFraction(vD.getX()) }; final BigFraction[] c3 = new BigFraction[] { new BigFraction(vA.getY()), new BigFraction(vB.getY()), new BigFraction(vC.getY()), new BigFraction(vD.getY()) }; final BigFraction[] c4 = new BigFraction[] { new BigFraction(vA.getZ()), new BigFraction(vB.getZ()), new BigFraction(vC.getZ()), new BigFraction(vD.getZ()) }; final BigFraction[] c1 = new BigFraction[] { 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 BigFraction centerX = m12.divide(twoM11); final BigFraction centerY = m13.divide(twoM11).negate(); final BigFraction centerZ = m14.divide(twoM11); final BigFraction dx = c2[0].subtract(centerX); final BigFraction dy = c3[0].subtract(centerY); final BigFraction dz = c4[0].subtract(centerZ); final BigFraction r2 = dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz)); return new EnclosingBall<Euclidean3D, Vector3D>(new Vector3D(centerX.doubleValue(), centerY.doubleValue(), centerZ.doubleValue()), FastMath.sqrt(r2.doubleValue()), vA, vB, vC, vD); } } } } }
Compute a dimension 4 minor, when 4th column is known to be filled with 1.0.
Params:
  • c1 – first column
  • c2 – second column
  • c3 – third column
Returns:value of the minor computed has an exact fraction
/** 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]))); } }