/*
 * 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.
 * @version $Id: SphereGenerator.java 1564921 2014-02-05 20:42:58Z luc $
 * @since 3.3
 */
public class SphereGenerator implements SupportBallGenerator<Euclidean3D, Vector3D> {

    /** {@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 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])));
    }

}
