/*
    * 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.geometry.enclosing.euclidean.threed;
  
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.List;
  
  import org.apache.commons.geometry.core.precision.DoublePrecisionContext;
  import org.apache.commons.geometry.enclosing.EnclosingBall;
  import org.apache.commons.geometry.enclosing.SupportBallGenerator;
  import org.apache.commons.geometry.enclosing.euclidean.twod.DiskGenerator;
  import org.apache.commons.geometry.euclidean.threed.EmbeddingPlane;
  import org.apache.commons.geometry.euclidean.threed.Planes;
  import org.apache.commons.geometry.euclidean.threed.Vector3D;
  import org.apache.commons.geometry.euclidean.twod.Vector2D;
  import org.apache.commons.numbers.fraction.BigFraction;
  
  /** Class generating a sphere from its support points.
   */
  public class SphereGenerator implements SupportBallGenerator<Vector3D> {
  
      /** Precision context used to compare floating point numbers. */
      private final DoublePrecisionContext precision;
  
      /** Construct a new instance with the given precision context.
       * @param precision precision context used to compare floating point numbers
       */
      public SphereGenerator(final DoublePrecisionContext precision) {
          this.precision = precision;
      }
  
      /** {@inheritDoc} */
      @Override
      public EnclosingBall<Vector3D> ballOnSupport(final List<Vector3D> support) {
          if (support.isEmpty()) {
              return new EnclosingBall<>(Vector3D.ZERO, Double.NEGATIVE_INFINITY, Collections.emptyList());
          }
          final Vector3D vA = support.get(0);
          if (support.size() < 2) {
              return new EnclosingBall<>(vA, 0, Collections.singletonList(vA));
          }
          final Vector3D vB = support.get(1);
          if (support.size() < 3) {
              return new EnclosingBall<>(Vector3D.linearCombination(0.5, vA, 0.5, vB),
                                         0.5 * vA.distance(vB),
                                         Arrays.asList(vA, vB));
          }
          final Vector3D vC = support.get(2);
          if (support.size() < 4) {
              final EmbeddingPlane p = Planes.fromPoints(vA, vB, vC, precision).getEmbedding();
              final EnclosingBall<Vector2D> disk =
                      new DiskGenerator().ballOnSupport(Arrays.asList(p.toSubspace(vA),
                                                                      p.toSubspace(vB),
                                                                      p.toSubspace(vC)));
  
              // convert back to 3D
              return new EnclosingBall<>(p.toSpace(disk.getCenter()),
                                                              disk.getRadius(),
                                                              Arrays.asList(vA, vB, vC));
  
          }
          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 = {
             BigFraction.from(vA.getX()), BigFraction.from(vB.getX()),
             BigFraction.from(vC.getX()), BigFraction.from(vD.getX())
         };
         final BigFraction[] c3 = {
             BigFraction.from(vA.getY()), BigFraction.from(vB.getY()),
             BigFraction.from(vC.getY()), BigFraction.from(vD.getY())
         };
         final BigFraction[] c4 = {
             BigFraction.from(vA.getZ()), BigFraction.from(vB.getZ()),
             BigFraction.from(vC.getZ()), BigFraction.from(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 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<>(Vector3D.of(centerX.doubleValue(),
                                                centerY.doubleValue(),
                                                centerZ.doubleValue()),
                                    Math.sqrt(r2.doubleValue()),
                                    Arrays.asList(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])));
     }
 }