/*
    * 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.euclidean.threed;
  
  import java.util.function.UnaryOperator;
  
  import org.apache.commons.geometry.core.GeometryTestUtils;
  import org.apache.commons.geometry.core.precision.DoublePrecisionContext;
  import org.apache.commons.geometry.core.precision.EpsilonDoublePrecisionContext;
  import org.apache.commons.geometry.euclidean.EuclideanTestUtils;
  import org.apache.commons.geometry.euclidean.EuclideanTestUtils.PermuteCallback3D;
  import org.apache.commons.geometry.euclidean.threed.rotation.QuaternionRotation;
  import org.apache.commons.geometry.euclidean.threed.rotation.StandardRotations;
  import org.apache.commons.numbers.angle.PlaneAngleRadians;
  import org.junit.Assert;
  import org.junit.Test;
  
  public class AffineTransformMatrix3DTest {
  
      private static final double EPS = 1e-12;
  
      private static final DoublePrecisionContext TEST_PRECISION =
              new EpsilonDoublePrecisionContext(EPS);
  
      @Test
      public void testOf() {
          // arrange
          final double[] arr = {
              1, 2, 3, 4,
              5, 6, 7, 8,
              9, 10, 11, 12
          };
  
          // act
          final AffineTransformMatrix3D transform = AffineTransformMatrix3D.of(arr);
  
          // assert
          final double[] result = transform.toArray();
          Assert.assertNotSame(arr, result);
          Assert.assertArrayEquals(arr, result, 0.0);
      }
  
      @Test
      public void testOf_invalidDimensions() {
          // act/assert
          GeometryTestUtils.assertThrows(() -> AffineTransformMatrix3D.of(1, 2),
                  IllegalArgumentException.class, "Dimension mismatch: 2 != 12");
      }
  
      @Test
      public void testFromColumnVectors_threeVectors() {
          // arrange
          final Vector3D u = Vector3D.of(1, 2, 3);
          final Vector3D v = Vector3D.of(4, 5, 6);
          final Vector3D w = Vector3D.of(7, 8, 9);
  
          // act
          final AffineTransformMatrix3D transform = AffineTransformMatrix3D.fromColumnVectors(u, v, w);
  
          // assert
          Assert.assertArrayEquals(new double[] {
              1, 4, 7, 0,
              2, 5, 8, 0,
              3, 6, 9, 0
          }, transform.toArray(), 0.0);
      }
  
      @Test
      public void testFromColumnVectors_fourVectors() {
          // arrange
          final Vector3D u = Vector3D.of(1, 2, 3);
          final Vector3D v = Vector3D.of(4, 5, 6);
          final Vector3D w = Vector3D.of(7, 8, 9);
          final Vector3D t = Vector3D.of(10, 11, 12);
  
          // act
          final AffineTransformMatrix3D transform = AffineTransformMatrix3D.fromColumnVectors(u, v, w, t);
  
          // assert
          Assert.assertArrayEquals(new double[] {
              1, 4, 7, 10,
              2, 5, 8, 11,
              3, 6, 9, 12
          }, transform.toArray(), 0.0);
      }
 
     @Test
     public void testFrom() {
         // act/assert
         Assert.assertArrayEquals(new double[] {
             1, 0, 0, 0,
             0, 1, 0, 0,
             0, 0, 1, 0
         }, AffineTransformMatrix3D.from(UnaryOperator.identity()).toArray(), EPS);
         Assert.assertArrayEquals(new double[] {
             1, 0, 0, 2,
             0, 1, 0, 3,
             0, 0, 1, -4
         }, AffineTransformMatrix3D.from(v -> v.add(Vector3D.of(2, 3, -4))).toArray(), EPS);
         Assert.assertArrayEquals(new double[] {
             3, 0, 0, 0,
             0, 3, 0, 0,
             0, 0, 3, 0
         }, AffineTransformMatrix3D.from(v -> v.multiply(3)).toArray(), EPS);
         Assert.assertArrayEquals(new double[] {
             3, 0, 0, 6,
             0, 3, 0, 9,
             0, 0, 3, 12
         }, AffineTransformMatrix3D.from(v -> v.add(Vector3D.of(2, 3, 4)).multiply(3)).toArray(), EPS);
     }
 
     @Test
     public void testFrom_invalidFunction() {
         // act/assert
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.from(v -> v.multiply(0));
         }, IllegalArgumentException.class);
     }
 
     @Test
     public void testIdentity() {
         // act
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity();
 
         // assert
         final double[] expected = {
             1, 0, 0, 0,
             0, 1, 0, 0,
             0, 0, 1, 0
         };
         Assert.assertArrayEquals(expected, transform.toArray(), 0.0);
     }
 
     @Test
     public void testCreateTranslation_xyz() {
         // act
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createTranslation(2, 3, 4);
 
         // assert
         final double[] expected = {
             1, 0, 0, 2,
             0, 1, 0, 3,
             0, 0, 1, 4
         };
         Assert.assertArrayEquals(expected, transform.toArray(), 0.0);
     }
 
     @Test
     public void testCreateTranslation_vector() {
         // act
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createTranslation(Vector3D.of(5, 6, 7));
 
         // assert
         final double[] expected = {
             1, 0, 0, 5,
             0, 1, 0, 6,
             0, 0, 1, 7
         };
         Assert.assertArrayEquals(expected, transform.toArray(), 0.0);
     }
 
     @Test
     public void testCreateScale_xyz() {
         // act
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createScale(2, 3, 4);
 
         // assert
         final double[] expected = {
             2, 0, 0, 0,
             0, 3, 0, 0,
             0, 0, 4, 0
         };
         Assert.assertArrayEquals(expected, transform.toArray(), 0.0);
     }
 
     @Test
     public void testTranslate_xyz() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     2, 0, 0, 10,
                     0, 3, 0, 11,
                     0, 0, 4, 12
                 );
 
         // act
         final AffineTransformMatrix3D result = a.translate(4, 5, 6);
 
         // assert
         final double[] expected = {
             2, 0, 0, 14,
             0, 3, 0, 16,
             0, 0, 4, 18
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testTranslate_vector() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     2, 0, 0, 10,
                     0, 3, 0, 11,
                     0, 0, 4, 12
                 );
 
         // act
         final AffineTransformMatrix3D result = a.translate(Vector3D.of(7, 8, 9));
 
         // assert
         final double[] expected = {
             2, 0, 0, 17,
             0, 3, 0, 19,
             0, 0, 4, 21
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testCreateScale_vector() {
         // act
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createScale(Vector3D.of(4, 5, 6));
 
         // assert
         final double[] expected = {
             4, 0, 0, 0,
             0, 5, 0, 0,
             0, 0, 6, 0
         };
         Assert.assertArrayEquals(expected, transform.toArray(), 0.0);
     }
 
     @Test
     public void testCreateScale_singleValue() {
         // act
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createScale(7);
 
         // assert
         final double[] expected = {
             7, 0, 0, 0,
             0, 7, 0, 0,
             0, 0, 7, 0
         };
         Assert.assertArrayEquals(expected, transform.toArray(), 0.0);
     }
 
     @Test
     public void testScale_xyz() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     2, 0, 0, 10,
                     0, 3, 0, 11,
                     0, 0, 4, 12
                 );
 
         // act
         final AffineTransformMatrix3D result = a.scale(4, 5, 6);
 
         // assert
         final double[] expected = {
             8, 0, 0, 40,
             0, 15, 0, 55,
             0, 0, 24, 72
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testScale_vector() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     2, 0, 0, 10,
                     0, 3, 0, 11,
                     0, 0, 4, 12
                 );
 
         // act
         final AffineTransformMatrix3D result = a.scale(Vector3D.of(7, 8, 9));
 
         // assert
         final double[] expected = {
             14, 0, 0, 70,
             0, 24, 0, 88,
             0, 0, 36, 108
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testScale_singleValue() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     2, 0, 0, 10,
                     0, 3, 0, 11,
                     0, 0, 4, 12
                 );
 
         // act
         final AffineTransformMatrix3D result = a.scale(10);
 
         // assert
         final double[] expected = {
             20, 0, 0, 100,
             0, 30, 0, 110,
             0, 0, 40, 120
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testCreateRotation() {
         // arrange
         final Vector3D center = Vector3D.of(1, 2, 3);
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO);
 
         // act
         final AffineTransformMatrix3D result = AffineTransformMatrix3D.createRotation(center, rotation);
 
         // assert
         final double[] expected = {
             0, -1, 0, 3,
             1, 0, 0, 1,
             0, 0, 1, 0
         };
         Assert.assertArrayEquals(expected, result.toArray(), EPS);
     }
 
     @Test
     public void testRotate() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     1, 2, 3, 4,
                     5, 6, 7, 8,
                     9, 10, 11, 12
                 );
 
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO);
 
         // act
         final AffineTransformMatrix3D result = a.rotate(rotation);
 
         // assert
         final double[] expected = {
             -5, -6, -7, -8,
             1, 2, 3, 4,
             9, 10, 11, 12
         };
         Assert.assertArrayEquals(expected, result.toArray(), EPS);
     }
 
     @Test
     public void testRotate_aroundCenter() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     1, 2, 3, 4,
                     5, 6, 7, 8,
                     9, 10, 11, 12
                 );
 
         final Vector3D center = Vector3D.of(1, 2, 3);
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO);
 
         // act
         final AffineTransformMatrix3D result = a.rotate(center, rotation);
 
         // assert
         final double[] expected = {
             -5, -6, -7, -5,
             1, 2, 3, 5,
             9, 10, 11, 12
         };
         Assert.assertArrayEquals(expected, result.toArray(), EPS);
     }
 
     @Test
     public void testApply_identity() {
         // arrange
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity();
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D v = Vector3D.of(x, y, z);
 
             EuclideanTestUtils.assertCoordinatesEqual(v, transform.apply(v), EPS);
         });
     }
 
     @Test
     public void testApply_translate() {
         // arrange
         final Vector3D translation = Vector3D.of(1.1, -PlaneAngleRadians.PI, 5.5);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .translate(translation);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = vec.add(translation);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testApply_scale() {
         // arrange
         final Vector3D factors = Vector3D.of(2.0, -3.0, 4.0);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(factors);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = Vector3D.of(factors.getX() * x, factors.getY() * y, factors.getZ() * z);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testApply_translateThenScale() {
         // arrange
         final Vector3D translation = Vector3D.of(-2.0, -3.0, -4.0);
         final Vector3D scale = Vector3D.of(5.0, 6.0, 7.0);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .translate(translation)
                 .scale(scale);
 
         // act/assert
         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-5, -12, -21), transform.apply(Vector3D.of(1, 1, 1)), EPS);
 
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = Vector3D.of(
                         (x + translation.getX()) * scale.getX(),
                         (y + translation.getY()) * scale.getY(),
                         (z + translation.getZ()) * scale.getZ()
                     );
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testApply_scaleThenTranslate() {
         // arrange
         final Vector3D scale = Vector3D.of(5.0, 6.0, 7.0);
         final Vector3D translation = Vector3D.of(-2.0, -3.0, -4.0);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(scale)
                 .translate(translation);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = Vector3D.of(
                         (x * scale.getX()) + translation.getX(),
                         (y * scale.getY()) + translation.getY(),
                         (z * scale.getZ()) + translation.getZ()
                     );
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testApply_rotate() {
         // arrange
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.of(1, 1, 1), 2.0 * PlaneAngleRadians.PI / 3.0);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity().rotate(rotation);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = StandardRotations.PLUS_DIAGONAL_TWO_THIRDS_PI.apply(vec);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testApply_rotate_aroundCenter() {
         // arrange
         final double scaleFactor = 2;
         final Vector3D center = Vector3D.of(3, -4, 5);
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(scaleFactor)
                 .rotate(center, rotation);
 
         // act/assert
         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(3, -3, 2), transform.apply(Vector3D.of(2, -2, 1)), EPS);
 
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = StandardRotations.PLUS_Z_HALF_PI.apply(vec.multiply(scaleFactor).subtract(center)).add(center);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testApplyVector_identity() {
         // arrange
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity();
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D v = Vector3D.of(x, y, z);
 
             EuclideanTestUtils.assertCoordinatesEqual(v, transform.applyVector(v), EPS);
         });
     }
 
     @Test
     public void testApplyVector_translate() {
         // arrange
         final Vector3D translation = Vector3D.of(1.1, -PlaneAngleRadians.PI, 5.5);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .translate(translation);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             EuclideanTestUtils.assertCoordinatesEqual(vec, transform.applyVector(vec), EPS);
         });
     }
 
     @Test
     public void testApplyVector_scale() {
         // arrange
         final Vector3D factors = Vector3D.of(2.0, -3.0, 4.0);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(factors);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = Vector3D.of(factors.getX() * x, factors.getY() * y, factors.getZ() * z);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.applyVector(vec), EPS);
         });
     }
 
     @Test
     public void testApplyVector_representsDisplacement() {
         // arrange
         final Vector3D p1 = Vector3D.of(1, 2, 3);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(1.5)
                 .translate(4, 6, 5)
                 .rotate(QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO));
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D p2 = Vector3D.of(x, y, z);
             final Vector3D input = p1.subtract(p2);
 
             final Vector3D expected = transform.apply(p1).subtract(transform.apply(p2));
 
             EuclideanTestUtils.assertCoordinatesEqual(expected, transform.applyVector(input), EPS);
         });
     }
 
     @Test
     public void testApplyDirection_identity() {
         // arrange
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity();
 
         // act/assert
         EuclideanTestUtils.permuteSkipZero(-5, 5, 0.5, (x, y, z) -> {
             final Vector3D v = Vector3D.of(x, y, z);
 
             EuclideanTestUtils.assertCoordinatesEqual(v.normalize(), transform.applyDirection(v), EPS);
         });
     }
 
     @Test
     public void testApplyDirection_translate() {
         // arrange
         final Vector3D translation = Vector3D.of(1.1, -PlaneAngleRadians.PI, 5.5);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .translate(translation);
 
         // act/assert
         EuclideanTestUtils.permuteSkipZero(-5, 5, 0.5, (x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             EuclideanTestUtils.assertCoordinatesEqual(vec.normalize(), transform.applyDirection(vec), EPS);
         });
     }
 
     @Test
     public void testApplyDirection_scale() {
         // arrange
         final Vector3D factors = Vector3D.of(2.0, -3.0, 4.0);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(factors);
 
         // act/assert
         EuclideanTestUtils.permuteSkipZero(-5, 5, 0.5, (x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = Vector3D.of(factors.getX() * x, factors.getY() * y, factors.getZ() * z).normalize();
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.applyDirection(vec), EPS);
         });
     }
 
     @Test
     public void testApplyDirection_representsNormalizedDisplacement() {
         // arrange
         final Vector3D p1 = Vector3D.of(1, 2, 3);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.identity()
                 .scale(1.5)
                 .translate(4, 6, 5)
                 .rotate(QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO));
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D p2 = Vector3D.of(x, y, z);
             final Vector3D input = p1.subtract(p2);
 
             final Vector3D expected = transform.apply(p1).subtract(transform.apply(p2)).normalize();
 
             EuclideanTestUtils.assertCoordinatesEqual(expected, transform.applyDirection(input), EPS);
         });
     }
 
     @Test
     public void testApplyDirection_illegalNorm() {
         // act/assert
         GeometryTestUtils.assertThrows(() -> AffineTransformMatrix3D.createScale(1, 0, 1).applyDirection(Vector3D.Unit.PLUS_Y),
                 IllegalArgumentException.class);
         GeometryTestUtils.assertThrows(() -> AffineTransformMatrix3D.createScale(2).applyDirection(Vector3D.ZERO),
                 IllegalArgumentException.class);
     }
 
     @Test
     public void testMultiply() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     1, 2, 3, 4,
                     5, 6, 7, 8,
                     9, 10, 11, 12
                 );
         final AffineTransformMatrix3D b = AffineTransformMatrix3D.of(
                     13, 14, 15, 16,
                     17, 18, 19, 20,
                     21, 22, 23, 24
                 );
 
         // act
         final AffineTransformMatrix3D result = a.multiply(b);
 
         // assert
         final double[] arr = result.toArray();
         Assert.assertArrayEquals(new double[] {
             110, 116, 122, 132,
             314, 332, 350, 376,
             518, 548, 578, 620
         }, arr, EPS);
     }
 
     @Test
     public void testDeterminant() {
         // act/assert
         Assert.assertEquals(1.0, AffineTransformMatrix3D.identity().determinant(), EPS);
         Assert.assertEquals(1.0, AffineTransformMatrix3D.of(
                 1, 0, 0, 10,
                 0, 1, 0, 11,
                 0, 0, 1, 12
             ).determinant(), EPS);
         Assert.assertEquals(-1.0, AffineTransformMatrix3D.of(
                 -1, 0, 0, 10,
                 0, 1, 0, 11,
                 0, 0, 1, 12
             ).determinant(), EPS);
         Assert.assertEquals(1.0, AffineTransformMatrix3D.of(
                 -1, 0, 0, 10,
                 0, -1, 0, 11,
                 0, 0, 1, 12
             ).determinant(), EPS);
         Assert.assertEquals(-1.0, AffineTransformMatrix3D.of(
                 -1, 0, 0, 10,
                 0, -1, 0, 11,
                 0, 0, -1, 12
             ).determinant(), EPS);
         Assert.assertEquals(49.0, AffineTransformMatrix3D.of(
                 2, -3, 1, 10,
                 2, 0, -1, 11,
                 1, 4, 5, -12
             ).determinant(), EPS);
         Assert.assertEquals(0.0, AffineTransformMatrix3D.of(
                 1, 2, 3, 0,
                 4, 5, 6, 0,
                 7, 8, 9, 0
             ).determinant(), EPS);
     }
 
     @Test
     public void testPreservesOrientation() {
         // act/assert
         Assert.assertTrue(AffineTransformMatrix3D.identity().preservesOrientation());
         Assert.assertTrue(AffineTransformMatrix3D.of(
                 1, 0, 0, 10,
                 0, 1, 0, 11,
                 0, 0, 1, 12
             ).preservesOrientation());
         Assert.assertTrue(AffineTransformMatrix3D.of(
                 2, -3, 1, 10,
                 2, 0, -1, 11,
                 1, 4, 5, -12
             ).preservesOrientation());
 
         Assert.assertFalse(AffineTransformMatrix3D.of(
                 -1, 0, 0, 10,
                 0, 1, 0, 11,
                 0, 0, 1, 12
             ).preservesOrientation());
 
         Assert.assertTrue(AffineTransformMatrix3D.of(
                 -1, 0, 0, 10,
                 0, -1, 0, 11,
                 0, 0, 1, 12
             ).preservesOrientation());
 
         Assert.assertFalse(AffineTransformMatrix3D.of(
                 -1, 0, 0, 10,
                 0, -1, 0, 11,
                 0, 0, -1, 12
             ).preservesOrientation());
         Assert.assertFalse(AffineTransformMatrix3D.of(
                 1, 2, 3, 0,
                 4, 5, 6, 0,
                 7, 8, 9, 0
             ).preservesOrientation());
     }
 
     @Test
     public void testMultiply_combinesTransformOperations() {
         // arrange
         final Vector3D translation1 = Vector3D.of(1, 2, 3);
         final double scale = 2.0;
         final Vector3D translation2 = Vector3D.of(4, 5, 6);
 
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.createTranslation(translation1);
         final AffineTransformMatrix3D b = AffineTransformMatrix3D.createScale(scale);
         final AffineTransformMatrix3D c = AffineTransformMatrix3D.identity();
         final AffineTransformMatrix3D d = AffineTransformMatrix3D.createTranslation(translation2);
 
         // act
         final AffineTransformMatrix3D transform = d.multiply(c).multiply(b).multiply(a);
 
         // assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = vec
                     .add(translation1)
                     .multiply(scale)
                     .add(translation2);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testPremultiply() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     1, 2, 3, 4,
                     5, 6, 7, 8,
                     9, 10, 11, 12
                 );
         final AffineTransformMatrix3D b = AffineTransformMatrix3D.of(
                     13, 14, 15, 16,
                     17, 18, 19, 20,
                     21, 22, 23, 24
                 );
 
         // act
         final AffineTransformMatrix3D result = b.premultiply(a);
 
         // assert
         final double[] arr = result.toArray();
         Assert.assertArrayEquals(new double[] {
             110, 116, 122, 132,
             314, 332, 350, 376,
             518, 548, 578, 620
         }, arr, EPS);
     }
 
     @Test
     public void testPremultiply_combinesTransformOperations() {
         // arrange
         final Vector3D translation1 = Vector3D.of(1, 2, 3);
         final double scale = 2.0;
         final Vector3D translation2 = Vector3D.of(4, 5, 6);
 
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.createTranslation(translation1);
         final AffineTransformMatrix3D b = AffineTransformMatrix3D.createScale(scale);
         final AffineTransformMatrix3D c = AffineTransformMatrix3D.identity();
         final AffineTransformMatrix3D d = AffineTransformMatrix3D.createTranslation(translation2);
 
         // act
         final AffineTransformMatrix3D transform = a.premultiply(b).premultiply(c).premultiply(d);
 
         // assert
         runWithCoordinates((x, y, z) -> {
             final Vector3D vec = Vector3D.of(x, y, z);
 
             final Vector3D expectedVec = vec
                     .add(translation1)
                     .multiply(scale)
                     .add(translation2);
 
             EuclideanTestUtils.assertCoordinatesEqual(expectedVec, transform.apply(vec), EPS);
         });
     }
 
     @Test
     public void testInverse_identity() {
         // act
         final AffineTransformMatrix3D inverse = AffineTransformMatrix3D.identity().inverse();
 
         // assert
         final double[] expected = {
             1, 0, 0, 0,
             0, 1, 0, 0,
             0, 0, 1, 0
         };
         Assert.assertArrayEquals(expected, inverse.toArray(), 0.0);
     }
 
     @Test
     public void testInverse_multiplyByInverse_producesIdentity() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     1, 3, 7, 8,
                     2, 4, 9, 12,
                     5, 6, 10, 11
                 );
 
         final AffineTransformMatrix3D inv = a.inverse();
 
         // act
         final AffineTransformMatrix3D result = inv.multiply(a);
 
         // assert
         final double[] expected = {
             1, 0, 0, 0,
             0, 1, 0, 0,
             0, 0, 1, 0
         };
         Assert.assertArrayEquals(expected, result.toArray(), EPS);
     }
 
     @Test
     public void testInverse_translate() {
         // arrange
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createTranslation(1, -2, 4);
 
         // act
         final AffineTransformMatrix3D inverse = transform.inverse();
 
         // assert
         final double[] expected = {
             1, 0, 0, -1,
             0, 1, 0, 2,
             0, 0, 1, -4
         };
         Assert.assertArrayEquals(expected, inverse.toArray(), 0.0);
     }
 
     @Test
     public void testInverse_scale() {
         // arrange
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createScale(10, -2, 4);
 
         // act
         final AffineTransformMatrix3D inverse = transform.inverse();
 
         // assert
         final double[] expected = {
             0.1, 0, 0, 0,
             0, -0.5, 0, 0,
             0, 0, 0.25, 0
         };
         Assert.assertArrayEquals(expected, inverse.toArray(), 0.0);
     }
 
     @Test
     public void testInverse_rotate() {
         // arrange
         final Vector3D center = Vector3D.of(1, 2, 3);
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Z, PlaneAngleRadians.PI_OVER_TWO);
 
         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.createRotation(center, rotation);
 
         // act
         final AffineTransformMatrix3D inverse = transform.inverse();
 
         // assert
         final double[] expected = {
             0, 1, 0, -1,
             -1, 0, 0, 3,
             0, 0, 1, 0
         };
         Assert.assertArrayEquals(expected, inverse.toArray(), EPS);
     }
 
     @Test
     public void testInverse_undoesOriginalTransform() {
         // arrange
         final Vector3D v1 = Vector3D.ZERO;
         final Vector3D v2 = Vector3D.Unit.PLUS_X;
         final Vector3D v3 = Vector3D.of(1, 1, 1);
         final Vector3D v4 = Vector3D.of(-2, 3, 4);
 
         final Vector3D center = Vector3D.of(1, 2, 3);
         final QuaternionRotation rotation = QuaternionRotation.fromAxisAngle(Vector3D.of(1, 2, 3), 0.25);
 
         // act/assert
         runWithCoordinates((x, y, z) -> {
             final AffineTransformMatrix3D transform = AffineTransformMatrix3D
                         .createTranslation(x, y, z)
                         .scale(2, 3, 4)
                         .rotate(center, rotation)
                         .translate(x / 3, y / 3, z / 3);
 
             final AffineTransformMatrix3D inverse = transform.inverse();
 
             EuclideanTestUtils.assertCoordinatesEqual(v1, inverse.apply(transform.apply(v1)), EPS);
             EuclideanTestUtils.assertCoordinatesEqual(v2, inverse.apply(transform.apply(v2)), EPS);
             EuclideanTestUtils.assertCoordinatesEqual(v3, inverse.apply(transform.apply(v3)), EPS);
             EuclideanTestUtils.assertCoordinatesEqual(v4, inverse.apply(transform.apply(v4)), EPS);
         });
     }
 
     @Test
     public void testInverse_nonInvertible() {
         // act/assert
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     0, 0, 0, 0,
                     0, 0, 0, 0,
                     0, 0, 0, 0).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; matrix determinant is 0.0");
 
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     1, 0, 0, 0,
                     0, 1, 0, 0,
                     0, 0, Double.NaN, 0).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; matrix determinant is NaN");
 
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     1, 0, 0, 0,
                     0, Double.NEGATIVE_INFINITY, 0, 0,
                     0, 0, 1, 0).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; matrix determinant is NaN");
 
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     Double.POSITIVE_INFINITY, 0, 0, 0,
                     0, 1, 0, 0,
                     0, 0, 1, 0).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; matrix determinant is NaN");
 
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     1, 0, 0, Double.NaN,
                     0, 1, 0, 0,
                     0, 0, 1, 0).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; invalid matrix element: NaN");
 
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     1, 0, 0, 0,
                     0, 1, 0, Double.POSITIVE_INFINITY,
                     0, 0, 1, 0).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; invalid matrix element: Infinity");
 
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.of(
                     1, 0, 0, 0,
                     0, 1, 0, 0,
                     0, 0, 1, Double.NEGATIVE_INFINITY).inverse();
         }, IllegalStateException.class, "Matrix is not invertible; invalid matrix element: -Infinity");
     }
 
     @Test
     public void testLinear() {
         // arrange
         final AffineTransformMatrix3D mat = AffineTransformMatrix3D.of(
                 2, 3, 4, 5,
                 6, 7, 8, 9,
                 10, 11, 12, 13);
 
         // act
         final AffineTransformMatrix3D result = mat.linear();
 
         // assert
         final double[] expected = {
             2, 3, 4, 0,
             6, 7, 8, 0,
             10, 11, 12, 0
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testLinearTranspose() {
         // arrange
         final AffineTransformMatrix3D mat = AffineTransformMatrix3D.of(
                 2, 3, 4, 5,
                 6, 7, 8, 9,
                 10, 11, 12, 13);
 
         // act
         final AffineTransformMatrix3D result = mat.linearTranspose();
 
         // assert
         final double[] expected = {
             2, 6, 10, 0,
             3, 7, 11, 0,
             4, 8, 12, 0
         };
         Assert.assertArrayEquals(expected, result.toArray(), 0.0);
     }
 
     @Test
     public void testNormalTransform() {
         // act/assert
         checkNormalTransform(AffineTransformMatrix3D.identity());
 
         checkNormalTransform(AffineTransformMatrix3D.createTranslation(2, 3, 4));
         checkNormalTransform(AffineTransformMatrix3D.createTranslation(-3, -4, -5));
 
         checkNormalTransform(AffineTransformMatrix3D.createScale(2, 5, 0.5));
         checkNormalTransform(AffineTransformMatrix3D.createScale(-3, 4, 2));
         checkNormalTransform(AffineTransformMatrix3D.createScale(-0.1, -0.5, 0.8));
         checkNormalTransform(AffineTransformMatrix3D.createScale(-2, -5, -8));
 
         final QuaternionRotation rotA = QuaternionRotation.fromAxisAngle(Vector3D.of(2, 3, 4), 0.75 * Math.PI);
         final QuaternionRotation rotB = QuaternionRotation.fromAxisAngle(Vector3D.of(-1, 1, -1), 1.75 * Math.PI);
 
         checkNormalTransform(AffineTransformMatrix3D.createRotation(Vector3D.of(1, 1, 1), rotA));
         checkNormalTransform(AffineTransformMatrix3D.createRotation(Vector3D.of(-1, -1, -1), rotB));
 
         checkNormalTransform(AffineTransformMatrix3D.createTranslation(2, 3, 4)
                 .scale(7, 5, 4)
                 .rotate(rotA));
         checkNormalTransform(AffineTransformMatrix3D.createRotation(Vector3D.ZERO, rotB)
                 .translate(7, 5, 4)
                 .rotate(rotA)
                 .scale(2, 3, 0.5));
     }
 
     private void checkNormalTransform(final AffineTransformMatrix3D transform) {
         final AffineTransformMatrix3D normalTransform = transform.normalTransform();
 
         final Vector3D p1 = Vector3D.of(-0.25, 0.75, 0.5);
         final Vector3D p2 = Vector3D.of(0.5, -0.75, 0.25);
 
         final Vector3D t1 = transform.apply(p1);
         final Vector3D t2 = transform.apply(p2);
 
         EuclideanTestUtils.permute(-10, 10, 1, (x, y, z) -> {
             final Vector3D p3 = Vector3D.of(x, y, z);
             final Vector3D n = Planes.fromPoints(p1, p2, p3, TEST_PRECISION).getNormal();
 
             final Vector3D t3 = transform.apply(p3);
 
             final Plane tPlane = transform.preservesOrientation() ?
                     Planes.fromPoints(t1, t2, t3, TEST_PRECISION) :
                     Planes.fromPoints(t1, t3, t2, TEST_PRECISION);
             final Vector3D expected = tPlane.getNormal();
 
             final Vector3D actual = normalTransform.apply(n).normalize();
 
             EuclideanTestUtils.assertCoordinatesEqual(expected, actual, EPS);
         });
     }
 
     @Test
     public void testNormalTransform_nonInvertible() {
         // act/assert
         GeometryTestUtils.assertThrows(() -> {
             AffineTransformMatrix3D.createScale(0).normalTransform();
         }, IllegalStateException.class);
     }
 
     @Test
     public void testHashCode() {
         // arrange
         final double[] values = {
             1, 2, 3, 4,
             5, 6, 7, 8,
             9, 10, 11, 12
         };
 
         // act/assert
         final int orig = AffineTransformMatrix3D.of(values).hashCode();
         final int same = AffineTransformMatrix3D.of(values).hashCode();
 
         Assert.assertEquals(orig, same);
 
         double[] temp;
         for (int i = 0; i < values.length; ++i) {
             temp = values.clone();
             temp[i] = 0;
 
             final int modified = AffineTransformMatrix3D.of(temp).hashCode();
 
             Assert.assertNotEquals(orig, modified);
         }
     }
 
     @Test
     public void testEquals() {
         // arrange
         final double[] values = {
             1, 2, 3, 4,
             5, 6, 7, 8,
             9, 10, 11, 12
         };
 
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(values);
 
         // act/assert
         Assert.assertEquals(a, a);
 
         Assert.assertFalse(a.equals(null));
         Assert.assertFalse(a.equals(new Object()));
 
         double[] temp;
         for (int i = 0; i < values.length; ++i) {
             temp = values.clone();
             temp[i] = 0;
 
             final AffineTransformMatrix3D modified = AffineTransformMatrix3D.of(temp);
 
             Assert.assertNotEquals(a, modified);
         }
     }
 
     @Test
     public void testEqualsAndHashCode_signedZeroConsistency() {
         // arrange
         final double[] arrWithPosZero = {
             1.0, 0.0, 0.0, 0.0,
             0.0, 1.0, 0.0, 0.0,
             0.0, 0.0, 1.0, 0.0,
         };
         final double[] arrWithNegZero = {
             1.0, 0.0, 0.0, 0.0,
             0.0, 1.0, 0.0, 0.0,
             0.0, 0.0, 1.0, -0.0,
         };
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(arrWithPosZero);
         final AffineTransformMatrix3D b = AffineTransformMatrix3D.of(arrWithNegZero);
         final AffineTransformMatrix3D c = AffineTransformMatrix3D.of(arrWithPosZero);
         final AffineTransformMatrix3D d = AffineTransformMatrix3D.of(arrWithNegZero);
 
         // act/assert
         Assert.assertFalse(a.equals(b));
         Assert.assertNotEquals(a.hashCode(), b.hashCode());
 
         Assert.assertTrue(a.equals(c));
         Assert.assertEquals(a.hashCode(), c.hashCode());
 
         Assert.assertTrue(b.equals(d));
         Assert.assertEquals(b.hashCode(), d.hashCode());
     }
 
     @Test
     public void testToString() {
         // arrange
         final AffineTransformMatrix3D a = AffineTransformMatrix3D.of(
                     1, 2, 3, 4,
                     5, 6, 7, 8,
                     9, 10, 11, 12
                 );
 
         // act
         final String result = a.toString();
 
         // assert
         Assert.assertEquals(
                 "[ 1.0, 2.0, 3.0, 4.0; " +
                 "5.0, 6.0, 7.0, 8.0; " +
                 "9.0, 10.0, 11.0, 12.0 ]", result);
     }
 
     /**
      * Run the given test callback with a wide range of (x, y, z) inputs.
      * @param test
      */
     private static void runWithCoordinates(final PermuteCallback3D test) {
         EuclideanTestUtils.permute(-1e-2, 1e-2, 5e-3, test);
         EuclideanTestUtils.permute(-1e2, 1e2, 5, test);
     }
 }