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    1   /*
    2    * Licensed to the Apache Software Foundation (ASF) under one or more
    3    * contributor license agreements.  See the NOTICE file distributed with
    4    * this work for additional information regarding copyright ownership.
    5    * The ASF licenses this file to You under the Apache License, Version 2.0
    6    * (the "License"); you may not use this file except in compliance with
    7    * the License.  You may obtain a copy of the License at
    8    *
    9    *      http://www.apache.org/licenses/LICENSE-2.0
    10   *
    11   * Unless required by applicable law or agreed to in writing, software
    12   * distributed under the License is distributed on an "AS IS" BASIS,
    13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    14   * See the License for the specific language governing permissions and
    15   * limitations under the License.
    16   */
    17  package org.apache.commons.geometry.euclidean.threed.line;
    18
    19  import org.apache.commons.geometry.core.GeometryTestUtils;
    20  import org.apache.commons.geometry.core.Transform;
    21  import org.apache.commons.geometry.euclidean.EuclideanTestUtils;
    22  import org.apache.commons.geometry.euclidean.oned.Vector1D;
    23  import org.apache.commons.geometry.euclidean.threed.AffineTransformMatrix3D;
    24  import org.apache.commons.geometry.euclidean.threed.Vector3D;
    25  import org.apache.commons.geometry.euclidean.threed.rotation.QuaternionRotation;
    26  import org.apache.commons.numbers.angle.Angle;
    27  import org.apache.commons.numbers.core.Precision;
    28  import org.junit.jupiter.api.Assertions;
    29  import org.junit.jupiter.api.Test;
    30
    31  class Line3DTest {
    32
    33      private static final double TEST_EPS = 1e-10;
    34
    35      private static final Precision.DoubleEquivalence TEST_PRECISION =
    36              Precision.doubleEquivalenceOfEpsilon(TEST_EPS);
    37
    38      @Test
    39      void testFromPointAndDirection() {
    40          // arrange
    41          final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(-1, 1, 0), Vector3D.Unit.PLUS_Y, TEST_PRECISION);
    42
    43          // act/assert
    44          EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-1, 0, 0), line.getOrigin(), TEST_EPS);
    45          EuclideanTestUtils.assertCoordinatesEqual(Vector3D.Unit.PLUS_Y, line.getDirection(), TEST_EPS);
    46          Assertions.assertSame(TEST_PRECISION, line.getPrecision());
    47      }
    48
    49      @Test
    50      void testFromPointAndDirection_normalizesDirection() {
    51          // arrange
    52          final Line3D line = Lines3D.fromPointAndDirection(Vector3D.ZERO, Vector3D.of(1, 1, 1), TEST_PRECISION);
    53
    54          // act/assert
    55          EuclideanTestUtils.assertCoordinatesEqual(Vector3D.ZERO, line.getOrigin(), TEST_EPS);
    56
    57          final double invSqrt3 = 1.0 / Math.sqrt(3);
    58          EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(invSqrt3, invSqrt3, invSqrt3), line.getDirection(), TEST_EPS);
    59          Assertions.assertSame(TEST_PRECISION, line.getPrecision());
    60      }
    61
    62      @Test
    63      void testFromPointAndDirection_illegalDirectionNorm() {
    64          // act/assert
    65          GeometryTestUtils.assertThrowsWithMessage(() -> {
    66              Lines3D.fromPointAndDirection(Vector3D.ZERO, Vector3D.ZERO, TEST_PRECISION);
    67          }, IllegalArgumentException.class, "Line direction cannot be zero");
    68
    69          GeometryTestUtils.assertThrowsWithMessage(() -> {
    70              Lines3D.fromPointAndDirection(Vector3D.ZERO, Vector3D.of(1e-12, 1e-12, 1e-12), TEST_PRECISION);
    71          }, IllegalArgumentException.class, "Line direction cannot be zero");
    72      }
    73
    74      @Test
    75      void testFromPoints() {
    76          // arrange
    77          final Line3D line = Lines3D.fromPoints(Vector3D.of(-1, 1, 0), Vector3D.of(-1, 7, 0), TEST_PRECISION);
    78
    79          // act/assert
    80          EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-1, 0, 0), line.getOrigin(), TEST_EPS);
    81          EuclideanTestUtils.assertCoordinatesEqual(Vector3D.Unit.PLUS_Y, line.getDirection(), TEST_EPS);
    82          Assertions.assertSame(TEST_PRECISION, line.getPrecision());
    83      }
    84
    85      @Test
    86      void testFromPoints_pointsTooClose() {
    87          // act/assert
    88          Assertions.assertThrows(IllegalArgumentException.class, () -> Lines3D.fromPoints(Vector3D.of(1, 1, 1),
    89                  Vector3D.of(1, 1, 1 + 1e-16), TEST_PRECISION));
    90      }
    91
    92      @Test
    93      void testTransform() {
    94          // arrange
    95          final Vector3D pt = Vector3D.of(1, 2, 3);
    96          final Line3D line = Lines3D.fromPointAndDirection(pt, Vector3D.of(1, 1, 1), TEST_PRECISION);
    97
    98          final AffineTransformMatrix3D mat = AffineTransformMatrix3D.createRotation(pt,
    99                  QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Y, Angle.PI_OVER_TWO));
    100
    101         // act
    102         final Line3D result = line.transform(mat);
    103
    104         // assert
    105         Assertions.assertTrue(result.contains(pt));
    106         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(1, 1, -1).normalize(), result.getDirection(), TEST_EPS);
    107     }
    108
    109     @Test
    110     void testTransform_reflectionInOneAxis() {
    111         // arrange
    112         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(1, 0, 0), Vector3D.of(1, 1, 1), TEST_PRECISION);
    113
    114         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.from(v -> Vector3D.of(v.getX(), v.getY(), -v.getZ()));
    115
    116         // act
    117         final Line3D result = line.transform(transform);
    118
    119         // assert
    120         Assertions.assertTrue(result.contains(Vector3D.of(1, 0, 0)));
    121         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(1, 1, -1).normalize(), result.getDirection(), TEST_EPS);
    122     }
    123
    124     @Test
    125     void testTransform_reflectionInTwoAxes() {
    126         // arrange
    127         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(1, 0, 0), Vector3D.of(1, 1, 1), TEST_PRECISION);
    128
    129         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.from(v -> Vector3D.of(v.getX(), -v.getY(), -v.getZ()));
    130
    131         // act
    132         final Line3D result = line.transform(transform);
    133
    134         // assert
    135         Assertions.assertTrue(result.contains(Vector3D.of(1, 0, 0)));
    136         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(1, -1, -1).normalize(), result.getDirection(), TEST_EPS);
    137     }
    138
    139     @Test
    140     void testTransform_reflectionInThreeAxes() {
    141         // arrange
    142         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(1, 0, 0), Vector3D.of(1, 1, 1), TEST_PRECISION);
    143
    144         final AffineTransformMatrix3D transform = AffineTransformMatrix3D.from(Vector3D::negate);
    145
    146         // act
    147         final Line3D result = line.transform(transform);
    148
    149         // assert
    150         Assertions.assertTrue(result.contains(Vector3D.of(-1, 0, 0)));
    151         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-1, -1, -1).normalize(), result.getDirection(), TEST_EPS);
    152     }
    153
    154     @Test
    155     void testSubspaceTransform() {
    156         // arrange
    157         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(0, 0, 1), Vector3D.of(1, 0, 0), TEST_PRECISION);
    158
    159         final Transform<Vector3D> transform = AffineTransformMatrix3D.identity()
    160                 .scale(2, 1, 1)
    161                 .translate(0.5, 1, 0)
    162                 .rotate(QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Y, Angle.PI_OVER_TWO));
    163
    164         // act
    165         final Line3D.SubspaceTransform result = line.subspaceTransform(transform);
    166
    167         // assert
    168         final Line3D tLine = result.getLine();
    169         final Transform<Vector1D> tSub = result.getTransform();
    170
    171         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(1, 1, 0), tLine.getOrigin(), TEST_EPS);
    172         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(0, 0, -1), tLine.getDirection(), TEST_EPS);
    173
    174         Assertions.assertEquals(0.5, tSub.apply(Vector1D.ZERO).getX(), TEST_EPS);
    175         Assertions.assertEquals(4.5, tSub.apply(Vector1D.of(2)).getX(), TEST_EPS);
    176     }
    177
    178     @Test
    179     void testAbscissa() {
    180         // arrange
    181         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(0, 0, -1), Vector3D.of(4, 3, 0), TEST_PRECISION);
    182
    183         // act/assert
    184         Assertions.assertEquals(0.0, line.abscissa(line.getOrigin()), TEST_EPS);
    185
    186         Assertions.assertEquals(5.0, line.abscissa(Vector3D.of(4, 3, 0)), TEST_EPS);
    187         Assertions.assertEquals(5.0, line.abscissa(Vector3D.of(4, 3, 10)), TEST_EPS);
    188
    189         Assertions.assertEquals(-5.0, line.abscissa(Vector3D.of(-4, -3, 0)), TEST_EPS);
    190         Assertions.assertEquals(-5.0, line.abscissa(Vector3D.of(-4, -3, -10)), TEST_EPS);
    191     }
    192
    193     @Test
    194     void testToSubspace() {
    195         // arrange
    196         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(0, 0, -1), Vector3D.of(4, 3, 0), TEST_PRECISION);
    197
    198         // act/assert
    199         Assertions.assertEquals(0.0, line.toSubspace(line.getOrigin()).getX(), TEST_EPS);
    200
    201         Assertions.assertEquals(5.0, line.toSubspace(Vector3D.of(4, 3, -1)).getX(), TEST_EPS);
    202         Assertions.assertEquals(5.0, line.toSubspace(Vector3D.of(4, 3, 10)).getX(), TEST_EPS);
    203
    204         Assertions.assertEquals(-5.0, line.toSubspace(Vector3D.of(-4, -3, -1)).getX(), TEST_EPS);
    205         Assertions.assertEquals(-5.0, line.toSubspace(Vector3D.of(-4, -3, -10)).getX(), TEST_EPS);
    206     }
    207
    208     @Test
    209     void testPointAt() {
    210         // arrange
    211         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(0, 0, -1), Vector3D.of(4, 3, 0), TEST_PRECISION);
    212
    213         // act/assert
    214         EuclideanTestUtils.assertCoordinatesEqual(line.getOrigin(), line.pointAt(0.0), TEST_EPS);
    215         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(4, 3, -1), line.pointAt(5.0), TEST_EPS);
    216         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-4, -3, -1), line.pointAt(-5.0), TEST_EPS);
    217     }
    218
    219     @Test
    220     void testToSpace() {
    221         // arrange
    222         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.of(0, 0, -1), Vector3D.of(4, 3, 0), TEST_PRECISION);
    223
    224         // act/assert
    225         EuclideanTestUtils.assertCoordinatesEqual(line.getOrigin(), line.toSpace(Vector1D.of(0.0)), TEST_EPS);
    226         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(4, 3, -1), line.toSpace(Vector1D.of(5.0)), TEST_EPS);
    227         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-4, -3, -1), line.toSpace(Vector1D.of(-5.0)), TEST_EPS);
    228     }
    229
    230     @Test
    231     void testContains() {
    232         final Vector3D p1 = Vector3D.of(0, 0, 1);
    233         final Line3D l = Lines3D.fromPoints(p1, Vector3D.of(0, 0, 2), TEST_PRECISION);
    234         Assertions.assertTrue(l.contains(p1));
    235         Assertions.assertTrue(l.contains(Vector3D.Sum.of(p1).addScaled(0.3, l.getDirection()).get()));
    236         final Vector3D u = l.getDirection().orthogonal();
    237         final Vector3D v = l.getDirection().cross(u);
    238         for (double alpha = 0; alpha < 2 * Math.PI; alpha += 0.3) {
    239             Assertions.assertFalse(l.contains(p1.add(Vector3D.Sum.create().addScaled(Math.cos(alpha), u).addScaled(
    240                     Math.sin(alpha), v).get())));
    241         }
    242     }
    243
    244     @Test
    245     void testSimilar() {
    246         final Vector3D p1  = Vector3D.of(1.2, 3.4, -5.8);
    247         final Vector3D p2  = Vector3D.of(3.4, -5.8, 1.2);
    248         final Line3D lA  = Lines3D.fromPoints(p1, p2, TEST_PRECISION);
    249         final Line3D lB  = Lines3D.fromPoints(p2, p1, TEST_PRECISION);
    250         Assertions.assertTrue(lA.isSimilarTo(lB));
    251         Assertions.assertFalse(lA.isSimilarTo(Lines3D.fromPoints(p1, p1.add(lA.getDirection().orthogonal()), TEST_PRECISION)));
    252     }
    253
    254     @Test
    255     void testPointDistance() {
    256         final Line3D l = Lines3D.fromPoints(Vector3D.of(0, 1, 1), Vector3D.of(0, 2, 2), TEST_PRECISION);
    257         Assertions.assertEquals(Math.sqrt(3.0 / 2.0), l.distance(Vector3D.of(1, 0, 1)), TEST_EPS);
    258         Assertions.assertEquals(0, l.distance(Vector3D.of(0, -4, -4)), TEST_EPS);
    259     }
    260
    261     @Test
    262     void testLineDistance() {
    263         final Line3D l = Lines3D.fromPoints(Vector3D.of(0, 1, 1), Vector3D.of(0, 2, 2), TEST_PRECISION);
    264         Assertions.assertEquals(1.0,
    265                             l.distance(Lines3D.fromPoints(Vector3D.of(1, 0, 1), Vector3D.of(1, 0, 2), TEST_PRECISION)),
    266                             1.0e-10);
    267         Assertions.assertEquals(0.5,
    268                             l.distance(Lines3D.fromPoints(Vector3D.of(-0.5, 0, 0), Vector3D.of(-0.5, -1, -1), TEST_PRECISION)),
    269                             1.0e-10);
    270         Assertions.assertEquals(0.0,
    271                             l.distance(l),
    272                             1.0e-10);
    273         Assertions.assertEquals(0.0,
    274                             l.distance(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(0, -5, -5), TEST_PRECISION)),
    275                             1.0e-10);
    276         Assertions.assertEquals(0.0,
    277                             l.distance(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(0, -3, -4), TEST_PRECISION)),
    278                             1.0e-10);
    279         Assertions.assertEquals(0.0,
    280                             l.distance(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(1, -4, -4), TEST_PRECISION)),
    281                             1.0e-10);
    282         Assertions.assertEquals(Math.sqrt(8),
    283                             l.distance(Lines3D.fromPoints(Vector3D.of(0, -4, 0), Vector3D.of(1, -4, 0), TEST_PRECISION)),
    284                             1.0e-10);
    285     }
    286
    287     @Test
    288     void testClosest() {
    289         final Line3D l = Lines3D.fromPoints(Vector3D.of(0, 1, 1), Vector3D.of(0, 2, 2), TEST_PRECISION);
    290         Assertions.assertEquals(0.0,
    291                             l.closest(Lines3D.fromPoints(Vector3D.of(1, 0, 1), Vector3D.of(1, 0, 2), TEST_PRECISION)).distance(Vector3D.of(0, 0, 0)),
    292                             1.0e-10);
    293         Assertions.assertEquals(0.5,
    294                             l.closest(Lines3D.fromPoints(Vector3D.of(-0.5, 0, 0), Vector3D.of(-0.5, -1, -1), TEST_PRECISION)).distance(Vector3D.of(-0.5, 0, 0)),
    295                             1.0e-10);
    296         Assertions.assertEquals(0.0,
    297                             l.closest(l).distance(Vector3D.of(0, 0, 0)),
    298                             1.0e-10);
    299         Assertions.assertEquals(0.0,
    300                             l.closest(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(0, -5, -5), TEST_PRECISION)).distance(Vector3D.of(0, 0, 0)),
    301                             1.0e-10);
    302         Assertions.assertEquals(0.0,
    303                             l.closest(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(0, -3, -4), TEST_PRECISION)).distance(Vector3D.of(0, -4, -4)),
    304                             1.0e-10);
    305         Assertions.assertEquals(0.0,
    306                             l.closest(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(1, -4, -4), TEST_PRECISION)).distance(Vector3D.of(0, -4, -4)),
    307                             1.0e-10);
    308         Assertions.assertEquals(0.0,
    309                             l.closest(Lines3D.fromPoints(Vector3D.of(0, -4, 0), Vector3D.of(1, -4, 0), TEST_PRECISION)).distance(Vector3D.of(0, -2, -2)),
    310                             1.0e-10);
    311     }
    312
    313     @Test
    314     void testIntersection() {
    315         final Line3D l = Lines3D.fromPoints(Vector3D.of(0, 1, 1), Vector3D.of(0, 2, 2), TEST_PRECISION);
    316         Assertions.assertNull(l.intersection(Lines3D.fromPoints(Vector3D.of(1, 0, 1), Vector3D.of(1, 0, 2), TEST_PRECISION)));
    317         Assertions.assertNull(l.intersection(Lines3D.fromPoints(Vector3D.of(-0.5, 0, 0), Vector3D.of(-0.5, -1, -1), TEST_PRECISION)));
    318         Assertions.assertEquals(0.0,
    319                             l.intersection(l).distance(Vector3D.of(0, 0, 0)),
    320                             1.0e-10);
    321         Assertions.assertEquals(0.0,
    322                             l.intersection(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(0, -5, -5), TEST_PRECISION)).distance(Vector3D.of(0, 0, 0)),
    323                             1.0e-10);
    324         Assertions.assertEquals(0.0,
    325                             l.intersection(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(0, -3, -4), TEST_PRECISION)).distance(Vector3D.of(0, -4, -4)),
    326                             1.0e-10);
    327         Assertions.assertEquals(0.0,
    328                             l.intersection(Lines3D.fromPoints(Vector3D.of(0, -4, -4), Vector3D.of(1, -4, -4), TEST_PRECISION)).distance(Vector3D.of(0, -4, -4)),
    329                             1.0e-10);
    330         Assertions.assertNull(l.intersection(Lines3D.fromPoints(Vector3D.of(0, -4, 0), Vector3D.of(1, -4, 0), TEST_PRECISION)));
    331     }
    332
    333     @Test
    334     void testReverse() {
    335         // arrange
    336         final Line3D line = Lines3D.fromPoints(Vector3D.of(1653345.6696423641, 6170370.041579291, 90000),
    337                              Vector3D.of(1650757.5050732433, 6160710.879908984, 0.9),
    338                              TEST_PRECISION);
    339         final Vector3D expected = line.getDirection().negate();
    340
    341         // act
    342         final Line3D reversed = line.reverse();
    343
    344         // assert
    345         EuclideanTestUtils.assertCoordinatesEqual(expected, reversed.getDirection(), TEST_EPS);
    346     }
    347
    348     @Test
    349     void testSpan() {
    350         // arrange
    351         final Line3D line = Lines3D.fromPoints(Vector3D.ZERO, Vector3D.Unit.PLUS_X, TEST_PRECISION);
    352
    353         // act
    354         final LineConvexSubset3D span = line.span();
    355
    356         // assert
    357         Assertions.assertTrue(span.isInfinite());
    358         Assertions.assertFalse(span.isFinite());
    359
    360         Assertions.assertNull(span.getStartPoint());
    361         Assertions.assertNull(span.getEndPoint());
    362
    363         Assertions.assertNull(span.getCentroid());
    364         Assertions.assertNull(span.getBounds());
    365
    366         GeometryTestUtils.assertNegativeInfinity(span.getSubspaceStart());
    367         GeometryTestUtils.assertPositiveInfinity(span.getSubspaceEnd());
    368
    369         GeometryTestUtils.assertPositiveInfinity(span.getSize());
    370
    371         Assertions.assertSame(line, span.getLine());
    372         Assertions.assertTrue(span.getInterval().isFull());
    373     }
    374
    375     @Test
    376     void testSpan_contains() {
    377         // arrange
    378         final double delta = 1e-12;
    379
    380         final LineConvexSubset3D span = Lines3D.fromPoints(Vector3D.ZERO, Vector3D.Unit.PLUS_X, TEST_PRECISION).span();
    381
    382         for (double x = -10; x <= 10; x += 0.5) {
    383
    384             // act/assert
    385             Assertions.assertFalse(span.contains(Vector3D.of(0, 1, 0)));
    386             Assertions.assertFalse(span.contains(Vector3D.of(0, 0, 1)));
    387
    388             Assertions.assertTrue(span.contains(Vector3D.of(x, 0, 0)));
    389             Assertions.assertTrue(span.contains(Vector3D.of(x + delta, delta, delta)));
    390         }
    391     }
    392
    393     @Test
    394     void testSpan_transform() {
    395         // arrange
    396         final AffineTransformMatrix3D t = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Y, 0.5 * Math.PI)
    397                 .toMatrix()
    398                 .translate(Vector3D.Unit.PLUS_Y);
    399
    400         final LineConvexSubset3D span = Lines3D.fromPointAndDirection(Vector3D.of(1, 0, 0), Vector3D.Unit.PLUS_X, TEST_PRECISION)
    401                 .span();
    402
    403         // act
    404         final LineConvexSubset3D result = span.transform(t);
    405
    406         // assert
    407         Assertions.assertNull(result.getStartPoint());
    408         Assertions.assertNull(result.getEndPoint());
    409
    410         Assertions.assertTrue(result.contains(Vector3D.of(0, 1, -1)));
    411         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.Unit.MINUS_Z, result.getLine().getDirection(), TEST_EPS);
    412     }
    413
    414     @Test
    415     void testSpan_transform_reflection() {
    416         // arrange
    417         final AffineTransformMatrix3D t = QuaternionRotation.fromAxisAngle(Vector3D.Unit.PLUS_Y, 0.5 * Math.PI)
    418                 .toMatrix()
    419                 .translate(Vector3D.Unit.PLUS_Y)
    420                 .scale(1, 1, -2);
    421
    422         final LineConvexSubset3D span = Lines3D.fromPointAndDirection(Vector3D.of(1, 0, 0),
    423                 Vector3D.Unit.PLUS_X, TEST_PRECISION).span();
    424
    425         // act
    426         final LineConvexSubset3D result = span.transform(t);
    427
    428         // assert
    429         Assertions.assertNull(result.getStartPoint());
    430         Assertions.assertNull(result.getEndPoint());
    431
    432         Assertions.assertTrue(result.contains(Vector3D.of(0, 1, 2)));
    433         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.Unit.PLUS_Z, result.getLine().getDirection(), TEST_EPS);
    434     }
    435
    436     @Test
    437     void testSpan_toString() {
    438         // arrange
    439         final LineConvexSubset3D span = Lines3D.fromPointAndDirection(Vector3D.ZERO, Vector3D.Unit.PLUS_X, TEST_PRECISION)
    440                 .span();
    441
    442         // act
    443         final String str = span.toString();
    444
    445         // assert
    446         GeometryTestUtils.assertContains("LineSpanningSubset3D[origin= (0", str);
    447         GeometryTestUtils.assertContains(", direction= (1", str);
    448     }
    449
    450     @Test
    451     void testSubsetMethods() {
    452         // arrange
    453         final Line3D line = Lines3D.fromPoints(Vector3D.of(0, 3, 0), Vector3D.of(1, 3, 0), TEST_PRECISION);
    454
    455         // act/assert
    456         final Segment3D doubleArgResult = line.segment(3, 4);
    457         Assertions.assertSame(line, doubleArgResult.getLine());
    458         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(3, 3, 0), doubleArgResult.getStartPoint(), TEST_EPS);
    459         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(4, 3, 0), doubleArgResult.getEndPoint(), TEST_EPS);
    460
    461         final Segment3D ptArgResult = line.segment(Vector3D.of(0, 4, 0), Vector3D.of(2, 5, 1));
    462         Assertions.assertSame(line, ptArgResult.getLine());
    463         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(0, 3, 0), ptArgResult.getStartPoint(), TEST_EPS);
    464         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(2, 3, 0), ptArgResult.getEndPoint(), TEST_EPS);
    465
    466         final Ray3D rayDoubleResult = line.rayFrom(2);
    467         Assertions.assertSame(line, rayDoubleResult.getLine());
    468         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(2, 3, 0), rayDoubleResult.getStartPoint(), TEST_EPS);
    469         Assertions.assertNull(rayDoubleResult.getEndPoint());
    470
    471         final Ray3D rayPtResult = line.rayFrom(Vector3D.of(1, 4, 0));
    472         Assertions.assertSame(line, rayPtResult.getLine());
    473         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(1, 3, 0), rayPtResult.getStartPoint(), TEST_EPS);
    474         Assertions.assertNull(rayPtResult.getEndPoint());
    475
    476         final ReverseRay3D toDoubleResult = line.reverseRayTo(-1);
    477         Assertions.assertSame(line, toDoubleResult.getLine());
    478         Assertions.assertNull(toDoubleResult.getStartPoint());
    479         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(-1, 3, 0), toDoubleResult.getEndPoint(), TEST_EPS);
    480
    481         final ReverseRay3D toPtResult = line.reverseRayTo(Vector3D.of(1, 4, 0));
    482         Assertions.assertSame(line, toPtResult.getLine());
    483         Assertions.assertNull(toPtResult.getStartPoint());
    484         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(1, 3, 0), toPtResult.getEndPoint(), TEST_EPS);
    485     }
    486
    487     @Test
    488     void testEq() {
    489         // arrange
    490         final Precision.DoubleEquivalence precision = Precision.doubleEquivalenceOfEpsilon(1e-3);
    491
    492         final Vector3D p = Vector3D.of(1, 2, 3);
    493         final Vector3D dir = Vector3D.of(1, 0, 0);
    494
    495         final Line3D a = Lines3D.fromPointAndDirection(p, dir, precision);
    496         final Line3D b = Lines3D.fromPointAndDirection(Vector3D.ZERO, dir, precision);
    497         final Line3D c = Lines3D.fromPointAndDirection(p, Vector3D.of(1, 1, 0), precision);
    498
    499         final Line3D d = Lines3D.fromPointAndDirection(p, dir, precision);
    500         final Line3D e = Lines3D.fromPointAndDirection(p.add(Vector3D.of(1e-4, 1e-4, 1e-4)), dir, precision);
    501         final Line3D f = Lines3D.fromPointAndDirection(p, Vector3D.of(1 + 1e-4, 1e-4, 1e-4), precision);
    502
    503         // act/assert
    504         Assertions.assertTrue(a.eq(a, precision));
    505
    506         Assertions.assertTrue(a.eq(d, precision));
    507         Assertions.assertTrue(d.eq(a, precision));
    508
    509         Assertions.assertTrue(a.eq(e, precision));
    510         Assertions.assertTrue(e.eq(a, precision));
    511
    512         Assertions.assertTrue(a.eq(f, precision));
    513         Assertions.assertTrue(f.eq(a, precision));
    514
    515         Assertions.assertFalse(a.eq(b, precision));
    516         Assertions.assertFalse(a.eq(c, precision));
    517     }
    518
    519     @Test
    520     void testHashCode() {
    521         // arrange
    522         final Line3D a = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, 6), TEST_PRECISION);
    523         final Line3D b = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, -1), Vector3D.of(4, 5, 6), TEST_PRECISION);
    524         final Line3D c = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, -1), TEST_PRECISION);
    525         final Line3D d = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, 6), Precision.doubleEquivalenceOfEpsilon(TEST_EPS + 1e-3));
    526
    527         final Line3D e = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, 6), TEST_PRECISION);
    528
    529         final int hash = a.hashCode();
    530
    531         // act/assert
    532         Assertions.assertEquals(hash, a.hashCode());
    533
    534         Assertions.assertNotEquals(hash, b.hashCode());
    535         Assertions.assertNotEquals(hash, c.hashCode());
    536         Assertions.assertNotEquals(hash, d.hashCode());
    537
    538         Assertions.assertEquals(hash, e.hashCode());
    539     }
    540
    541     @Test
    542     void testEquals() {
    543         // arrange
    544         final Line3D a = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, 6), TEST_PRECISION);
    545         final Line3D b = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, -1), Vector3D.of(4, 5, 6), TEST_PRECISION);
    546         final Line3D c = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, -1), TEST_PRECISION);
    547         final Line3D d = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, 6), Precision.doubleEquivalenceOfEpsilon(TEST_EPS + 1e-3));
    548
    549         final Line3D e = Lines3D.fromPointAndDirection(Vector3D.of(1, 2, 3), Vector3D.of(4, 5, 6), TEST_PRECISION);
    550
    551         // act/assert
    552         GeometryTestUtils.assertSimpleEqualsCases(a);
    553
    554         Assertions.assertNotEquals(a, b);
    555         Assertions.assertNotEquals(a, c);
    556         Assertions.assertNotEquals(a, d);
    557
    558         Assertions.assertEquals(a, e);
    559         Assertions.assertEquals(e, a);
    560     }
    561
    562     @Test
    563     void testToString() {
    564         // arrange
    565         final Line3D line = Lines3D.fromPointAndDirection(Vector3D.ZERO, Vector3D.Unit.PLUS_X, TEST_PRECISION);
    566
    567         // act
    568         final String str = line.toString();
    569
    570         // assert
    571         Assertions.assertTrue(str.contains("Line3D"));
    572         Assertions.assertTrue(str.matches(".*origin= \\(0(\\.0)?, 0(\\.0)?, 0(\\.0)?\\).*"));
    573         Assertions.assertTrue(str.matches(".*direction= \\(1(\\.0)?, 0(\\.0)?, 0(\\.0)?\\).*"));
    574     }
    575 }