ConvexHullBuilderTest.java
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* 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
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*
* https://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,
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* See the License for the specific language governing permissions and
* limitations under the License.
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package org.apache.commons.geometry.euclidean.twod.hull;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import org.apache.commons.geometry.core.Region;
import org.apache.commons.geometry.core.RegionLocation;
import org.apache.commons.geometry.euclidean.twod.ConvexArea;
import org.apache.commons.geometry.euclidean.twod.Vector2D;
import org.apache.commons.geometry.euclidean.twod.hull.ConvexHull2D.Builder;
import org.apache.commons.numbers.core.Precision;
import org.apache.commons.numbers.core.Sum;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;
import org.junit.jupiter.api.Assertions;
import org.junit.jupiter.api.BeforeEach;
import org.junit.jupiter.api.Test;
/**
* Test class for MonotoneChain.
*/
class ConvexHullBuilderTest {
private static final double TEST_EPS = 1e-10;
private static final Precision.DoubleEquivalence TEST_PRECISION =
Precision.doubleEquivalenceOfEpsilon(TEST_EPS);
private ConvexHull2D.Builder generator;
private UniformRandomProvider random;
@BeforeEach
void setUp() {
// by default, do not include collinear points
generator = createConvexHullGenerator(false);
random = RandomSource.XO_SHI_RO_256_PP.create(10);
}
// ------------------------------------------------------------------------------
@Test
void testConvergenceException() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(1, 5));
points.add(Vector2D.of(0, 7));
points.add(Vector2D.of(1, 10));
points.add(Vector2D.of(1, 20));
points.add(Vector2D.of(20, 20));
points.add(Vector2D.of(20, 40));
points.add(Vector2D.of(40, 1));
// act/assert
ConvexHull2D.Builder builder = new ConvexHull2D.Builder(true, Precision.doubleEquivalenceOfEpsilon(1));
builder.append(points);
Assertions.assertThrows(IllegalStateException.class, builder::build);
}
@Test
void testEmpty() {
// act
generator.append(Collections.emptyList());
final ConvexHull2D hull = generator.build();
// assert
Assertions.assertEquals(0, hull.getVertices().size());
Assertions.assertEquals(0, hull.getPath().getElements().size());
Assertions.assertNull(hull.getRegion());
}
@Test
void testOnePoint() {
// arrange
final List<Vector2D> points = createRandomPoints(1);
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
Assertions.assertEquals(1, hull.getVertices().size());
Assertions.assertEquals(0, hull.getPath().getElements().size());
Assertions.assertNull(hull.getRegion());
}
@Test
void testTwoPoints() {
// arrange
final List<Vector2D> points = createRandomPoints(2);
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
Assertions.assertEquals(2, hull.getVertices().size());
Assertions.assertEquals(1, hull.getPath().getElements().size());
Assertions.assertNull(hull.getRegion());
}
@Test
void testAllIdentical() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(1, 1));
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
Assertions.assertEquals(1, hull.getVertices().size());
Assertions.assertEquals(0, hull.getPath().getElements().size());
Assertions.assertNull(hull.getRegion());
}
@Test
void testConvexHull() {
// execute 100 random variations
for (int i = 0; i < 100; i++) {
// randomize the size from 4 to 100
final int size = (int) Math.floor(random.nextDouble() * 96.0 + 4.0);
final List<Vector2D> points = createRandomPoints(size);
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
checkConvexHull(points, hull);
}
}
@Test
void testCollinearPoints() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(4, 1));
points.add(Vector2D.of(10, 1));
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
checkConvexHull(points, hull);
}
@Test
void testCollinearPointsReverse() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(10, 1));
points.add(Vector2D.of(4, 1));
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
checkConvexHull(points, hull);
}
@Test
void testCollinearPointsIncluded() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(4, 1));
points.add(Vector2D.of(10, 1));
// act
ConvexHull2D.Builder builder = createConvexHullGenerator(true);
builder.append(points);
final ConvexHull2D hull = builder.build();
// assert
checkConvexHull(points, hull, true);
}
@Test
void testCollinearPointsIncludedReverse() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(10, 1));
points.add(Vector2D.of(4, 1));
// act
ConvexHull2D.Builder builder = createConvexHullGenerator(true);
builder.append(points);
final ConvexHull2D hull = builder.build();
// assert
checkConvexHull(points, hull, true);
}
@Test
void testCollinearPointsIncludedColinearToFirstSide() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(10, 1));
points.add(Vector2D.of(1.5, 2.5));
// act
ConvexHull2D.Builder builder = createConvexHullGenerator(true);
builder.append(points);
final ConvexHull2D hull = builder.build();
// assert
checkConvexHull(points, hull, true);
}
@Test
void testCollinearPointsExcludedColinearToFirstSide() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(10, 1));
points.add(Vector2D.of(1.5, 2.5));
// act
ConvexHull2D.Builder builder = createConvexHullGenerator(false);
builder.append(points);
final ConvexHull2D hull = builder.build();
points.remove(Vector2D.of(1.5, 2.5));
// assert
checkConvexHull(points, hull, false);
}
@Test
void testIdenticalPoints() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(4, 1));
points.add(Vector2D.of(1, 1));
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
checkConvexHull(points, hull);
}
@Test
void testIdenticalPoints2() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(4, 1));
points.add(Vector2D.of(1, 1));
// act
ConvexHull2D.Builder builder = createConvexHullGenerator(true);
builder.append(points);
final ConvexHull2D hull = builder.build();
// assert
checkConvexHull(points, hull, true);
}
@Test
void testClosePoints() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(1, 1));
points.add(Vector2D.of(2, 2));
points.add(Vector2D.of(2, 4));
points.add(Vector2D.of(4, 1));
points.add(Vector2D.of(1.00001, 1));
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
checkConvexHull(points, hull);
}
@Test
void testOrderisIrrelevant() {
// arrange
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(0, 0));
points.add(Vector2D.of(6, 6));
points.add(Vector2D.of(3, 4));
points.add(Vector2D.of(12, 0));
// act
generator.append(points);
final ConvexHull2D hull = generator.build();
// assert
checkConvexHull(points, hull);
}
@Test
void testCollinearPointOnExistingBoundary() {
// --- arrange
// MATH-1135: check that collinear points on the hull are handled correctly
// when only a minimal hull shall be constructed
final Collection<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(7.3152, 34.7472));
points.add(Vector2D.of(6.400799999999997, 34.747199999999985));
points.add(Vector2D.of(5.486399999999997, 34.7472));
points.add(Vector2D.of(4.876799999999999, 34.7472));
points.add(Vector2D.of(4.876799999999999, 34.1376));
points.add(Vector2D.of(4.876799999999999, 30.48));
points.add(Vector2D.of(6.0959999999999965, 30.48));
points.add(Vector2D.of(6.0959999999999965, 34.1376));
points.add(Vector2D.of(7.315199999999996, 34.1376));
points.add(Vector2D.of(7.3152, 30.48));
// --- act
generator.append(points);
final ConvexHull2D hull = generator.build();
// --- assert
checkConvexHull(points, hull);
}
@Test
void testCollinearPointsInAnyOrder_threeCollinearPoints() {
// --- arrange
// MATH-1148: collinear points on the hull might be in any order
// make sure that they are processed in the proper order
// for each algorithm.
final List<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(16.078200000000184, -36.52519999989808));
points.add(Vector2D.of(19.164300000000186, -36.52519999989808));
points.add(Vector2D.of(19.1643, -25.28136477910407));
points.add(Vector2D.of(19.1643, -17.678400000004157));
// --- act/assert
ConvexHull2D.Builder builder = createConvexHullGenerator(false);
builder.append(points);
ConvexHull2D hull = builder.build();
checkConvexHull(points, hull);
builder = createConvexHullGenerator(true);
builder.append(points);
hull = builder.build();
checkConvexHull(points, hull, true);
}
@Test
void testCollinearPointsInAnyOrder_multipleCollinearPoints() {
// --- arrange
// MATH-1148: collinear points on the hull might be in any order
// make sure that they are processed in the proper order
// for each algorithm.
final List<Vector2D> points = new ArrayList<>();
points.add(Vector2D.of(0, -29.959696875));
points.add(Vector2D.of(0, -31.621809375));
points.add(Vector2D.of(0, -28.435696875));
points.add(Vector2D.of(0, -33.145809375));
points.add(Vector2D.of(3.048, -33.145809375));
points.add(Vector2D.of(3.048, -31.621809375));
points.add(Vector2D.of(3.048, -29.959696875));
points.add(Vector2D.of(4.572, -33.145809375));
points.add(Vector2D.of(4.572, -28.435696875));
// --- act/assert
Builder builder = createConvexHullGenerator(false);
builder.append(points);
ConvexHull2D hull = builder.build();
checkConvexHull(points, hull);
builder = createConvexHullGenerator(true);
builder.append(points);
hull = builder.build();
checkConvexHull(points, hull, true);
}
@Test
void testIssue1123() {
// arrange
final List<Vector2D> points = new ArrayList<>();
final int[][] data = {
{-11, -1}, {-11, 0}, {-11, 1},
{-10, -3}, {-10, -2}, {-10, -1}, {-10, 0}, {-10, 1},
{-10, 2}, {-10, 3}, {-9, -4}, {-9, -3}, {-9, -2},
{-9, -1}, {-9, 0}, {-9, 1}, {-9, 2}, {-9, 3},
{-9, 4}, {-8, -5}, {-8, -4}, {-8, -3}, {-8, -2},
{-8, -1}, {-8, 0}, {-8, 1}, {-8, 2}, {-8, 3},
{-8, 4}, {-8, 5}, {-7, -6}, {-7, -5}, {-7, -4},
{-7, -3}, {-7, -2}, {-7, -1}, {-7, 0}, {-7, 1},
{-7, 2}, {-7, 3}, {-7, 4}, {-7, 5}, {-7, 6},
{-6, -7}, {-6, -6}, {-6, -5}, {-6, -4}, {-6, -3},
{-6, -2}, {-6, -1}, {-6, 0}, {-6, 1}, {-6, 2},
{-6, 3}, {-6, 4}, {-6, 5}, {-6, 6}, {-6, 7},
{-5, -7}, {-5, -6}, {-5, -5}, {-5, -4}, {-5, -3},
{-5, -2}, {-5, 4}, {-5, 5}, {-5, 6}, {-5, 7},
{-4, -7}, {-4, -6}, {-4, -5}, {-4, -4}, {-4, -3},
{-4, -2}, {-4, 4}, {-4, 5}, {-4, 6}, {-4, 7},
{-3, -8}, {-3, -7}, {-3, -6}, {-3, -5}, {-3, -4},
{-3, -3}, {-3, -2}, {-3, 4}, {-3, 5}, {-3, 6},
{-3, 7}, {-3, 8}, {-2, -8}, {-2, -7}, {-2, -6},
{-2, -5}, {-2, -4}, {-2, -3}, {-2, -2}, {-2, 4},
{-2, 5}, {-2, 6}, {-2, 7}, {-2, 8}, {-1, -8},
{-1, -7}, {-1, -6}, {-1, -5}, {-1, -4}, {-1, -3},
{-1, -2}, {-1, 4}, {-1, 5}, {-1, 6}, {-1, 7},
{-1, 8}, {0, -8}, {0, -7}, {0, -6}, {0, -5},
{0, -4}, {0, -3}, {0, -2}, {0, 4}, {0, 5}, {0, 6},
{0, 7}, {0, 8}, {1, -8}, {1, -7}, {1, -6}, {1, -5},
{1, -4}, {1, -3}, {1, -2}, {1, -1}, {1, 0}, {1, 1},
{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7},
{1, 8}, {2, -8}, {2, -7}, {2, -6}, {2, -5},
{2, -4}, {2, -3}, {2, -2}, {2, -1}, {2, 0}, {2, 1},
{2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {2, 7},
{2, 8}, {3, -8}, {3, -7}, {3, -6}, {3, -5},
{3, -4}, {3, -3}, {3, -2}, {3, -1}, {3, 0}, {3, 1},
{3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6}, {3, 7},
{3, 8}, {4, -7}, {4, -6}, {4, -5}, {4, -4},
{4, -3}, {4, -2}, {4, -1}, {4, 0}, {4, 1}, {4, 2},
{4, 3}, {4, 4}, {4, 5}, {4, 6}, {4, 7}, {5, -7},
{5, -6}, {5, -5}, {5, -4}, {5, -3}, {5, -2},
{5, -1}, {5, 0}, {5, 1}, {5, 2}, {5, 3}, {5, 4},
{5, 5}, {5, 6}, {5, 7}, {6, -7}, {6, -6}, {6, -5},
{6, -4}, {6, -3}, {6, -2}, {6, -1}, {6, 0}, {6, 1},
{6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}, {6, 7},
{7, -6}, {7, -5}, {7, -4}, {7, -3}, {7, -2},
{7, -1}, {7, 0}, {7, 1}, {7, 2}, {7, 3}, {7, 4},
{7, 5}, {7, 6}, {8, -5}, {8, -4}, {8, -3}, {8, -2},
{8, -1}, {8, 0}, {8, 1}, {8, 2}, {8, 3}, {8, 4},
{8, 5}, {9, -4}, {9, -3}, {9, -2}, {9, -1}, {9, 0},
{9, 1}, {9, 2}, {9, 3}, {9, 4}, {10, -3}, {10, -2},
{10, -1}, {10, 0}, {10, 1}, {10, 2}, {10, 3},
{11, -1}, {11, 0}, {11, 1}
};
for (final int[] line : data) {
points.add(Vector2D.of(line[0], line[1]));
}
final Vector2D[] referenceHull = {
Vector2D.of(-11.0, -1.0),
Vector2D.of(-10.0, -3.0),
Vector2D.of(-6.0, -7.0),
Vector2D.of(-3.0, -8.0),
Vector2D.of(3.0, -8.0),
Vector2D.of(6.0, -7.0),
Vector2D.of(10.0, -3.0),
Vector2D.of(11.0, -1.0),
Vector2D.of(11.0, 1.0),
Vector2D.of(10.0, 3.0),
Vector2D.of(6.0, 7.0),
Vector2D.of(3.0, 8.0),
Vector2D.of(-3.0, 8.0),
Vector2D.of(-6.0, 7.0),
Vector2D.of(-10.0, 3.0),
Vector2D.of(-11.0, 1.0),
};
// act
generator.append(points);
final ConvexHull2D convHull = generator.build();
final Region<Vector2D> hullRegion = convHull.getRegion();
// assert
Assertions.assertEquals(274.0, hullRegion.getSize(), 1.0e-12);
double perimeter = 0;
for (int i = 0; i < referenceHull.length; ++i) {
perimeter += referenceHull[i].distance(
referenceHull[(i + 1) % referenceHull.length]);
}
Assertions.assertEquals(perimeter, hullRegion.getBoundarySize(), 1.0e-12);
for (final Vector2D vector2D : referenceHull) {
Assertions.assertEquals(RegionLocation.BOUNDARY, hullRegion.classify(vector2D));
}
}
// ------------------------------------------------------------------------------
private ConvexHull2D.Builder createConvexHullGenerator(final boolean includeCollinearPoints) {
return new ConvexHull2D.Builder(includeCollinearPoints, TEST_PRECISION);
}
private List<Vector2D> createRandomPoints(final int size) {
// create the cloud container
final List<Vector2D> points = new ArrayList<>(size);
// fill the cloud with a random distribution of points
for (int i = 0; i < size; i++) {
points.add(Vector2D.of(random.nextDouble() * 2.0 - 1.0, random.nextDouble() * 2.0 - 1.0));
}
return points;
}
private void checkConvexHull(final Collection<Vector2D> points, final ConvexHull2D hull) {
checkConvexHull(points, hull, false);
}
private void checkConvexHull(final Collection<Vector2D> points, final ConvexHull2D hull,
final boolean includesCollinearPoints) {
Assertions.assertNotNull(hull);
Assertions.assertTrue(isConvex(hull, includesCollinearPoints));
checkPointsInsideHullRegion(points, hull, includesCollinearPoints);
}
// verify that the constructed hull is really convex
private boolean isConvex(final ConvexHull2D hull, final boolean includesCollinearPoints) {
final List<Vector2D> points = hull.getVertices();
int sign = 0;
final int size = points.size();
for (int i = 0; i < size; i++) {
final Vector2D p1 = points.get(i == 0 ? size - 1 : i - 1);
final Vector2D p2 = points.get(i);
final Vector2D p3 = points.get(i == size - 1 ? 0 : i + 1);
final Vector2D d1 = p2.subtract(p1);
final Vector2D d2 = p3.subtract(p2);
Assertions.assertTrue(d1.norm() > 1e-10);
Assertions.assertTrue(d2.norm() > 1e-10);
final double cross = Sum.create()
.addProduct(d1.getX(), d2.getY())
.addProduct(-d1.getY(), d2.getX()).getAsDouble();
final int cmp = Precision.compareTo(cross, 0.0, TEST_EPS);
if (sign != 0 && cmp != sign && (!includesCollinearPoints || cmp != 0)) {
// in case of collinear points the cross product will be zero
return false;
}
sign = cmp;
}
return true;
}
// verify that all points are inside the convex hull region
private void checkPointsInsideHullRegion(final Collection<? extends Vector2D> points,
final ConvexHull2D hull,
final boolean includesCollinearPoints) {
final Collection<Vector2D> hullVertices = hull.getVertices();
final ConvexArea region = hull.getRegion();
for (final Vector2D p : points) {
final RegionLocation location = region.classify(p);
Assertions.assertNotEquals(RegionLocation.OUTSIDE, location);
if (location == RegionLocation.BOUNDARY && includesCollinearPoints) {
Assertions.assertTrue(hullVertices.contains(p));
}
}
}
}