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* 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.
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package org.apache.commons.math3.geometry.euclidean.threed;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.text.NumberFormat;
import java.util.Locale;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.geometry.Space;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
import org.junit.Assert;
import org.junit.Test;
public class Vector3DTest {
@Test
public void testConstructors() throws DimensionMismatchException {
double r = FastMath.sqrt(2) /2;
checkVector(new Vector3D(2, new Vector3D(FastMath.PI / 3, -FastMath.PI / 4)),
r, r * FastMath.sqrt(3), -2 * r);
checkVector(new Vector3D(2, Vector3D.PLUS_I,
-3, Vector3D.MINUS_K),
2, 0, 3);
checkVector(new Vector3D(2, Vector3D.PLUS_I,
5, Vector3D.PLUS_J,
-3, Vector3D.MINUS_K),
2, 5, 3);
checkVector(new Vector3D(2, Vector3D.PLUS_I,
5, Vector3D.PLUS_J,
5, Vector3D.MINUS_J,
-3, Vector3D.MINUS_K),
2, 0, 3);
checkVector(new Vector3D(new double[] { 2, 5, -3 }),
2, 5, -3);
}
@Test
public void testSpace() {
Space space = new Vector3D(1, 2, 2).getSpace();
Assert.assertEquals(3, space.getDimension());
Assert.assertEquals(2, space.getSubSpace().getDimension());
Space deserialized = (Space) TestUtils.serializeAndRecover(space);
Assert.assertTrue(space == deserialized);
}
@Test
public void testZero() {
Assert.assertEquals(0, new Vector3D(1, 2, 2).getZero().getNorm(), 1.0e-15);
}
@Test
public void testEquals() {
Vector3D u1 = new Vector3D(1, 2, 3);
Vector3D u2 = new Vector3D(1, 2, 3);
Assert.assertTrue(u1.equals(u1));
Assert.assertTrue(u1.equals(u2));
Assert.assertFalse(u1.equals(new Rotation(1, 0, 0, 0, false)));
Assert.assertFalse(u1.equals(new Vector3D(1, 2, 3 + 10 * Precision.EPSILON)));
Assert.assertFalse(u1.equals(new Vector3D(1, 2 + 10 * Precision.EPSILON, 3)));
Assert.assertFalse(u1.equals(new Vector3D(1 + 10 * Precision.EPSILON, 2, 3)));
Assert.assertTrue(new Vector3D(0, Double.NaN, 0).equals(new Vector3D(0, 0, Double.NaN)));
}
@Test
public void testHash() {
Assert.assertEquals(new Vector3D(0, Double.NaN, 0).hashCode(), new Vector3D(0, 0, Double.NaN).hashCode());
Vector3D u = new Vector3D(1, 2, 3);
Vector3D v = new Vector3D(1, 2, 3 + 10 * Precision.EPSILON);
Assert.assertTrue(u.hashCode() != v.hashCode());
}
@Test
public void testInfinite() {
Assert.assertTrue(new Vector3D(1, 1, Double.NEGATIVE_INFINITY).isInfinite());
Assert.assertTrue(new Vector3D(1, Double.NEGATIVE_INFINITY, 1).isInfinite());
Assert.assertTrue(new Vector3D(Double.NEGATIVE_INFINITY, 1, 1).isInfinite());
Assert.assertFalse(new Vector3D(1, 1, 2).isInfinite());
Assert.assertFalse(new Vector3D(1, Double.NaN, Double.NEGATIVE_INFINITY).isInfinite());
}
@Test
public void testNaN() {
Assert.assertTrue(new Vector3D(1, 1, Double.NaN).isNaN());
Assert.assertTrue(new Vector3D(1, Double.NaN, 1).isNaN());
Assert.assertTrue(new Vector3D(Double.NaN, 1, 1).isNaN());
Assert.assertFalse(new Vector3D(1, 1, 2).isNaN());
Assert.assertFalse(new Vector3D(1, 1, Double.NEGATIVE_INFINITY).isNaN());
}
@Test
public void testToString() {
Assert.assertEquals("{3; 2; 1}", new Vector3D(3, 2, 1).toString());
NumberFormat format = new DecimalFormat("0.000", new DecimalFormatSymbols(Locale.US));
Assert.assertEquals("{3.000; 2.000; 1.000}", new Vector3D(3, 2, 1).toString(format));
}
@Test(expected=DimensionMismatchException.class)
public void testWrongDimension() throws DimensionMismatchException {
new Vector3D(new double[] { 2, 5 });
}
@Test
public void testCoordinates() {
Vector3D v = new Vector3D(1, 2, 3);
Assert.assertTrue(FastMath.abs(v.getX() - 1) < 1.0e-12);
Assert.assertTrue(FastMath.abs(v.getY() - 2) < 1.0e-12);
Assert.assertTrue(FastMath.abs(v.getZ() - 3) < 1.0e-12);
double[] coordinates = v.toArray();
Assert.assertTrue(FastMath.abs(coordinates[0] - 1) < 1.0e-12);
Assert.assertTrue(FastMath.abs(coordinates[1] - 2) < 1.0e-12);
Assert.assertTrue(FastMath.abs(coordinates[2] - 3) < 1.0e-12);
}
@Test
public void testNorm1() {
Assert.assertEquals(0.0, Vector3D.ZERO.getNorm1(), 0);
Assert.assertEquals(6.0, new Vector3D(1, -2, 3).getNorm1(), 0);
}
@Test
public void testNorm() {
Assert.assertEquals(0.0, Vector3D.ZERO.getNorm(), 0);
Assert.assertEquals(FastMath.sqrt(14), new Vector3D(1, 2, 3).getNorm(), 1.0e-12);
}
@Test
public void testNormSq() {
Assert.assertEquals(0.0, new Vector3D(0, 0, 0).getNormSq(), 0);
Assert.assertEquals(14, new Vector3D(1, 2, 3).getNormSq(), 1.0e-12);
}
@Test
public void testNormInf() {
Assert.assertEquals(0.0, Vector3D.ZERO.getNormInf(), 0);
Assert.assertEquals(3.0, new Vector3D(1, -2, 3).getNormInf(), 0);
}
@Test
public void testDistance1() {
Vector3D v1 = new Vector3D(1, -2, 3);
Vector3D v2 = new Vector3D(-4, 2, 0);
Assert.assertEquals(0.0, Vector3D.distance1(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);
Assert.assertEquals(12.0, Vector3D.distance1(v1, v2), 1.0e-12);
Assert.assertEquals(v1.subtract(v2).getNorm1(), Vector3D.distance1(v1, v2), 1.0e-12);
}
@Test
public void testDistance() {
Vector3D v1 = new Vector3D(1, -2, 3);
Vector3D v2 = new Vector3D(-4, 2, 0);
Assert.assertEquals(0.0, Vector3D.distance(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);
Assert.assertEquals(FastMath.sqrt(50), Vector3D.distance(v1, v2), 1.0e-12);
Assert.assertEquals(v1.subtract(v2).getNorm(), Vector3D.distance(v1, v2), 1.0e-12);
}
@Test
public void testDistanceSq() {
Vector3D v1 = new Vector3D(1, -2, 3);
Vector3D v2 = new Vector3D(-4, 2, 0);
Assert.assertEquals(0.0, Vector3D.distanceSq(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);
Assert.assertEquals(50.0, Vector3D.distanceSq(v1, v2), 1.0e-12);
Assert.assertEquals(Vector3D.distance(v1, v2) * Vector3D.distance(v1, v2),
Vector3D.distanceSq(v1, v2), 1.0e-12);
}
@Test
public void testDistanceInf() {
Vector3D v1 = new Vector3D(1, -2, 3);
Vector3D v2 = new Vector3D(-4, 2, 0);
Assert.assertEquals(0.0, Vector3D.distanceInf(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);
Assert.assertEquals(5.0, Vector3D.distanceInf(v1, v2), 1.0e-12);
Assert.assertEquals(v1.subtract(v2).getNormInf(), Vector3D.distanceInf(v1, v2), 1.0e-12);
}
@Test
public void testSubtract() {
Vector3D v1 = new Vector3D(1, 2, 3);
Vector3D v2 = new Vector3D(-3, -2, -1);
v1 = v1.subtract(v2);
checkVector(v1, 4, 4, 4);
checkVector(v2.subtract(v1), -7, -6, -5);
checkVector(v2.subtract(3, v1), -15, -14, -13);
}
@Test
public void testAdd() {
Vector3D v1 = new Vector3D(1, 2, 3);
Vector3D v2 = new Vector3D(-3, -2, -1);
v1 = v1.add(v2);
checkVector(v1, -2, 0, 2);
checkVector(v2.add(v1), -5, -2, 1);
checkVector(v2.add(3, v1), -9, -2, 5);
}
@Test
public void testScalarProduct() {
Vector3D v = new Vector3D(1, 2, 3);
v = v.scalarMultiply(3);
checkVector(v, 3, 6, 9);
checkVector(v.scalarMultiply(0.5), 1.5, 3, 4.5);
}
@Test
public void testVectorialProducts() {
Vector3D v1 = new Vector3D(2, 1, -4);
Vector3D v2 = new Vector3D(3, 1, -1);
Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v1, v2) - 11) < 1.0e-12);
Vector3D v3 = Vector3D.crossProduct(v1, v2);
checkVector(v3, 3, -10, -1);
Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v1, v3)) < 1.0e-12);
Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v2, v3)) < 1.0e-12);
}
@Test
public void testCrossProductCancellation() {
Vector3D v1 = new Vector3D(9070467121.0, 4535233560.0, 1);
Vector3D v2 = new Vector3D(9070467123.0, 4535233561.0, 1);
checkVector(Vector3D.crossProduct(v1, v2), -1, 2, 1);
double scale = FastMath.scalb(1.0, 100);
Vector3D big1 = new Vector3D(scale, v1);
Vector3D small2 = new Vector3D(1 / scale, v2);
checkVector(Vector3D.crossProduct(big1, small2), -1, 2, 1);
}
@Test
public void testAngular() {
Assert.assertEquals(0, Vector3D.PLUS_I.getAlpha(), 1.0e-10);
Assert.assertEquals(0, Vector3D.PLUS_I.getDelta(), 1.0e-10);
Assert.assertEquals(FastMath.PI / 2, Vector3D.PLUS_J.getAlpha(), 1.0e-10);
Assert.assertEquals(0, Vector3D.PLUS_J.getDelta(), 1.0e-10);
Assert.assertEquals(0, Vector3D.PLUS_K.getAlpha(), 1.0e-10);
Assert.assertEquals(FastMath.PI / 2, Vector3D.PLUS_K.getDelta(), 1.0e-10);
Vector3D u = new Vector3D(-1, 1, -1);
Assert.assertEquals(3 * FastMath.PI /4, u.getAlpha(), 1.0e-10);
Assert.assertEquals(-1.0 / FastMath.sqrt(3), FastMath.sin(u.getDelta()), 1.0e-10);
}
@Test
public void testAngularSeparation() throws MathArithmeticException {
Vector3D v1 = new Vector3D(2, -1, 4);
Vector3D k = v1.normalize();
Vector3D i = k.orthogonal();
Vector3D v2 = k.scalarMultiply(FastMath.cos(1.2)).add(i.scalarMultiply(FastMath.sin(1.2)));
Assert.assertTrue(FastMath.abs(Vector3D.angle(v1, v2) - 1.2) < 1.0e-12);
}
@Test
public void testNormalize() throws MathArithmeticException {
Assert.assertEquals(1.0, new Vector3D(5, -4, 2).normalize().getNorm(), 1.0e-12);
try {
Vector3D.ZERO.normalize();
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException ae) {
// expected behavior
}
}
@Test
public void testNegate() {
checkVector(new Vector3D(0.1, 2.5, 1.3).negate(), -0.1, -2.5, -1.3);
}
@Test
public void testOrthogonal() throws MathArithmeticException {
Vector3D v1 = new Vector3D(0.1, 2.5, 1.3);
Assert.assertEquals(0.0, Vector3D.dotProduct(v1, v1.orthogonal()), 1.0e-12);
Vector3D v2 = new Vector3D(2.3, -0.003, 7.6);
Assert.assertEquals(0.0, Vector3D.dotProduct(v2, v2.orthogonal()), 1.0e-12);
Vector3D v3 = new Vector3D(-1.7, 1.4, 0.2);
Assert.assertEquals(0.0, Vector3D.dotProduct(v3, v3.orthogonal()), 1.0e-12);
Vector3D v4 = new Vector3D(4.2, 0.1, -1.8);
Assert.assertEquals(0.0, Vector3D.dotProduct(v4, v4.orthogonal()), 1.0e-12);
try {
new Vector3D(0, 0, 0).orthogonal();
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException ae) {
// expected behavior
}
}
@Test
public void testAngle() throws MathArithmeticException {
Assert.assertEquals(0.22572612855273393616,
Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(4, 5, 6)),
1.0e-12);
Assert.assertEquals(7.98595620686106654517199e-8,
Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(2, 4, 6.000001)),
1.0e-12);
Assert.assertEquals(3.14159257373023116985197793156,
Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(-2, -4, -6.000001)),
1.0e-12);
try {
Vector3D.angle(Vector3D.ZERO, Vector3D.PLUS_I);
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException ae) {
// expected behavior
}
}
@Test
public void testAccurateDotProduct() {
// the following two vectors are nearly but not exactly orthogonal
// naive dot product (i.e. computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z
// leads to a result of 0.0, instead of the correct -1.855129...
Vector3D u1 = new Vector3D(-1321008684645961.0 / 268435456.0,
-5774608829631843.0 / 268435456.0,
-7645843051051357.0 / 8589934592.0);
Vector3D u2 = new Vector3D(-5712344449280879.0 / 2097152.0,
-4550117129121957.0 / 2097152.0,
8846951984510141.0 / 131072.0);
double sNaive = u1.getX() * u2.getX() + u1.getY() * u2.getY() + u1.getZ() * u2.getZ();
double sAccurate = u1.dotProduct(u2);
Assert.assertEquals(0.0, sNaive, 1.0e-30);
Assert.assertEquals(-2088690039198397.0 / 1125899906842624.0, sAccurate, 1.0e-16);
}
@Test
public void testDotProduct() {
// we compare accurate versus naive dot product implementations
// on regular vectors (i.e. not extreme cases like in the previous test)
Well1024a random = new Well1024a(553267312521321234l);
for (int i = 0; i < 10000; ++i) {
double ux = 10000 * random.nextDouble();
double uy = 10000 * random.nextDouble();
double uz = 10000 * random.nextDouble();
double vx = 10000 * random.nextDouble();
double vy = 10000 * random.nextDouble();
double vz = 10000 * random.nextDouble();
double sNaive = ux * vx + uy * vy + uz * vz;
double sAccurate = new Vector3D(ux, uy, uz).dotProduct(new Vector3D(vx, vy, vz));
Assert.assertEquals(sNaive, sAccurate, 2.5e-16 * sAccurate);
}
}
@Test
public void testAccurateCrossProduct() {
// the vectors u1 and u2 are nearly but not exactly anti-parallel
// (7.31e-16 degrees from 180 degrees) naive cross product (i.e.
// computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z
// leads to a result of [0.0009765, -0.0001220, -0.0039062],
// instead of the correct [0.0006913, -0.0001254, -0.0007909]
final Vector3D u1 = new Vector3D(-1321008684645961.0 / 268435456.0,
-5774608829631843.0 / 268435456.0,
-7645843051051357.0 / 8589934592.0);
final Vector3D u2 = new Vector3D( 1796571811118507.0 / 2147483648.0,
7853468008299307.0 / 2147483648.0,
2599586637357461.0 / 17179869184.0);
final Vector3D u3 = new Vector3D(12753243807587107.0 / 18446744073709551616.0,
-2313766922703915.0 / 18446744073709551616.0,
-227970081415313.0 / 288230376151711744.0);
Vector3D cNaive = new Vector3D(u1.getY() * u2.getZ() - u1.getZ() * u2.getY(),
u1.getZ() * u2.getX() - u1.getX() * u2.getZ(),
u1.getX() * u2.getY() - u1.getY() * u2.getX());
Vector3D cAccurate = u1.crossProduct(u2);
Assert.assertTrue(u3.distance(cNaive) > 2.9 * u3.getNorm());
Assert.assertEquals(0.0, u3.distance(cAccurate), 1.0e-30 * cAccurate.getNorm());
}
@Test
public void testCrossProduct() {
// we compare accurate versus naive cross product implementations
// on regular vectors (i.e. not extreme cases like in the previous test)
Well1024a random = new Well1024a(885362227452043214l);
for (int i = 0; i < 10000; ++i) {
double ux = 10000 * random.nextDouble();
double uy = 10000 * random.nextDouble();
double uz = 10000 * random.nextDouble();
double vx = 10000 * random.nextDouble();
double vy = 10000 * random.nextDouble();
double vz = 10000 * random.nextDouble();
Vector3D cNaive = new Vector3D(uy * vz - uz * vy, uz * vx - ux * vz, ux * vy - uy * vx);
Vector3D cAccurate = new Vector3D(ux, uy, uz).crossProduct(new Vector3D(vx, vy, vz));
Assert.assertEquals(0.0, cAccurate.distance(cNaive), 6.0e-15 * cAccurate.getNorm());
}
}
private void checkVector(Vector3D v, double x, double y, double z) {
Assert.assertEquals(x, v.getX(), 1.0e-12);
Assert.assertEquals(y, v.getY(), 1.0e-12);
Assert.assertEquals(z, v.getZ(), 1.0e-12);
}
}