/*
* 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.math.geometry;
import org.apache.commons.math.geometry.CardanEulerSingularityException;
import org.apache.commons.math.geometry.NotARotationMatrixException;
import org.apache.commons.math.geometry.Rotation;
import org.apache.commons.math.geometry.RotationOrder;
import org.apache.commons.math.geometry.Vector3D;
import org.apache.commons.math.util.FastMath;
import org.apache.commons.math.util.MathUtils;
import junit.framework.*;
public class RotationTest
extends TestCase {
public RotationTest(String name) {
super(name);
}
public void testIdentity() {
Rotation r = Rotation.IDENTITY;
checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_I);
checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.PLUS_J);
checkVector(r.applyTo(Vector3D.PLUS_K), Vector3D.PLUS_K);
checkAngle(r.getAngle(), 0);
r = new Rotation(-1, 0, 0, 0, false);
checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_I);
checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.PLUS_J);
checkVector(r.applyTo(Vector3D.PLUS_K), Vector3D.PLUS_K);
checkAngle(r.getAngle(), 0);
r = new Rotation(42, 0, 0, 0, true);
checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_I);
checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.PLUS_J);
checkVector(r.applyTo(Vector3D.PLUS_K), Vector3D.PLUS_K);
checkAngle(r.getAngle(), 0);
}
public void testAxisAngle() {
Rotation r = new Rotation(new Vector3D(10, 10, 10), 2 * FastMath.PI / 3);
checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_J);
checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.PLUS_K);
checkVector(r.applyTo(Vector3D.PLUS_K), Vector3D.PLUS_I);
double s = 1 / FastMath.sqrt(3);
checkVector(r.getAxis(), new Vector3D(s, s, s));
checkAngle(r.getAngle(), 2 * FastMath.PI / 3);
try {
new Rotation(new Vector3D(0, 0, 0), 2 * FastMath.PI / 3);
fail("an exception should have been thrown");
} catch (ArithmeticException e) {
}
r = new Rotation(Vector3D.PLUS_K, 1.5 * FastMath.PI);
checkVector(r.getAxis(), new Vector3D(0, 0, -1));
checkAngle(r.getAngle(), 0.5 * FastMath.PI);
r = new Rotation(Vector3D.PLUS_J, FastMath.PI);
checkVector(r.getAxis(), Vector3D.PLUS_J);
checkAngle(r.getAngle(), FastMath.PI);
checkVector(Rotation.IDENTITY.getAxis(), Vector3D.PLUS_I);
}
public void testRevert() {
Rotation r = new Rotation(0.001, 0.36, 0.48, 0.8, true);
Rotation reverted = r.revert();
checkRotation(r.applyTo(reverted), 1, 0, 0, 0);
checkRotation(reverted.applyTo(r), 1, 0, 0, 0);
assertEquals(r.getAngle(), reverted.getAngle(), 1.0e-12);
assertEquals(-1, Vector3D.dotProduct(r.getAxis(), reverted.getAxis()), 1.0e-12);
}
public void testVectorOnePair() {
Vector3D u = new Vector3D(3, 2, 1);
Vector3D v = new Vector3D(-4, 2, 2);
Rotation r = new Rotation(u, v);
checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));
checkAngle(new Rotation(u, u.negate()).getAngle(), FastMath.PI);
try {
new Rotation(u, Vector3D.ZERO);
fail("an exception should have been thrown");
} catch (IllegalArgumentException e) {
// expected behavior
}
}
public void testVectorTwoPairs() {
Vector3D u1 = new Vector3D(3, 0, 0);
Vector3D u2 = new Vector3D(0, 5, 0);
Vector3D v1 = new Vector3D(0, 0, 2);
Vector3D v2 = new Vector3D(-2, 0, 2);
Rotation r = new Rotation(u1, u2, v1, v2);
checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_K);
checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.MINUS_I);
r = new Rotation(u1, u2, u1.negate(), u2.negate());
Vector3D axis = r.getAxis();
if (Vector3D.dotProduct(axis, Vector3D.PLUS_K) > 0) {
checkVector(axis, Vector3D.PLUS_K);
} else {
checkVector(axis, Vector3D.MINUS_K);
}
checkAngle(r.getAngle(), FastMath.PI);
double sqrt = FastMath.sqrt(2) / 2;
r = new Rotation(Vector3D.PLUS_I, Vector3D.PLUS_J,
new Vector3D(0.5, 0.5, sqrt),
new Vector3D(0.5, 0.5, -sqrt));
checkRotation(r, sqrt, 0.5, 0.5, 0);
r = new Rotation(u1, u2, u1, Vector3D.crossProduct(u1, u2));
checkRotation(r, sqrt, -sqrt, 0, 0);
checkRotation(new Rotation(u1, u2, u1, u2), 1, 0, 0, 0);
try {
new Rotation(u1, u2, Vector3D.ZERO, v2);
fail("an exception should have been thrown");
} catch (IllegalArgumentException e) {
// expected behavior
}
}
public void testMatrix()
throws NotARotationMatrixException {
try {
new Rotation(new double[][] {
{ 0.0, 1.0, 0.0 },
{ 1.0, 0.0, 0.0 }
}, 1.0e-7);
fail("Expecting NotARotationMatrixException");
} catch (NotARotationMatrixException nrme) {
// expected behavior
}
try {
new Rotation(new double[][] {
{ 0.445888, 0.797184, -0.407040 },
{ 0.821760, -0.184320, 0.539200 },
{ -0.354816, 0.574912, 0.737280 }
}, 1.0e-7);
fail("Expecting NotARotationMatrixException");
} catch (NotARotationMatrixException nrme) {
// expected behavior
}
try {
new Rotation(new double[][] {
{ 0.4, 0.8, -0.4 },
{ -0.4, 0.6, 0.7 },
{ 0.8, -0.2, 0.5 }
}, 1.0e-15);
fail("Expecting NotARotationMatrixException");
} catch (NotARotationMatrixException nrme) {
// expected behavior
}
checkRotation(new Rotation(new double[][] {
{ 0.445888, 0.797184, -0.407040 },
{ -0.354816, 0.574912, 0.737280 },
{ 0.821760, -0.184320, 0.539200 }
}, 1.0e-10),
0.8, 0.288, 0.384, 0.36);
checkRotation(new Rotation(new double[][] {
{ 0.539200, 0.737280, 0.407040 },
{ 0.184320, -0.574912, 0.797184 },
{ 0.821760, -0.354816, -0.445888 }
}, 1.0e-10),
0.36, 0.8, 0.288, 0.384);
checkRotation(new Rotation(new double[][] {
{ -0.445888, 0.797184, -0.407040 },
{ 0.354816, 0.574912, 0.737280 },
{ 0.821760, 0.184320, -0.539200 }
}, 1.0e-10),
0.384, 0.36, 0.8, 0.288);
checkRotation(new Rotation(new double[][] {
{ -0.539200, 0.737280, 0.407040 },
{ -0.184320, -0.574912, 0.797184 },
{ 0.821760, 0.354816, 0.445888 }
}, 1.0e-10),
0.288, 0.384, 0.36, 0.8);
double[][] m1 = { { 0.0, 1.0, 0.0 },
{ 0.0, 0.0, 1.0 },
{ 1.0, 0.0, 0.0 } };
Rotation r = new Rotation(m1, 1.0e-7);
checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_K);
checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.PLUS_I);
checkVector(r.applyTo(Vector3D.PLUS_K), Vector3D.PLUS_J);
double[][] m2 = { { 0.83203, -0.55012, -0.07139 },
{ 0.48293, 0.78164, -0.39474 },
{ 0.27296, 0.29396, 0.91602 } };
r = new Rotation(m2, 1.0e-12);
double[][] m3 = r.getMatrix();
double d00 = m2[0][0] - m3[0][0];
double d01 = m2[0][1] - m3[0][1];
double d02 = m2[0][2] - m3[0][2];
double d10 = m2[1][0] - m3[1][0];
double d11 = m2[1][1] - m3[1][1];
double d12 = m2[1][2] - m3[1][2];
double d20 = m2[2][0] - m3[2][0];
double d21 = m2[2][1] - m3[2][1];
double d22 = m2[2][2] - m3[2][2];
assertTrue(FastMath.abs(d00) < 6.0e-6);
assertTrue(FastMath.abs(d01) < 6.0e-6);
assertTrue(FastMath.abs(d02) < 6.0e-6);
assertTrue(FastMath.abs(d10) < 6.0e-6);
assertTrue(FastMath.abs(d11) < 6.0e-6);
assertTrue(FastMath.abs(d12) < 6.0e-6);
assertTrue(FastMath.abs(d20) < 6.0e-6);
assertTrue(FastMath.abs(d21) < 6.0e-6);
assertTrue(FastMath.abs(d22) < 6.0e-6);
assertTrue(FastMath.abs(d00) > 4.0e-7);
assertTrue(FastMath.abs(d01) > 4.0e-7);
assertTrue(FastMath.abs(d02) > 4.0e-7);
assertTrue(FastMath.abs(d10) > 4.0e-7);
assertTrue(FastMath.abs(d11) > 4.0e-7);
assertTrue(FastMath.abs(d12) > 4.0e-7);
assertTrue(FastMath.abs(d20) > 4.0e-7);
assertTrue(FastMath.abs(d21) > 4.0e-7);
assertTrue(FastMath.abs(d22) > 4.0e-7);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
double m3tm3 = m3[i][0] * m3[j][0]
+ m3[i][1] * m3[j][1]
+ m3[i][2] * m3[j][2];
if (i == j) {
assertTrue(FastMath.abs(m3tm3 - 1.0) < 1.0e-10);
} else {
assertTrue(FastMath.abs(m3tm3) < 1.0e-10);
}
}
}
checkVector(r.applyTo(Vector3D.PLUS_I),
new Vector3D(m3[0][0], m3[1][0], m3[2][0]));
checkVector(r.applyTo(Vector3D.PLUS_J),
new Vector3D(m3[0][1], m3[1][1], m3[2][1]));
checkVector(r.applyTo(Vector3D.PLUS_K),
new Vector3D(m3[0][2], m3[1][2], m3[2][2]));
double[][] m4 = { { 1.0, 0.0, 0.0 },
{ 0.0, -1.0, 0.0 },
{ 0.0, 0.0, -1.0 } };
r = new Rotation(m4, 1.0e-7);
checkAngle(r.getAngle(), FastMath.PI);
try {
double[][] m5 = { { 0.0, 0.0, 1.0 },
{ 0.0, 1.0, 0.0 },
{ 1.0, 0.0, 0.0 } };
r = new Rotation(m5, 1.0e-7);
fail("got " + r + ", should have caught an exception");
} catch (NotARotationMatrixException e) {
// expected
}
}
public void testAngles()
throws CardanEulerSingularityException {
RotationOrder[] CardanOrders = {
RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,
RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX
};
for (int i = 0; i < CardanOrders.length; ++i) {
for (double alpha1 = 0.1; alpha1 < 6.2; alpha1 += 0.3) {
for (double alpha2 = -1.55; alpha2 < 1.55; alpha2 += 0.3) {
for (double alpha3 = 0.1; alpha3 < 6.2; alpha3 += 0.3) {
Rotation r = new Rotation(CardanOrders[i], alpha1, alpha2, alpha3);
double[] angles = r.getAngles(CardanOrders[i]);
checkAngle(angles[0], alpha1);
checkAngle(angles[1], alpha2);
checkAngle(angles[2], alpha3);
}
}
}
}
RotationOrder[] EulerOrders = {
RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,
RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ
};
for (int i = 0; i < EulerOrders.length; ++i) {
for (double alpha1 = 0.1; alpha1 < 6.2; alpha1 += 0.3) {
for (double alpha2 = 0.05; alpha2 < 3.1; alpha2 += 0.3) {
for (double alpha3 = 0.1; alpha3 < 6.2; alpha3 += 0.3) {
Rotation r = new Rotation(EulerOrders[i],
alpha1, alpha2, alpha3);
double[] angles = r.getAngles(EulerOrders[i]);
checkAngle(angles[0], alpha1);
checkAngle(angles[1], alpha2);
checkAngle(angles[2], alpha3);
}
}
}
}
}
public void testSingularities() {
RotationOrder[] CardanOrders = {
RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,
RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX
};
double[] singularCardanAngle = { FastMath.PI / 2, -FastMath.PI / 2 };
for (int i = 0; i < CardanOrders.length; ++i) {
for (int j = 0; j < singularCardanAngle.length; ++j) {
Rotation r = new Rotation(CardanOrders[i], 0.1, singularCardanAngle[j], 0.3);
try {
r.getAngles(CardanOrders[i]);
fail("an exception should have been caught");
} catch (CardanEulerSingularityException cese) {
// expected behavior
}
}
}
RotationOrder[] EulerOrders = {
RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,
RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ
};
double[] singularEulerAngle = { 0, FastMath.PI };
for (int i = 0; i < EulerOrders.length; ++i) {
for (int j = 0; j < singularEulerAngle.length; ++j) {
Rotation r = new Rotation(EulerOrders[i], 0.1, singularEulerAngle[j], 0.3);
try {
r.getAngles(EulerOrders[i]);
fail("an exception should have been caught");
} catch (CardanEulerSingularityException cese) {
// expected behavior
}
}
}
}
public void testQuaternion() {
Rotation r1 = new Rotation(new Vector3D(2, -3, 5), 1.7);
double n = 23.5;
Rotation r2 = new Rotation(n * r1.getQ0(), n * r1.getQ1(),
n * r1.getQ2(), n * r1.getQ3(),
true);
for (double x = -0.9; x < 0.9; x += 0.2) {
for (double y = -0.9; y < 0.9; y += 0.2) {
for (double z = -0.9; z < 0.9; z += 0.2) {
Vector3D u = new Vector3D(x, y, z);
checkVector(r2.applyTo(u), r1.applyTo(u));
}
}
}
r1 = new Rotation( 0.288, 0.384, 0.36, 0.8, false);
checkRotation(r1, -r1.getQ0(), -r1.getQ1(), -r1.getQ2(), -r1.getQ3());
}
public void testCompose() {
Rotation r1 = new Rotation(new Vector3D(2, -3, 5), 1.7);
Rotation r2 = new Rotation(new Vector3D(-1, 3, 2), 0.3);
Rotation r3 = r2.applyTo(r1);
for (double x = -0.9; x < 0.9; x += 0.2) {
for (double y = -0.9; y < 0.9; y += 0.2) {
for (double z = -0.9; z < 0.9; z += 0.2) {
Vector3D u = new Vector3D(x, y, z);
checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));
}
}
}
}
public void testComposeInverse() {
Rotation r1 = new Rotation(new Vector3D(2, -3, 5), 1.7);
Rotation r2 = new Rotation(new Vector3D(-1, 3, 2), 0.3);
Rotation r3 = r2.applyInverseTo(r1);
for (double x = -0.9; x < 0.9; x += 0.2) {
for (double y = -0.9; y < 0.9; y += 0.2) {
for (double z = -0.9; z < 0.9; z += 0.2) {
Vector3D u = new Vector3D(x, y, z);
checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));
}
}
}
}
public void testApplyInverseTo() {
Rotation r = new Rotation(new Vector3D(2, -3, 5), 1.7);
for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
for (double phi = -1.55; phi < 1.55; phi += 0.2) {
Vector3D u = new Vector3D(FastMath.cos(lambda) * FastMath.cos(phi),
FastMath.sin(lambda) * FastMath.cos(phi),
FastMath.sin(phi));
r.applyInverseTo(r.applyTo(u));
checkVector(u, r.applyInverseTo(r.applyTo(u)));
checkVector(u, r.applyTo(r.applyInverseTo(u)));
}
}
r = Rotation.IDENTITY;
for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
for (double phi = -1.55; phi < 1.55; phi += 0.2) {
Vector3D u = new Vector3D(FastMath.cos(lambda) * FastMath.cos(phi),
FastMath.sin(lambda) * FastMath.cos(phi),
FastMath.sin(phi));
checkVector(u, r.applyInverseTo(r.applyTo(u)));
checkVector(u, r.applyTo(r.applyInverseTo(u)));
}
}
r = new Rotation(Vector3D.PLUS_K, FastMath.PI);
for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
for (double phi = -1.55; phi < 1.55; phi += 0.2) {
Vector3D u = new Vector3D(FastMath.cos(lambda) * FastMath.cos(phi),
FastMath.sin(lambda) * FastMath.cos(phi),
FastMath.sin(phi));
checkVector(u, r.applyInverseTo(r.applyTo(u)));
checkVector(u, r.applyTo(r.applyInverseTo(u)));
}
}
}
private void checkVector(Vector3D v1, Vector3D v2) {
assertTrue(v1.subtract(v2).getNorm() < 1.0e-10);
}
private void checkAngle(double a1, double a2) {
assertEquals(a1, MathUtils.normalizeAngle(a2, a1), 1.0e-10);
}
private void checkRotation(Rotation r, double q0, double q1, double q2, double q3) {
assertEquals(0, Rotation.distance(r, new Rotation(q0, q1, q2, q3, false)), 1.0e-12);
}
}