/*
* 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.
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package org.apache.commons.math3.geometry.euclidean.threed;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.random.UnitSphereRandomVectorGenerator;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
import org.junit.Assert;
import org.junit.Test;
public class FieldRotationDSTest {
@Test
public void testIdentity() {
FieldRotation<DerivativeStructure> r = createRotation(1, 0, 0, 0, false);
checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
checkAngle(r.getAngle(), 0);
r = createRotation(-1, 0, 0, 0, false);
checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
checkAngle(r.getAngle(), 0);
r = createRotation(42, 0, 0, 0, true);
checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
checkAngle(r.getAngle(), 0);
}
@Test
public void testAxisAngle() throws MathIllegalArgumentException {
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createAxis(10, 10, 10), createAngle(2 * FastMath.PI / 3));
checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 1, 0));
checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 0, 1));
checkVector(r.applyTo(createVector(0, 0, 1)), createVector(1, 0, 0));
double s = 1 / FastMath.sqrt(3);
checkVector(r.getAxis(), createVector(s, s, s));
checkAngle(r.getAngle(), 2 * FastMath.PI / 3);
try {
new FieldRotation<DerivativeStructure>(createAxis(0, 0, 0), createAngle(2 * FastMath.PI / 3));
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException e) {
}
r = new FieldRotation<DerivativeStructure>(createAxis(0, 0, 1), createAngle(1.5 * FastMath.PI));
checkVector(r.getAxis(), createVector(0, 0, -1));
checkAngle(r.getAngle(), 0.5 * FastMath.PI);
r = new FieldRotation<DerivativeStructure>(createAxis(0, 1, 0), createAngle(FastMath.PI));
checkVector(r.getAxis(), createVector(0, 1, 0));
checkAngle(r.getAngle(), FastMath.PI);
checkVector(createRotation(1, 0, 0, 0, false).getAxis(), createVector(1, 0, 0));
}
@Test
public void testRevert() {
double a = 0.001;
double b = 0.36;
double c = 0.48;
double d = 0.8;
FieldRotation<DerivativeStructure> r = createRotation(a, b, c, d, true);
double a2 = a * a;
double b2 = b * b;
double c2 = c * c;
double d2 = d * d;
double den = (a2 + b2 + c2 + d2) * FastMath.sqrt(a2 + b2 + c2 + d2);
Assert.assertEquals((b2 + c2 + d2) / den, r.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(-a * b / den, r.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(-a * c / den, r.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(-a * d / den, r.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(-b * a / den, r.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals((a2 + c2 + d2) / den, r.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(-b * c / den, r.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(-b * d / den, r.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(-c * a / den, r.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(-c * b / den, r.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals((a2 + b2 + d2) / den, r.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(-c * d / den, r.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(-d * a / den, r.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(-d * b / den, r.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(-d * c / den, r.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals((a2 + b2 + c2) / den, r.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
FieldRotation<DerivativeStructure> reverted = r.revert();
FieldRotation<DerivativeStructure> rrT = r.applyTo(reverted);
checkRotationDS(rrT, 1, 0, 0, 0);
Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
FieldRotation<DerivativeStructure> rTr = reverted.applyTo(r);
checkRotationDS(rTr, 1, 0, 0, 0);
Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
Assert.assertEquals(r.getAngle().getReal(), reverted.getAngle().getReal(), 1.0e-15);
Assert.assertEquals(-1, FieldVector3D.dotProduct(r.getAxis(), reverted.getAxis()).getReal(), 1.0e-15);
}
@Test
public void testVectorOnePair() throws MathArithmeticException {
FieldVector3D<DerivativeStructure> u = createVector(3, 2, 1);
FieldVector3D<DerivativeStructure> v = createVector(-4, 2, 2);
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(u, v);
checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));
checkAngle(new FieldRotation<DerivativeStructure>(u, u.negate()).getAngle(), FastMath.PI);
try {
new FieldRotation<DerivativeStructure>(u, createVector(0, 0, 0));
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException e) {
// expected behavior
}
}
@Test
public void testVectorTwoPairs() throws MathArithmeticException {
FieldVector3D<DerivativeStructure> u1 = createVector(3, 0, 0);
FieldVector3D<DerivativeStructure> u2 = createVector(0, 5, 0);
FieldVector3D<DerivativeStructure> v1 = createVector(0, 0, 2);
FieldVector3D<DerivativeStructure> v2 = createVector(-2, 0, 2);
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(u1, u2, v1, v2);
checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
checkVector(r.applyTo(createVector(0, 1, 0)), createVector(-1, 0, 0));
r = new FieldRotation<DerivativeStructure>(u1, u2, u1.negate(), u2.negate());
FieldVector3D<DerivativeStructure> axis = r.getAxis();
if (FieldVector3D.dotProduct(axis, createVector(0, 0, 1)).getReal() > 0) {
checkVector(axis, createVector(0, 0, 1));
} else {
checkVector(axis, createVector(0, 0, -1));
}
checkAngle(r.getAngle(), FastMath.PI);
double sqrt = FastMath.sqrt(2) / 2;
r = new FieldRotation<DerivativeStructure>(createVector(1, 0, 0), createVector(0, 1, 0),
createVector(0.5, 0.5, sqrt),
createVector(0.5, 0.5, -sqrt));
checkRotationDS(r, sqrt, 0.5, 0.5, 0);
r = new FieldRotation<DerivativeStructure>(u1, u2, u1, FieldVector3D.crossProduct(u1, u2));
checkRotationDS(r, sqrt, -sqrt, 0, 0);
checkRotationDS(new FieldRotation<DerivativeStructure>(u1, u2, u1, u2), 1, 0, 0, 0);
try {
new FieldRotation<DerivativeStructure>(u1, u2, createVector(0, 0, 0), v2);
Assert.fail("an exception should have been thrown");
} catch (MathArithmeticException e) {
// expected behavior
}
}
@Test
public void testMatrix()
throws NotARotationMatrixException {
try {
createRotation(new double[][] {
{ 0.0, 1.0, 0.0 },
{ 1.0, 0.0, 0.0 }
}, 1.0e-7);
Assert.fail("Expecting NotARotationMatrixException");
} catch (NotARotationMatrixException nrme) {
// expected behavior
}
try {
createRotation(new double[][] {
{ 0.445888, 0.797184, -0.407040 },
{ 0.821760, -0.184320, 0.539200 },
{ -0.354816, 0.574912, 0.737280 }
}, 1.0e-7);
Assert.fail("Expecting NotARotationMatrixException");
} catch (NotARotationMatrixException nrme) {
// expected behavior
}
try {
createRotation(new double[][] {
{ 0.4, 0.8, -0.4 },
{ -0.4, 0.6, 0.7 },
{ 0.8, -0.2, 0.5 }
}, 1.0e-15);
Assert.fail("Expecting NotARotationMatrixException");
} catch (NotARotationMatrixException nrme) {
// expected behavior
}
checkRotationDS(createRotation(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);
checkRotationDS(createRotation(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);
checkRotationDS(createRotation(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);
checkRotationDS(createRotation(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 } };
FieldRotation<DerivativeStructure> r = createRotation(m1, 1.0e-7);
checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
checkVector(r.applyTo(createVector(0, 1, 0)), createVector(1, 0, 0));
checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 1, 0));
double[][] m2 = { { 0.83203, -0.55012, -0.07139 },
{ 0.48293, 0.78164, -0.39474 },
{ 0.27296, 0.29396, 0.91602 } };
r = createRotation(m2, 1.0e-12);
DerivativeStructure[][] m3 = r.getMatrix();
double d00 = m2[0][0] - m3[0][0].getReal();
double d01 = m2[0][1] - m3[0][1].getReal();
double d02 = m2[0][2] - m3[0][2].getReal();
double d10 = m2[1][0] - m3[1][0].getReal();
double d11 = m2[1][1] - m3[1][1].getReal();
double d12 = m2[1][2] - m3[1][2].getReal();
double d20 = m2[2][0] - m3[2][0].getReal();
double d21 = m2[2][1] - m3[2][1].getReal();
double d22 = m2[2][2] - m3[2][2].getReal();
Assert.assertTrue(FastMath.abs(d00) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d01) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d02) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d10) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d11) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d12) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d20) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d21) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d22) < 6.0e-6);
Assert.assertTrue(FastMath.abs(d00) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d01) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d02) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d10) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d11) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d12) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d20) > 4.0e-7);
Assert.assertTrue(FastMath.abs(d21) > 4.0e-7);
Assert.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].getReal() * m3[j][0].getReal() +
m3[i][1].getReal() * m3[j][1].getReal() +
m3[i][2].getReal() * m3[j][2].getReal();
if (i == j) {
Assert.assertTrue(FastMath.abs(m3tm3 - 1.0) < 1.0e-10);
} else {
Assert.assertTrue(FastMath.abs(m3tm3) < 1.0e-10);
}
}
}
checkVector(r.applyTo(createVector(1, 0, 0)),
new FieldVector3D<DerivativeStructure>(m3[0][0], m3[1][0], m3[2][0]));
checkVector(r.applyTo(createVector(0, 1, 0)),
new FieldVector3D<DerivativeStructure>(m3[0][1], m3[1][1], m3[2][1]));
checkVector(r.applyTo(createVector(0, 0, 1)),
new FieldVector3D<DerivativeStructure>(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 = createRotation(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 = createRotation(m5, 1.0e-7);
Assert.fail("got " + r + ", should have caught an exception");
} catch (NotARotationMatrixException e) {
// expected
}
}
@Test
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) {
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(CardanOrders[i],
new DerivativeStructure(3, 1, 0, alpha1),
new DerivativeStructure(3, 1, 1, alpha2),
new DerivativeStructure(3, 1, 2, alpha3));
DerivativeStructure[] 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) {
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(EulerOrders[i],
new DerivativeStructure(3, 1, 0, alpha1),
new DerivativeStructure(3, 1, 1, alpha2),
new DerivativeStructure(3, 1, 2, alpha3));
DerivativeStructure[] angles = r.getAngles(EulerOrders[i]);
checkAngle(angles[0], alpha1);
checkAngle(angles[1], alpha2);
checkAngle(angles[2], alpha3);
}
}
}
}
}
@Test
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) {
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(CardanOrders[i],
new DerivativeStructure(3, 1, 0, 0.1),
new DerivativeStructure(3, 1, 1, singularCardanAngle[j]),
new DerivativeStructure(3, 1, 2, 0.3));
try {
r.getAngles(CardanOrders[i]);
Assert.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) {
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(EulerOrders[i],
new DerivativeStructure(3, 1, 0, 0.1),
new DerivativeStructure(3, 1, 1, singularEulerAngle[j]),
new DerivativeStructure(3, 1, 2, 0.3));
try {
r.getAngles(EulerOrders[i]);
Assert.fail("an exception should have been caught");
} catch (CardanEulerSingularityException cese) {
// expected behavior
}
}
}
}
@Test
public void testQuaternion() throws MathIllegalArgumentException {
FieldRotation<DerivativeStructure> r1 = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));
double n = 23.5;
FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(r1.getQ0().multiply(n), r1.getQ1().multiply(n),
r1.getQ2().multiply(n), r1.getQ3().multiply(n),
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) {
FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
checkVector(r2.applyTo(u), r1.applyTo(u));
}
}
}
r1 = createRotation(0.288, 0.384, 0.36, 0.8, false);
checkRotationDS(r1,
-r1.getQ0().getReal(), -r1.getQ1().getReal(),
-r1.getQ2().getReal(), -r1.getQ3().getReal());
Assert.assertEquals(0.288, r1.toRotation().getQ0(), 1.0e-15);
Assert.assertEquals(0.384, r1.toRotation().getQ1(), 1.0e-15);
Assert.assertEquals(0.36, r1.toRotation().getQ2(), 1.0e-15);
Assert.assertEquals(0.8, r1.toRotation().getQ3(), 1.0e-15);
}
@Test
public void testCompose() throws MathIllegalArgumentException {
FieldRotation<DerivativeStructure> r1 = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));
FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(createVector(-1, 3, 2), createAngle(0.3));
FieldRotation<DerivativeStructure> r3 = r2.applyTo(r1);
FieldRotation<DerivativeStructure> r3Double = r2.applyTo(new Rotation(r1.getQ0().getReal(),
r1.getQ1().getReal(),
r1.getQ2().getReal(),
r1.getQ3().getReal(),
false));
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) {
FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));
checkVector(r2.applyTo(r1.applyTo(u)), r3Double.applyTo(u));
}
}
}
}
@Test
public void testComposeInverse() throws MathIllegalArgumentException {
FieldRotation<DerivativeStructure> r1 = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));
FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(createVector(-1, 3, 2), createAngle(0.3));
FieldRotation<DerivativeStructure> r3 = r2.applyInverseTo(r1);
FieldRotation<DerivativeStructure> r3Double = r2.applyInverseTo(new Rotation(r1.getQ0().getReal(),
r1.getQ1().getReal(),
r1.getQ2().getReal(),
r1.getQ3().getReal(),
false));
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) {
FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));
checkVector(r2.applyInverseTo(r1.applyTo(u)), r3Double.applyTo(u));
}
}
}
}
@Test
public void testDoubleVectors() throws MathIllegalArgumentException {
Well1024a random = new Well1024a(0x180b41cfeeffaf67l);
UnitSphereRandomVectorGenerator g = new UnitSphereRandomVectorGenerator(3, random);
for (int i = 0; i < 10; ++i) {
double[] unit = g.nextVector();
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createVector(unit[0], unit[1], unit[2]),
createAngle(random.nextDouble()));
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) {
FieldVector3D<DerivativeStructure> uds = createVector(x, y, z);
FieldVector3D<DerivativeStructure> ruds = r.applyTo(uds);
FieldVector3D<DerivativeStructure> rIuds = r.applyInverseTo(uds);
Vector3D u = new Vector3D(x, y, z);
FieldVector3D<DerivativeStructure> ru = r.applyTo(u);
FieldVector3D<DerivativeStructure> rIu = r.applyInverseTo(u);
DerivativeStructure[] ruArray = new DerivativeStructure[3];
r.applyTo(new double[] { x, y, z}, ruArray);
DerivativeStructure[] rIuArray = new DerivativeStructure[3];
r.applyInverseTo(new double[] { x, y, z}, rIuArray);
checkVector(ruds, ru);
checkVector(ruds, new FieldVector3D<DerivativeStructure>(ruArray));
checkVector(rIuds, rIu);
checkVector(rIuds, new FieldVector3D<DerivativeStructure>(rIuArray));
}
}
}
}
}
@Test
public void testDoubleRotations() throws MathIllegalArgumentException {
Well1024a random = new Well1024a(0x180b41cfeeffaf67l);
UnitSphereRandomVectorGenerator g = new UnitSphereRandomVectorGenerator(3, random);
for (int i = 0; i < 10; ++i) {
double[] unit1 = g.nextVector();
Rotation r1 = new Rotation(new Vector3D(unit1[0], unit1[1], unit1[2]),
random.nextDouble());
FieldRotation<DerivativeStructure> r1Prime = new FieldRotation<DerivativeStructure>(new DerivativeStructure(4, 1, 0, r1.getQ0()),
new DerivativeStructure(4, 1, 1, r1.getQ1()),
new DerivativeStructure(4, 1, 2, r1.getQ2()),
new DerivativeStructure(4, 1, 3, r1.getQ3()),
false);
double[] unit2 = g.nextVector();
FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(createVector(unit2[0], unit2[1], unit2[2]),
createAngle(random.nextDouble()));
FieldRotation<DerivativeStructure> rA = FieldRotation.applyTo(r1, r2);
FieldRotation<DerivativeStructure> rB = r1Prime.applyTo(r2);
FieldRotation<DerivativeStructure> rC = FieldRotation.applyInverseTo(r1, r2);
FieldRotation<DerivativeStructure> rD = r1Prime.applyInverseTo(r2);
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) {
FieldVector3D<DerivativeStructure> uds = createVector(x, y, z);
checkVector(r1Prime.applyTo(uds), FieldRotation.applyTo(r1, uds));
checkVector(r1Prime.applyInverseTo(uds), FieldRotation.applyInverseTo(r1, uds));
checkVector(rA.applyTo(uds), rB.applyTo(uds));
checkVector(rA.applyInverseTo(uds), rB.applyInverseTo(uds));
checkVector(rC.applyTo(uds), rD.applyTo(uds));
checkVector(rC.applyInverseTo(uds), rD.applyInverseTo(uds));
}
}
}
}
}
@Test
public void testDerivatives() {
double eps = 5.0e-16;
double kx = 2;
double ky = -3;
double kz = 5;
double n2 = kx * kx + ky * ky + kz * kz;
double n = FastMath.sqrt(n2);
double theta = 1.7;
double cosTheta = FastMath.cos(theta);
double sinTheta = FastMath.sin(theta);
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createAxis(kx, ky, kz), createAngle(theta));
Vector3D a = new Vector3D(kx / n, ky / n, kz / n);
// Jacobian of the normalized rotation axis a with respect to the Cartesian vector k
RealMatrix dadk = MatrixUtils.createRealMatrix(new double[][] {
{ (ky * ky + kz * kz) / ( n * n2), -kx * ky / ( n * n2), -kx * kz / ( n * n2) },
{ -kx * ky / ( n * n2), (kx * kx + kz * kz) / ( n * n2), -ky * kz / ( n * n2) },
{ -kx * kz / ( n * n2), -ky * kz / ( n * n2), (kx * kx + ky * ky) / ( n * n2) }
});
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);
FieldVector3D<DerivativeStructure> v = r.applyTo(createVector(x, y, z));
// explicit formula for rotation of vector u around axis a with angle theta
double dot = Vector3D.dotProduct(u, a);
Vector3D cross = Vector3D.crossProduct(a, u);
double c1 = 1 - cosTheta;
double c2 = c1 * dot;
Vector3D rt = new Vector3D(cosTheta, u, c2, a, sinTheta, cross);
Assert.assertEquals(rt.getX(), v.getX().getReal(), eps);
Assert.assertEquals(rt.getY(), v.getY().getReal(), eps);
Assert.assertEquals(rt.getZ(), v.getZ().getReal(), eps);
// Jacobian of the image v = r(u) with respect to rotation axis a
// (analytical differentiation of the explicit formula)
RealMatrix dvda = MatrixUtils.createRealMatrix(new double[][] {
{ c1 * x * a.getX() + c2, c1 * y * a.getX() + sinTheta * z, c1 * z * a.getX() - sinTheta * y },
{ c1 * x * a.getY() - sinTheta * z, c1 * y * a.getY() + c2, c1 * z * a.getY() + sinTheta * x },
{ c1 * x * a.getZ() + sinTheta * y, c1 * y * a.getZ() - sinTheta * x, c1 * z * a.getZ() + c2 }
});
// compose Jacobians
RealMatrix dvdk = dvda.multiply(dadk);
// derivatives with respect to un-normalized axis
Assert.assertEquals(dvdk.getEntry(0, 0), v.getX().getPartialDerivative(1, 0, 0, 0), eps);
Assert.assertEquals(dvdk.getEntry(0, 1), v.getX().getPartialDerivative(0, 1, 0, 0), eps);
Assert.assertEquals(dvdk.getEntry(0, 2), v.getX().getPartialDerivative(0, 0, 1, 0), eps);
Assert.assertEquals(dvdk.getEntry(1, 0), v.getY().getPartialDerivative(1, 0, 0, 0), eps);
Assert.assertEquals(dvdk.getEntry(1, 1), v.getY().getPartialDerivative(0, 1, 0, 0), eps);
Assert.assertEquals(dvdk.getEntry(1, 2), v.getY().getPartialDerivative(0, 0, 1, 0), eps);
Assert.assertEquals(dvdk.getEntry(2, 0), v.getZ().getPartialDerivative(1, 0, 0, 0), eps);
Assert.assertEquals(dvdk.getEntry(2, 1), v.getZ().getPartialDerivative(0, 1, 0, 0), eps);
Assert.assertEquals(dvdk.getEntry(2, 2), v.getZ().getPartialDerivative(0, 0, 1, 0), eps);
// derivative with respect to rotation angle
// (analytical differentiation of the explicit formula)
Vector3D dvdTheta =
new Vector3D(-sinTheta, u, sinTheta * dot, a, cosTheta, cross);
Assert.assertEquals(dvdTheta.getX(), v.getX().getPartialDerivative(0, 0, 0, 1), eps);
Assert.assertEquals(dvdTheta.getY(), v.getY().getPartialDerivative(0, 0, 0, 1), eps);
Assert.assertEquals(dvdTheta.getZ(), v.getZ().getPartialDerivative(0, 0, 0, 1), eps);
}
}
}
}
@Test
public void testArray() throws MathIllegalArgumentException {
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createAxis(2, -3, 5), createAngle(1.7));
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) {
FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
FieldVector3D<DerivativeStructure> v = r.applyTo(u);
DerivativeStructure[] out = new DerivativeStructure[3];
r.applyTo(new DerivativeStructure[] { u.getX(), u.getY(), u.getZ() }, out);
Assert.assertEquals(v.getX().getReal(), out[0].getReal(), 1.0e-10);
Assert.assertEquals(v.getY().getReal(), out[1].getReal(), 1.0e-10);
Assert.assertEquals(v.getZ().getReal(), out[2].getReal(), 1.0e-10);
r.applyInverseTo(out, out);
Assert.assertEquals(u.getX().getReal(), out[0].getReal(), 1.0e-10);
Assert.assertEquals(u.getY().getReal(), out[1].getReal(), 1.0e-10);
Assert.assertEquals(u.getZ().getReal(), out[2].getReal(), 1.0e-10);
}
}
}
}
@Test
public void testApplyInverseTo() throws MathIllegalArgumentException {
DerivativeStructure[] in = new DerivativeStructure[3];
DerivativeStructure[] out = new DerivativeStructure[3];
DerivativeStructure[] rebuilt = new DerivativeStructure[3];
FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));
for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
for (double phi = -1.55; phi < 1.55; phi += 0.2) {
FieldVector3D<DerivativeStructure> u = createVector(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)));
in[0] = u.getX();
in[1] = u.getY();
in[2] = u.getZ();
r.applyTo(in, out);
r.applyInverseTo(out, rebuilt);
Assert.assertEquals(in[0].getReal(), rebuilt[0].getReal(), 1.0e-12);
Assert.assertEquals(in[1].getReal(), rebuilt[1].getReal(), 1.0e-12);
Assert.assertEquals(in[2].getReal(), rebuilt[2].getReal(), 1.0e-12);
}
}
r = createRotation(1, 0, 0, 0, false);
for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
for (double phi = -1.55; phi < 1.55; phi += 0.2) {
FieldVector3D<DerivativeStructure> u = createVector(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 FieldRotation<DerivativeStructure>(createVector(0, 0, 1), createAngle(FastMath.PI));
for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
for (double phi = -1.55; phi < 1.55; phi += 0.2) {
FieldVector3D<DerivativeStructure> u = createVector(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)));
}
}
}
@Test
public void testIssue639() throws MathArithmeticException{
FieldVector3D<DerivativeStructure> u1 = createVector(-1321008684645961.0 / 268435456.0,
-5774608829631843.0 / 268435456.0,
-3822921525525679.0 / 4294967296.0);
FieldVector3D<DerivativeStructure> u2 =createVector( -5712344449280879.0 / 2097152.0,
-2275058564560979.0 / 1048576.0,
4423475992255071.0 / 65536.0);
FieldRotation<DerivativeStructure> rot = new FieldRotation<DerivativeStructure>(u1, u2, createVector(1, 0, 0),createVector(0, 0, 1));
Assert.assertEquals( 0.6228370359608200639829222, rot.getQ0().getReal(), 1.0e-15);
Assert.assertEquals( 0.0257707621456498790029987, rot.getQ1().getReal(), 1.0e-15);
Assert.assertEquals(-0.0000000002503012255839931, rot.getQ2().getReal(), 1.0e-15);
Assert.assertEquals(-0.7819270390861109450724902, rot.getQ3().getReal(), 1.0e-15);
}
@Test
public void testIssue801() throws MathArithmeticException {
FieldVector3D<DerivativeStructure> u1 = createVector(0.9999988431610581, -0.0015210774290851095, 0.0);
FieldVector3D<DerivativeStructure> u2 = createVector(0.0, 0.0, 1.0);
FieldVector3D<DerivativeStructure> v1 = createVector(0.9999999999999999, 0.0, 0.0);
FieldVector3D<DerivativeStructure> v2 = createVector(0.0, 0.0, -1.0);
FieldRotation<DerivativeStructure> quat = new FieldRotation<DerivativeStructure>(u1, u2, v1, v2);
double q2 = quat.getQ0().getReal() * quat.getQ0().getReal() +
quat.getQ1().getReal() * quat.getQ1().getReal() +
quat.getQ2().getReal() * quat.getQ2().getReal() +
quat.getQ3().getReal() * quat.getQ3().getReal();
Assert.assertEquals(1.0, q2, 1.0e-14);
Assert.assertEquals(0.0, FieldVector3D.angle(v1, quat.applyTo(u1)).getReal(), 1.0e-14);
Assert.assertEquals(0.0, FieldVector3D.angle(v2, quat.applyTo(u2)).getReal(), 1.0e-14);
}
private void checkAngle(DerivativeStructure a1, double a2) {
Assert.assertEquals(a1.getReal(), MathUtils.normalizeAngle(a2, a1.getReal()), 1.0e-10);
}
private void checkRotationDS(FieldRotation<DerivativeStructure> r, double q0, double q1, double q2, double q3) {
FieldRotation<DerivativeStructure> rPrime = createRotation(q0, q1, q2, q3, false);
Assert.assertEquals(0, FieldRotation.distance(r, rPrime).getReal(), 1.0e-12);
}
private FieldRotation<DerivativeStructure> createRotation(double q0, double q1, double q2, double q3,
boolean needsNormalization) {
return new FieldRotation<DerivativeStructure>(new DerivativeStructure(4, 1, 0, q0),
new DerivativeStructure(4, 1, 1, q1),
new DerivativeStructure(4, 1, 2, q2),
new DerivativeStructure(4, 1, 3, q3),
needsNormalization);
}
private FieldRotation<DerivativeStructure> createRotation(double[][] m, double threshold) {
DerivativeStructure[][] mds = new DerivativeStructure[m.length][m[0].length];
int index = 0;
for (int i = 0; i < m.length; ++i) {
for (int j = 0; j < m[i].length; ++j) {
mds[i][j] = new DerivativeStructure(4, 1, index, m[i][j]);
index = (index + 1) % 4;
}
}
return new FieldRotation<DerivativeStructure>(mds, threshold);
}
private FieldVector3D<DerivativeStructure> createVector(double x, double y, double z) {
return new FieldVector3D<DerivativeStructure>(new DerivativeStructure(4, 1, x),
new DerivativeStructure(4, 1, y),
new DerivativeStructure(4, 1, z));
}
private FieldVector3D<DerivativeStructure> createAxis(double x, double y, double z) {
return new FieldVector3D<DerivativeStructure>(new DerivativeStructure(4, 1, 0, x),
new DerivativeStructure(4, 1, 1, y),
new DerivativeStructure(4, 1, 2, z));
}
private DerivativeStructure createAngle(double alpha) {
return new DerivativeStructure(4, 1, 3, alpha);
}
private void checkVector(FieldVector3D<DerivativeStructure> u, FieldVector3D<DerivativeStructure> v) {
Assert.assertEquals(u.getX().getReal(), v.getX().getReal(), 1.0e-12);
Assert.assertEquals(u.getY().getReal(), v.getY().getReal(), 1.0e-12);
Assert.assertEquals(u.getZ().getReal(), v.getZ().getReal(), 1.0e-12);
}
}