Java tutorial
/* Copyright 2002-2015 CS Systmes d'Information * Licensed to CS Systmes d'Information (CS) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * CS 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.orekit.utils; import java.util.ArrayList; import java.util.List; import java.util.Random; import org.apache.commons.math3.analysis.differentiation.DerivativeStructure; import org.apache.commons.math3.geometry.euclidean.threed.FieldRotation; import org.apache.commons.math3.geometry.euclidean.threed.FieldVector3D; import org.apache.commons.math3.geometry.euclidean.threed.Rotation; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.util.Pair; import org.junit.Assert; import org.junit.Test; import org.orekit.errors.OrekitException; import org.orekit.time.AbsoluteDate; public class FieldAngularCoordinatesTest { @Test public void testZeroRate() throws OrekitException { FieldAngularCoordinates<DerivativeStructure> angularCoordinates = new FieldAngularCoordinates<DerivativeStructure>( createRotation(0.48, 0.64, 0.36, 0.48, false), createVector(0, 0, 0, 4), createVector(0, 0, 0, 4)); Assert.assertEquals(createVector(0, 0, 0, 4), angularCoordinates.getRotationRate()); double dt = 10.0; FieldAngularCoordinates<DerivativeStructure> shifted = angularCoordinates.shiftedBy(dt); Assert.assertEquals(0.0, shifted.getRotationAcceleration().getNorm().getReal(), 1.0e-15); Assert.assertEquals(0.0, shifted.getRotationRate().getNorm().getReal(), 1.0e-15); Assert.assertEquals(0.0, FieldRotation.distance(angularCoordinates.getRotation(), shifted.getRotation()).getReal(), 1.0e-15); } @Test public void testShift() throws OrekitException { double rate = 2 * FastMath.PI / (12 * 60); FieldAngularCoordinates<DerivativeStructure> angularCoordinates = new FieldAngularCoordinates<DerivativeStructure>( createRotation(1, 0, 0, 0, false), new FieldVector3D<DerivativeStructure>(rate, createVector(0, 0, 1, 4)), createVector(0, 0, 0, 4)); Assert.assertEquals(rate, angularCoordinates.getRotationRate().getNorm().getReal(), 1.0e-10); double dt = 10.0; double alpha = rate * dt; FieldAngularCoordinates<DerivativeStructure> shifted = angularCoordinates.shiftedBy(dt); Assert.assertEquals(rate, shifted.getRotationRate().getNorm().getReal(), 1.0e-10); Assert.assertEquals(alpha, FieldRotation.distance(angularCoordinates.getRotation(), shifted.getRotation()).getReal(), 1.0e-10); FieldVector3D<DerivativeStructure> xSat = shifted.getRotation().applyInverseTo(createVector(1, 0, 0, 4)); Assert.assertEquals(0.0, xSat.subtract(createVector(FastMath.cos(alpha), FastMath.sin(alpha), 0, 4)).getNorm().getReal(), 1.0e-10); FieldVector3D<DerivativeStructure> ySat = shifted.getRotation().applyInverseTo(createVector(0, 1, 0, 4)); Assert.assertEquals(0.0, ySat.subtract(createVector(-FastMath.sin(alpha), FastMath.cos(alpha), 0, 4)).getNorm().getReal(), 1.0e-10); FieldVector3D<DerivativeStructure> zSat = shifted.getRotation().applyInverseTo(createVector(0, 0, 1, 4)); Assert.assertEquals(0.0, zSat.subtract(createVector(0, 0, 1, 4)).getNorm().getReal(), 1.0e-10); } @Test public void testToAC() { Random random = new Random(0xc9b4cf6c371108e0l); for (int i = 0; i < 100; ++i) { FieldRotation<DerivativeStructure> r = randomRotation(random); FieldVector3D<DerivativeStructure> o = randomVector(random, 1.0e-3); FieldVector3D<DerivativeStructure> a = randomVector(random, 1.0e-3); FieldAngularCoordinates<DerivativeStructure> acds = new FieldAngularCoordinates<DerivativeStructure>(r, o, a); AngularCoordinates ac = acds.toAngularCoordinates(); Assert.assertEquals(0, Rotation.distance(r.toRotation(), ac.getRotation()), 1.0e-15); Assert.assertEquals(0, FieldVector3D.distance(o, ac.getRotationRate()).getReal(), 1.0e-15); } } @Test public void testSpin() throws OrekitException { double rate = 2 * FastMath.PI / (12 * 60); FieldAngularCoordinates<DerivativeStructure> angularCoordinates = new FieldAngularCoordinates<DerivativeStructure>( createRotation(0.48, 0.64, 0.36, 0.48, false), new FieldVector3D<DerivativeStructure>(rate, createVector(0, 0, 1, 4)), createVector(0, 0, 0, 4)); Assert.assertEquals(rate, angularCoordinates.getRotationRate().getNorm().getReal(), 1.0e-10); double dt = 10.0; FieldAngularCoordinates<DerivativeStructure> shifted = angularCoordinates.shiftedBy(dt); Assert.assertEquals(rate, shifted.getRotationRate().getNorm().getReal(), 1.0e-10); Assert.assertEquals(rate * dt, FieldRotation.distance(angularCoordinates.getRotation(), shifted.getRotation()).getReal(), 1.0e-10); FieldVector3D<DerivativeStructure> shiftedX = shifted.getRotation() .applyInverseTo(createVector(1, 0, 0, 4)); FieldVector3D<DerivativeStructure> shiftedY = shifted.getRotation() .applyInverseTo(createVector(0, 1, 0, 4)); FieldVector3D<DerivativeStructure> shiftedZ = shifted.getRotation() .applyInverseTo(createVector(0, 0, 1, 4)); FieldVector3D<DerivativeStructure> originalX = angularCoordinates.getRotation() .applyInverseTo(createVector(1, 0, 0, 4)); FieldVector3D<DerivativeStructure> originalY = angularCoordinates.getRotation() .applyInverseTo(createVector(0, 1, 0, 4)); FieldVector3D<DerivativeStructure> originalZ = angularCoordinates.getRotation() .applyInverseTo(createVector(0, 0, 1, 4)); Assert.assertEquals(FastMath.cos(rate * dt), FieldVector3D.dotProduct(shiftedX, originalX).getReal(), 1.0e-10); Assert.assertEquals(FastMath.sin(rate * dt), FieldVector3D.dotProduct(shiftedX, originalY).getReal(), 1.0e-10); Assert.assertEquals(0.0, FieldVector3D.dotProduct(shiftedX, originalZ).getReal(), 1.0e-10); Assert.assertEquals(-FastMath.sin(rate * dt), FieldVector3D.dotProduct(shiftedY, originalX).getReal(), 1.0e-10); Assert.assertEquals(FastMath.cos(rate * dt), FieldVector3D.dotProduct(shiftedY, originalY).getReal(), 1.0e-10); Assert.assertEquals(0.0, FieldVector3D.dotProduct(shiftedY, originalZ).getReal(), 1.0e-10); Assert.assertEquals(0.0, FieldVector3D.dotProduct(shiftedZ, originalX).getReal(), 1.0e-10); Assert.assertEquals(0.0, FieldVector3D.dotProduct(shiftedZ, originalY).getReal(), 1.0e-10); Assert.assertEquals(1.0, FieldVector3D.dotProduct(shiftedZ, originalZ).getReal(), 1.0e-10); FieldVector3D<DerivativeStructure> forward = FieldAngularCoordinates .estimateRate(angularCoordinates.getRotation(), shifted.getRotation(), dt); Assert.assertEquals(0.0, forward.subtract(angularCoordinates.getRotationRate()).getNorm().getReal(), 1.0e-10); FieldVector3D<DerivativeStructure> reversed = FieldAngularCoordinates.estimateRate(shifted.getRotation(), angularCoordinates.getRotation(), dt); Assert.assertEquals(0.0, reversed.add(angularCoordinates.getRotationRate()).getNorm().getReal(), 1.0e-10); } @Test public void testReverseOffset() { Random random = new Random(0x4ecca9d57a8f1611l); for (int i = 0; i < 100; ++i) { FieldRotation<DerivativeStructure> r = randomRotation(random); FieldVector3D<DerivativeStructure> o = randomVector(random, 1.0e-3); FieldVector3D<DerivativeStructure> a = randomVector(random, 1.0e-3); FieldAngularCoordinates<DerivativeStructure> ac = new FieldAngularCoordinates<DerivativeStructure>(r, o, a); FieldAngularCoordinates<DerivativeStructure> sum = ac.addOffset(ac.revert()); Assert.assertEquals(0.0, sum.getRotation().getAngle().getReal(), 1.0e-15); Assert.assertEquals(0.0, sum.getRotationRate().getNorm().getReal(), 1.0e-15); } } @Test public void testNoCommute() { FieldAngularCoordinates<DerivativeStructure> ac1 = new FieldAngularCoordinates<DerivativeStructure>( createRotation(0.48, 0.64, 0.36, 0.48, false), createVector(0, 0, 0, 4), createVector(0, 0, 0, 4)); FieldAngularCoordinates<DerivativeStructure> ac2 = new FieldAngularCoordinates<DerivativeStructure>( createRotation(0.36, -0.48, 0.48, 0.64, false), createVector(0, 0, 0, 4), createVector(0, 0, 0, 4)); FieldAngularCoordinates<DerivativeStructure> add12 = ac1.addOffset(ac2); FieldAngularCoordinates<DerivativeStructure> add21 = ac2.addOffset(ac1); // the rotations are really different from each other Assert.assertEquals(2.574, FieldRotation.distance(add12.getRotation(), add21.getRotation()).getReal(), 1.0e-3); } @Test public void testRoundTripNoOp() { Random random = new Random(0x1e610cfe89306669l); for (int i = 0; i < 100; ++i) { FieldRotation<DerivativeStructure> r1 = randomRotation(random); FieldVector3D<DerivativeStructure> o1 = randomVector(random, 1.0e-2); FieldVector3D<DerivativeStructure> a1 = randomVector(random, 1.0e-2); FieldAngularCoordinates<DerivativeStructure> ac1 = new FieldAngularCoordinates<DerivativeStructure>(r1, o1, a1); FieldRotation<DerivativeStructure> r2 = randomRotation(random); FieldVector3D<DerivativeStructure> o2 = randomVector(random, 1.0e-2); FieldVector3D<DerivativeStructure> a2 = randomVector(random, 1.0e-2); FieldAngularCoordinates<DerivativeStructure> ac2 = new FieldAngularCoordinates<DerivativeStructure>(r2, o2, a2); FieldAngularCoordinates<DerivativeStructure> roundTripSA = ac1.subtractOffset(ac2).addOffset(ac2); Assert.assertEquals(0.0, FieldRotation.distance(ac1.getRotation(), roundTripSA.getRotation()).getReal(), 1.0e-15); Assert.assertEquals(0.0, FieldVector3D.distance(ac1.getRotationRate(), roundTripSA.getRotationRate()).getReal(), 2.0e-17); Assert.assertEquals(0.0, FieldVector3D .distance(ac1.getRotationAcceleration(), roundTripSA.getRotationAcceleration()).getReal(), 2.0e-17); FieldAngularCoordinates<DerivativeStructure> roundTripAS = ac1.addOffset(ac2).subtractOffset(ac2); Assert.assertEquals(0.0, FieldRotation.distance(ac1.getRotation(), roundTripAS.getRotation()).getReal(), 1.0e-15); Assert.assertEquals(0.0, FieldVector3D.distance(ac1.getRotationRate(), roundTripAS.getRotationRate()).getReal(), 2.0e-17); Assert.assertEquals(0.0, FieldVector3D .distance(ac1.getRotationAcceleration(), roundTripAS.getRotationAcceleration()).getReal(), 2.0e-17); } } @Test @Deprecated // to be removed when AngularCoordinates.interpolate is removed public void testInterpolationSimple() throws OrekitException { AbsoluteDate date = AbsoluteDate.GALILEO_EPOCH; double alpha0 = 0.5 * FastMath.PI; double omega = 0.5 * FastMath.PI; FieldAngularCoordinates<DerivativeStructure> reference = new FieldAngularCoordinates<DerivativeStructure>( createRotation(createVector(0, 0, 1, 4), alpha0), new FieldVector3D<DerivativeStructure>(omega, createVector(0, 0, -1, 4)), createVector(0, 0, 0, 4)); List<Pair<AbsoluteDate, FieldAngularCoordinates<DerivativeStructure>>> sample = new ArrayList<Pair<AbsoluteDate, FieldAngularCoordinates<DerivativeStructure>>>(); for (double dt : new double[] { 0.0, 0.5, 1.0 }) { sample.add(new Pair<AbsoluteDate, FieldAngularCoordinates<DerivativeStructure>>(date.shiftedBy(dt), reference.shiftedBy(dt))); } for (double dt = 0; dt < 1.0; dt += 0.001) { FieldAngularCoordinates<DerivativeStructure> interpolated = FieldAngularCoordinates .interpolate(date.shiftedBy(dt), true, sample); FieldRotation<DerivativeStructure> r = interpolated.getRotation(); FieldVector3D<DerivativeStructure> rate = interpolated.getRotationRate(); FieldVector3D<DerivativeStructure> acceleration = interpolated.getRotationAcceleration(); Assert.assertEquals(0.0, FieldRotation .distance(createRotation(createVector(0, 0, 1, 4), alpha0 + omega * dt), r).getReal(), 1.1e-15); Assert.assertEquals(0.0, FieldVector3D.distance(createVector(0, 0, -omega, 4), rate).getReal(), 4.0e-15); Assert.assertEquals(0.0, FieldVector3D.distance(createVector(0, 0, 0, 4), acceleration).getReal(), 3.2e-14); } } private FieldVector3D<DerivativeStructure> randomVector(Random random, double norm) { double n = random.nextDouble() * norm; double x = random.nextDouble(); double y = random.nextDouble(); double z = random.nextDouble(); return new FieldVector3D<DerivativeStructure>(n, createVector(x, y, z, 4).normalize()); } private FieldRotation<DerivativeStructure> randomRotation(Random random) { double q0 = random.nextDouble() * 2 - 1; double q1 = random.nextDouble() * 2 - 1; double q2 = random.nextDouble() * 2 - 1; double q3 = random.nextDouble() * 2 - 1; double q = FastMath.sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); return createRotation(q0 / q, q1 / q, q2 / q, q3 / q, false); } private FieldRotation<DerivativeStructure> createRotation(FieldVector3D<DerivativeStructure> axis, double angle) { return new FieldRotation<DerivativeStructure>(axis, new DerivativeStructure(4, 1, angle)); } 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 FieldVector3D<DerivativeStructure> createVector(double x, double y, double z, int params) { return new FieldVector3D<DerivativeStructure>(new DerivativeStructure(params, 1, 0, x), new DerivativeStructure(params, 1, 1, y), new DerivativeStructure(params, 1, 2, z)); } }