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17 package org.orekit.utils;
18
19 import org.hipparchus.analysis.differentiation.DerivativeStructure;
20 import org.hipparchus.analysis.differentiation.UnivariateDerivative1;
21 import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
22 import org.hipparchus.exception.MathIllegalArgumentException;
23 import org.hipparchus.geometry.euclidean.threed.FieldRotation;
24 import org.hipparchus.geometry.euclidean.threed.Rotation;
25 import org.hipparchus.geometry.euclidean.threed.RotationConvention;
26 import org.hipparchus.geometry.euclidean.threed.Vector3D;
27 import org.hipparchus.ode.ODEIntegrator;
28 import org.hipparchus.ode.ODEState;
29 import org.hipparchus.ode.ODEStateAndDerivative;
30 import org.hipparchus.ode.OrdinaryDifferentialEquation;
31 import org.hipparchus.ode.nonstiff.DormandPrince853Integrator;
32 import org.hipparchus.ode.sampling.ODEFixedStepHandler;
33 import org.hipparchus.ode.sampling.StepNormalizer;
34 import org.hipparchus.random.RandomGenerator;
35 import org.hipparchus.random.Well1024a;
36 import org.hipparchus.util.FastMath;
37 import org.hipparchus.util.MathArrays;
38 import org.hipparchus.util.Precision;
39 import org.junit.jupiter.api.Assertions;
40 import org.junit.jupiter.api.Test;
41 import org.orekit.errors.OrekitException;
42 import org.orekit.errors.OrekitMessages;
43
44 import java.lang.reflect.InvocationTargetException;
45 import java.lang.reflect.Method;
46
47 public class AngularCoordinatesTest {
48
49 @Test
50 public void testAccelerationModeling() {
51 double rate = 2 * FastMath.PI / (12 * 60);
52 double acc = 0.01;
53 double dt = 1.0;
54 int n = 2000;
55 final AngularCoordinates quadratic =
56 new AngularCoordinates(Rotation.IDENTITY,
57 new Vector3D(rate, Vector3D.PLUS_K),
58 new Vector3D(acc, Vector3D.PLUS_J));
59
60 final OrdinaryDifferentialEquation ode = new OrdinaryDifferentialEquation() {
61 public int getDimension() {
62 return 4;
63 }
64 public double[] computeDerivatives(final double t, final double[] q) {
65 final double omegaX = quadratic.getRotationRate().getX() + t * quadratic.getRotationAcceleration().getX();
66 final double omegaY = quadratic.getRotationRate().getY() + t * quadratic.getRotationAcceleration().getY();
67 final double omegaZ = quadratic.getRotationRate().getZ() + t * quadratic.getRotationAcceleration().getZ();
68 return new double[] {
69 0.5 * MathArrays.linearCombination(-q[1], omegaX, -q[2], omegaY, -q[3], omegaZ),
70 0.5 * MathArrays.linearCombination( q[0], omegaX, -q[3], omegaY, q[2], omegaZ),
71 0.5 * MathArrays.linearCombination( q[3], omegaX, q[0], omegaY, -q[1], omegaZ),
72 0.5 * MathArrays.linearCombination(-q[2], omegaX, q[1], omegaY, q[0], omegaZ)
73 };
74 }
75 };
76 ODEIntegrator integrator = new DormandPrince853Integrator(1.0e-6, 1.0, 1.0e-12, 1.0e-12);
77 integrator.addStepHandler(new StepNormalizer(dt / n, new ODEFixedStepHandler() {
78 private double tM4, tM3, tM2, tM1, t0, tP1, tP2, tP3, tP4;
79 private double[] yM4, yM3, yM2, yM1, y0, yP1, yP2, yP3, yP4;
80 private double[] ydM4, ydM3, ydM2, ydM1, yd0, ydP1, ydP2, ydP3, ydP4;
81 public void handleStep(ODEStateAndDerivative s, boolean isLast) {
82 tM4 = tM3; yM4 = yM3; ydM4 = ydM3;
83 tM3 = tM2; yM3 = yM2; ydM3 = ydM2;
84 tM2 = tM1; yM2 = yM1; ydM2 = ydM1;
85 tM1 = t0 ; yM1 = y0 ; ydM1 = yd0 ;
86 t0 = tP1; y0 = yP1; yd0 = ydP1;
87 tP1 = tP2; yP1 = yP2; ydP1 = ydP2;
88 tP2 = tP3; yP2 = yP3; ydP2 = ydP3;
89 tP3 = tP4; yP3 = yP4; ydP3 = ydP4;
90 tP4 = s.getTime();
91 yP4 = s.getPrimaryState();
92 ydP4 = s.getPrimaryDerivative();
93
94 if (yM4 != null) {
95 double dt = (tP4 - tM4) / 8;
96 final double c = 1.0 / (840 * dt);
97 final double[] ydd0 = {
98 -3 * c * (ydP4[0] - ydM4[0]) + 32 * c * (ydP3[0] - ydM3[0]) - 168 * c * (ydP2[0] - ydM2[0]) + 672 * c * (ydP1[0] - ydM1[0]),
99 -3 * c * (ydP4[1] - ydM4[1]) + 32 * c * (ydP3[1] - ydM3[1]) - 168 * c * (ydP2[1] - ydM2[1]) + 672 * c * (ydP1[1] - ydM1[1]),
100 -3 * c * (ydP4[2] - ydM4[2]) + 32 * c * (ydP3[2] - ydM3[2]) - 168 * c * (ydP2[2] - ydM2[2]) + 672 * c * (ydP1[2] - ydM1[2]),
101 -3 * c * (ydP4[3] - ydM4[3]) + 32 * c * (ydP3[3] - ydM3[3]) - 168 * c * (ydP2[3] - ydM2[3]) + 672 * c * (ydP1[3] - ydM1[3]),
102 };
103 AngularCoordinates ac = new AngularCoordinates(new FieldRotation<>(new UnivariateDerivative2(y0[0], yd0[0], ydd0[0]),
104 new UnivariateDerivative2(y0[1], yd0[1], ydd0[1]),
105 new UnivariateDerivative2(y0[2], yd0[2], ydd0[2]),
106 new UnivariateDerivative2(y0[3], yd0[3], ydd0[3]),
107 false));
108 Assertions.assertEquals(0.0,
109 Vector3D.distance(quadratic.getRotationAcceleration(),
110 ac.getRotationAcceleration()),
111 4.0e-13);
112 }
113
114 }
115 }));
116
117 double[] y = new double[] {
118 quadratic.getRotation().getQ0(),
119 quadratic.getRotation().getQ1(),
120 quadratic.getRotation().getQ2(),
121 quadratic.getRotation().getQ3()
122 };
123 integrator.integrate(ode, new ODEState(0, y), dt);
124
125 }
126
127 @Test
128 public void testDefaultConstructor() {
129 AngularCoordinates ac = new AngularCoordinates();
130 Assertions.assertEquals(0.0, ac.getRotationAcceleration().getNorm(), 1.0e-15);
131 Assertions.assertEquals(0.0, ac.getRotationRate().getNorm(), 1.0e-15);
132 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), Rotation.IDENTITY), 1.0e-10);
133 }
134
135 @Test
136 public void testDerivativesStructuresNeg() {
137 try {
138 AngularCoordinates.IDENTITY.toDerivativeStructureRotation(-1);
139 Assertions.fail("an exception should have been thrown");
140 } catch (OrekitException oe) {
141 Assertions.assertEquals(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, oe.getSpecifier());
142 Assertions.assertEquals(-1, ((Integer) (oe.getParts()[0])).intValue());
143 }
144
145 }
146
147 @Test
148 public void testDerivativesStructures3() {
149 try {
150 AngularCoordinates.IDENTITY.toDerivativeStructureRotation(3);
151 Assertions.fail("an exception should have been thrown");
152 } catch (OrekitException oe) {
153 Assertions.assertEquals(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, oe.getSpecifier());
154 Assertions.assertEquals(3, ((Integer) (oe.getParts()[0])).intValue());
155 }
156
157 }
158
159 @Test
160 public void testDerivativesStructures0() {
161 RandomGenerator random = new Well1024a(0x18a0a08fd63f047al);
162
163 Rotation r = randomRotation(random);
164 Vector3D o = randomVector(random, 1.0e-2);
165 Vector3D oDot = randomVector(random, 1.0e-2);
166 AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
167 AngularCoordinates rebuilt = new AngularCoordinates(ac.toDerivativeStructureRotation(0));
168 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
169 Assertions.assertEquals(0.0, rebuilt.getRotationRate().getNorm(), 1.0e-15);
170 Assertions.assertEquals(0.0, rebuilt.getRotationAcceleration().getNorm(), 1.0e-15);
171 }
172
173 @Test
174 public void testDerivativesStructures1() {
175 RandomGenerator random = new Well1024a(0x8f8fc6d27bbdc46dl);
176
177 Rotation r = randomRotation(random);
178 Vector3D o = randomVector(random, 1.0e-2);
179 Vector3D oDot = randomVector(random, 1.0e-2);
180 AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
181 AngularCoordinates rebuilt = new AngularCoordinates(ac.toDerivativeStructureRotation(1));
182 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
183 Assertions.assertEquals(0.0, Vector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()), 1.0e-15);
184 Assertions.assertEquals(0.0, rebuilt.getRotationAcceleration().getNorm(), 1.0e-15);
185 }
186
187 @Test
188 public void testDerivativesStructures2() {
189 RandomGenerator random = new Well1024a(0x1633878dddac047dl);
190
191 Rotation r = randomRotation(random);
192 Vector3D o = randomVector(random, 1.0e-2);
193 Vector3D oDot = randomVector(random, 1.0e-2);
194 AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
195 AngularCoordinates rebuilt = new AngularCoordinates(ac.toDerivativeStructureRotation(2));
196 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
197 Assertions.assertEquals(0.0, Vector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()), 1.0e-15);
198 Assertions.assertEquals(0.0, Vector3D.distance(ac.getRotationAcceleration(), rebuilt.getRotationAcceleration()), 1.0e-15);
199 }
200
201 @Test
202 public void testUnivariateDerivative1() {
203 RandomGenerator random = new Well1024a(0x6de8cce747539904l);
204
205 Rotation r = randomRotation(random);
206 Vector3D o = randomVector(random, 1.0e-2);
207 Vector3D oDot = randomVector(random, 1.0e-2);
208 AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
209 FieldRotation<UnivariateDerivative1> rotationUD = ac.toUnivariateDerivative1Rotation();
210 FieldRotation<DerivativeStructure> rotationDS = ac.toDerivativeStructureRotation(1);
211 Assertions.assertEquals(rotationDS.getQ0().getReal(), rotationUD.getQ0().getReal(), 1.0e-15);
212 Assertions.assertEquals(rotationDS.getQ1().getReal(), rotationUD.getQ1().getReal(), 1.0e-15);
213 Assertions.assertEquals(rotationDS.getQ2().getReal(), rotationUD.getQ2().getReal(), 1.0e-15);
214 Assertions.assertEquals(rotationDS.getQ3().getReal(), rotationUD.getQ3().getReal(), 1.0e-15);
215 Assertions.assertEquals(rotationDS.getQ0().getPartialDerivative(1), rotationUD.getQ0().getFirstDerivative(), 1.0e-15);
216 Assertions.assertEquals(rotationDS.getQ1().getPartialDerivative(1), rotationUD.getQ1().getFirstDerivative(), 1.0e-15);
217 Assertions.assertEquals(rotationDS.getQ2().getPartialDerivative(1), rotationUD.getQ2().getFirstDerivative(), 1.0e-15);
218 Assertions.assertEquals(rotationDS.getQ3().getPartialDerivative(1), rotationUD.getQ3().getFirstDerivative(), 1.0e-15);
219
220 AngularCoordinates rebuilt = new AngularCoordinates(rotationUD);
221 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
222 Assertions.assertEquals(0.0, Vector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()), 1.0e-15);
223
224 }
225
226 @Test
227 public void testUnivariateDerivative2() {
228 RandomGenerator random = new Well1024a(0x255710c8fa2247ecl);
229
230 Rotation r = randomRotation(random);
231 Vector3D o = randomVector(random, 1.0e-2);
232 Vector3D oDot = randomVector(random, 1.0e-2);
233 AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
234 FieldRotation<UnivariateDerivative2> rotationUD = ac.toUnivariateDerivative2Rotation();
235 FieldRotation<DerivativeStructure> rotationDS = ac.toDerivativeStructureRotation(2);
236 Assertions.assertEquals(rotationDS.getQ0().getReal(), rotationUD.getQ0().getReal(), 1.0e-15);
237 Assertions.assertEquals(rotationDS.getQ1().getReal(), rotationUD.getQ1().getReal(), 1.0e-15);
238 Assertions.assertEquals(rotationDS.getQ2().getReal(), rotationUD.getQ2().getReal(), 1.0e-15);
239 Assertions.assertEquals(rotationDS.getQ3().getReal(), rotationUD.getQ3().getReal(), 1.0e-15);
240 Assertions.assertEquals(rotationDS.getQ0().getPartialDerivative(1), rotationUD.getQ0().getFirstDerivative(), 1.0e-15);
241 Assertions.assertEquals(rotationDS.getQ1().getPartialDerivative(1), rotationUD.getQ1().getFirstDerivative(), 1.0e-15);
242 Assertions.assertEquals(rotationDS.getQ2().getPartialDerivative(1), rotationUD.getQ2().getFirstDerivative(), 1.0e-15);
243 Assertions.assertEquals(rotationDS.getQ3().getPartialDerivative(1), rotationUD.getQ3().getFirstDerivative(), 1.0e-15);
244 Assertions.assertEquals(rotationDS.getQ0().getPartialDerivative(2), rotationUD.getQ0().getSecondDerivative(), 1.0e-15);
245 Assertions.assertEquals(rotationDS.getQ1().getPartialDerivative(2), rotationUD.getQ1().getSecondDerivative(), 1.0e-15);
246 Assertions.assertEquals(rotationDS.getQ2().getPartialDerivative(2), rotationUD.getQ2().getSecondDerivative(), 1.0e-15);
247 Assertions.assertEquals(rotationDS.getQ3().getPartialDerivative(2), rotationUD.getQ3().getSecondDerivative(), 1.0e-15);
248
249 AngularCoordinates rebuilt = new AngularCoordinates(rotationUD);
250 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
251 Assertions.assertEquals(0.0, Vector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()), 1.0e-15);
252 Assertions.assertEquals(0.0, Vector3D.distance(ac.getRotationAcceleration(), rebuilt.getRotationAcceleration()), 1.0e-15);
253
254 }
255
256 @Test
257 public void testZeroRate() {
258 AngularCoordinates ac =
259 new AngularCoordinates(new Rotation(0.48, 0.64, 0.36, 0.48, false), Vector3D.ZERO, Vector3D.ZERO);
260 Assertions.assertEquals(Vector3D.ZERO, ac.getRotationRate());
261 double dt = 10.0;
262 AngularCoordinates shifted = ac.shiftedBy(dt);
263 Assertions.assertEquals(Vector3D.ZERO, shifted.getRotationAcceleration());
264 Assertions.assertEquals(Vector3D.ZERO, shifted.getRotationRate());
265 Assertions.assertEquals(0.0, Rotation.distance(ac.getRotation(), shifted.getRotation()), 1.0e-15);
266 }
267
268 @Test
269 public void testShiftWithoutAcceleration() {
270 double rate = 2 * FastMath.PI / (12 * 60);
271 AngularCoordinates ac =
272 new AngularCoordinates(Rotation.IDENTITY,
273 new Vector3D(rate, Vector3D.PLUS_K),
274 Vector3D.ZERO);
275 Assertions.assertEquals(rate, ac.getRotationRate().getNorm(), 1.0e-10);
276 double dt = 10.0;
277 double alpha = rate * dt;
278 AngularCoordinates shifted = ac.shiftedBy(dt);
279 Assertions.assertEquals(rate, shifted.getRotationRate().getNorm(), 1.0e-10);
280 Assertions.assertEquals(alpha, Rotation.distance(ac.getRotation(), shifted.getRotation()), 1.0e-15);
281
282 Vector3D xSat = shifted.getRotation().applyInverseTo(Vector3D.PLUS_I);
283 Assertions.assertEquals(0.0, xSat.subtract(new Vector3D(FastMath.cos(alpha), FastMath.sin(alpha), 0)).getNorm(), 1.0e-15);
284 Vector3D ySat = shifted.getRotation().applyInverseTo(Vector3D.PLUS_J);
285 Assertions.assertEquals(0.0, ySat.subtract(new Vector3D(-FastMath.sin(alpha), FastMath.cos(alpha), 0)).getNorm(), 1.0e-15);
286 Vector3D zSat = shifted.getRotation().applyInverseTo(Vector3D.PLUS_K);
287 Assertions.assertEquals(0.0, zSat.subtract(Vector3D.PLUS_K).getNorm(), 1.0e-15);
288
289 }
290
291 @Test
292 public void testShiftWithAcceleration() {
293 double rate = 2 * FastMath.PI / (12 * 60);
294 double acc = 0.001;
295 double dt = 1.0;
296 int n = 2000;
297 final AngularCoordinates quadratic =
298 new AngularCoordinates(Rotation.IDENTITY,
299 new Vector3D(rate, Vector3D.PLUS_K),
300 new Vector3D(acc, Vector3D.PLUS_J));
301 final AngularCoordinates linear =
302 new AngularCoordinates(quadratic.getRotation(), quadratic.getRotationRate(), Vector3D.ZERO);
303
304 final OrdinaryDifferentialEquation ode = new OrdinaryDifferentialEquation() {
305 public int getDimension() {
306 return 4;
307 }
308 public double[] computeDerivatives(final double t, final double[] q) {
309 final double omegaX = quadratic.getRotationRate().getX() + t * quadratic.getRotationAcceleration().getX();
310 final double omegaY = quadratic.getRotationRate().getY() + t * quadratic.getRotationAcceleration().getY();
311 final double omegaZ = quadratic.getRotationRate().getZ() + t * quadratic.getRotationAcceleration().getZ();
312 return new double[] {
313 0.5 * MathArrays.linearCombination(-q[1], omegaX, -q[2], omegaY, -q[3], omegaZ),
314 0.5 * MathArrays.linearCombination( q[0], omegaX, -q[3], omegaY, q[2], omegaZ),
315 0.5 * MathArrays.linearCombination( q[3], omegaX, q[0], omegaY, -q[1], omegaZ),
316 0.5 * MathArrays.linearCombination(-q[2], omegaX, q[1], omegaY, q[0], omegaZ)
317 };
318 }
319 };
320 ODEIntegrator integrator = new DormandPrince853Integrator(1.0e-6, 1.0, 1.0e-12, 1.0e-12);
321 integrator.addStepHandler(new StepNormalizer(dt / n, new ODEFixedStepHandler() {
322 public void handleStep(ODEStateAndDerivative s, boolean isLast) {
323 final double t = s.getTime();
324 final double[] y = s.getPrimaryState();
325 Rotation reference = new Rotation(y[0], y[1], y[2], y[3], true);
326
327
328 double expectedCubicError = 1.4544e-6 * t * t * t;
329 Assertions.assertEquals(expectedCubicError,
330 Rotation.distance(reference, quadratic.shiftedBy(t).getRotation()),
331 0.0001 * expectedCubicError);
332 Assertions.assertEquals(expectedCubicError,
333 Rotation.distance(reference, quadratic.rotationShiftedBy(t)),
334 0.0001 * expectedCubicError);
335
336
337 double expectedQuadraticError = 5.0e-4 * t * t;
338 Assertions.assertEquals(expectedQuadraticError,
339 Rotation.distance(reference, linear.shiftedBy(t).getRotation()),
340 0.00001 * expectedQuadraticError);
341 Assertions.assertEquals(expectedQuadraticError,
342 Rotation.distance(reference, linear.rotationShiftedBy(t)),
343 0.00001 * expectedQuadraticError);
344
345 }
346 }));
347
348 double[] y = new double[] {
349 quadratic.getRotation().getQ0(),
350 quadratic.getRotation().getQ1(),
351 quadratic.getRotation().getQ2(),
352 quadratic.getRotation().getQ3()
353 };
354 integrator.integrate(ode, new ODEState(0, y), dt);
355
356 }
357
358 @Test
359 public void testSpin() {
360 double rate = 2 * FastMath.PI / (12 * 60);
361 AngularCoordinates angularCoordinates =
362 new AngularCoordinates(new Rotation(0.48, 0.64, 0.36, 0.48, false),
363 new Vector3D(rate, Vector3D.PLUS_K));
364 Assertions.assertEquals(rate, angularCoordinates.getRotationRate().getNorm(), 1.0e-10);
365 double dt = 10.0;
366 AngularCoordinates shifted = angularCoordinates.shiftedBy(dt);
367 Assertions.assertEquals(rate, shifted.getRotationRate().getNorm(), 1.0e-10);
368 Assertions.assertEquals(rate * dt, Rotation.distance(angularCoordinates.getRotation(), shifted.getRotation()), 1.0e-10);
369
370 Vector3D shiftedX = shifted.getRotation().applyInverseTo(Vector3D.PLUS_I);
371 Vector3D shiftedY = shifted.getRotation().applyInverseTo(Vector3D.PLUS_J);
372 Vector3D shiftedZ = shifted.getRotation().applyInverseTo(Vector3D.PLUS_K);
373 Vector3D originalX = angularCoordinates.getRotation().applyInverseTo(Vector3D.PLUS_I);
374 Vector3D originalY = angularCoordinates.getRotation().applyInverseTo(Vector3D.PLUS_J);
375 Vector3D originalZ = angularCoordinates.getRotation().applyInverseTo(Vector3D.PLUS_K);
376 Assertions.assertEquals( FastMath.cos(rate * dt), Vector3D.dotProduct(shiftedX, originalX), 1.0e-10);
377 Assertions.assertEquals( FastMath.sin(rate * dt), Vector3D.dotProduct(shiftedX, originalY), 1.0e-10);
378 Assertions.assertEquals( 0.0, Vector3D.dotProduct(shiftedX, originalZ), 1.0e-10);
379 Assertions.assertEquals(-FastMath.sin(rate * dt), Vector3D.dotProduct(shiftedY, originalX), 1.0e-10);
380 Assertions.assertEquals( FastMath.cos(rate * dt), Vector3D.dotProduct(shiftedY, originalY), 1.0e-10);
381 Assertions.assertEquals( 0.0, Vector3D.dotProduct(shiftedY, originalZ), 1.0e-10);
382 Assertions.assertEquals( 0.0, Vector3D.dotProduct(shiftedZ, originalX), 1.0e-10);
383 Assertions.assertEquals( 0.0, Vector3D.dotProduct(shiftedZ, originalY), 1.0e-10);
384 Assertions.assertEquals( 1.0, Vector3D.dotProduct(shiftedZ, originalZ), 1.0e-10);
385
386 Vector3D forward = AngularCoordinates.estimateRate(angularCoordinates.getRotation(), shifted.getRotation(), dt);
387 Assertions.assertEquals(0.0, forward.subtract(angularCoordinates.getRotationRate()).getNorm(), 1.0e-10);
388
389 Vector3D reversed = AngularCoordinates.estimateRate(shifted.getRotation(), angularCoordinates.getRotation(), dt);
390 Assertions.assertEquals(0.0, reversed.add(angularCoordinates.getRotationRate()).getNorm(), 1.0e-10);
391
392 }
393
394 @Test
395 public void testReverseOffset() {
396 RandomGenerator random = new Well1024a(0x4ecca9d57a8f1611l);
397 for (int i = 0; i < 100; ++i) {
398 Rotation r = randomRotation(random);
399 Vector3D o = randomVector(random, 1.0e-3);
400 AngularCoordinates ac = new AngularCoordinates(r, o);
401 AngularCoordinates sum = ac.addOffset(ac.revert());
402 Assertions.assertEquals(0.0, sum.getRotation().getAngle(), 1.0e-15);
403 Assertions.assertEquals(0.0, sum.getRotationRate().getNorm(), 1.0e-15);
404 Assertions.assertEquals(0.0, sum.getRotationAcceleration().getNorm(), 1.0e-15);
405 }
406 }
407
408 @Test
409 public void testNoCommute() {
410 AngularCoordinates ac1 =
411 new AngularCoordinates(new Rotation(0.48, 0.64, 0.36, 0.48, false), Vector3D.ZERO);
412 AngularCoordinates ac2 =
413 new AngularCoordinates(new Rotation(0.36, -0.48, 0.48, 0.64, false), Vector3D.ZERO);
414
415 AngularCoordinates add12 = ac1.addOffset(ac2);
416 AngularCoordinates add21 = ac2.addOffset(ac1);
417
418
419 Assertions.assertEquals(2.574, Rotation.distance(add12.getRotation(), add21.getRotation()), 1.0e-3);
420
421 }
422
423 @Test
424 public void testRoundTripNoOp() {
425 RandomGenerator random = new Well1024a(0x1e610cfe89306669l);
426 for (int i = 0; i < 100; ++i) {
427
428 Rotation r1 = randomRotation(random);
429 Vector3D o1 = randomVector(random, 1.0e-2);
430 Vector3D oDot1 = randomVector(random, 1.0e-2);
431 AngularCoordinates ac1 = new AngularCoordinates(r1, o1, oDot1);
432
433 Rotation r2 = randomRotation(random);
434 Vector3D o2 = randomVector(random, 1.0e-2);
435 Vector3D oDot2 = randomVector(random, 1.0e-2);
436 AngularCoordinates ac2 = new AngularCoordinates(r2, o2, oDot2);
437
438 AngularCoordinates roundTripSA = ac1.subtractOffset(ac2).addOffset(ac2);
439 Assertions.assertEquals(0.0, Rotation.distance(ac1.getRotation(), roundTripSA.getRotation()), 5.0e-16);
440 Assertions.assertEquals(0.0, Vector3D.distance(ac1.getRotationRate(), roundTripSA.getRotationRate()), 2.0e-17);
441 Assertions.assertEquals(0.0, Vector3D.distance(ac1.getRotationAcceleration(), roundTripSA.getRotationAcceleration()), 2.0e-17);
442
443 AngularCoordinates roundTripAS = ac1.addOffset(ac2).subtractOffset(ac2);
444 Assertions.assertEquals(0.0, Rotation.distance(ac1.getRotation(), roundTripAS.getRotation()), 5.0e-16);
445 Assertions.assertEquals(0.0, Vector3D.distance(ac1.getRotationRate(), roundTripAS.getRotationRate()), 2.0e-17);
446 Assertions.assertEquals(0.0, Vector3D.distance(ac1.getRotationAcceleration(), roundTripAS.getRotationAcceleration()), 2.0e-17);
447
448 }
449 }
450
451 @Test
452 public void testRodriguesSymmetry() {
453
454
455 RandomGenerator random = new Well1024a(0xb1e615aaa8236b52l);
456 for (int i = 0; i < 1000; ++i) {
457 Rotation rotation = randomRotation(random);
458 Vector3D rotationRate = randomVector(random, 0.01);
459 Vector3D rotationAcceleration = randomVector(random, 0.01);
460 AngularCoordinates ac = new AngularCoordinates(rotation, rotationRate, rotationAcceleration);
461 AngularCoordinates rebuilt = AngularCoordinates.createFromModifiedRodrigues(ac.getModifiedRodrigues(1.0));
462 Assertions.assertEquals(0.0, Rotation.distance(rotation, rebuilt.getRotation()), 1.0e-14);
463 Assertions.assertEquals(0.0, Vector3D.distance(rotationRate, rebuilt.getRotationRate()), 1.0e-15);
464 Assertions.assertEquals(0.0, Vector3D.distance(rotationAcceleration, rebuilt.getRotationAcceleration()), 1.0e-15);
465 }
466
467 }
468
469 @Test
470 public void testRodriguesSpecialCases() {
471
472
473 double[][] identity = new AngularCoordinates(Rotation.IDENTITY, Vector3D.ZERO, Vector3D.ZERO).getModifiedRodrigues(1.0);
474 for (double[] row : identity) {
475 for (double element : row) {
476 Assertions.assertEquals(0.0, element, Precision.SAFE_MIN);
477 }
478 }
479 AngularCoordinates acId = AngularCoordinates.createFromModifiedRodrigues(identity);
480 Assertions.assertEquals(0.0, acId.getRotation().getAngle(), Precision.SAFE_MIN);
481 Assertions.assertEquals(0.0, acId.getRotationRate().getNorm(), Precision.SAFE_MIN);
482
483
484 RandomGenerator random = new Well1024a(0x2158523e6accb859l);
485 for (int i = 0; i < 100; ++i) {
486 Vector3D axis = randomVector(random, 1.0);
487 AngularCoordinates original = new AngularCoordinates(new Rotation(axis, FastMath.PI, RotationConvention.VECTOR_OPERATOR),
488 Vector3D.ZERO, Vector3D.ZERO);
489 AngularCoordinates rebuilt = AngularCoordinates.createFromModifiedRodrigues(original.getModifiedRodrigues(1.0));
490 Assertions.assertEquals(FastMath.PI, rebuilt.getRotation().getAngle(), 1.0e-15);
491 Assertions.assertEquals(0.0, FastMath.sin(Vector3D.angle(axis, rebuilt.getRotation().getAxis(RotationConvention.VECTOR_OPERATOR))), 1.0e-15);
492 Assertions.assertEquals(0.0, rebuilt.getRotationRate().getNorm(), 1.0e-16);
493 }
494
495 }
496
497 @Test
498 public void testInverseCrossProducts()
499 {
500 checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_J);
501 checkInverse(Vector3D.ZERO, Vector3D.ZERO, Vector3D.ZERO);
502 checkInverse(Vector3D.ZERO, Vector3D.ZERO, Vector3D.PLUS_J);
503 checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_K, Vector3D.PLUS_J);
504 checkInverse(Vector3D.ZERO, Vector3D.PLUS_K, Vector3D.ZERO);
505 checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_K);
506 checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_I);
507 checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, new Vector3D(1, 0, -1).normalize());
508 checkInverse(Vector3D.ZERO, Vector3D.PLUS_I, Vector3D.ZERO, Vector3D.PLUS_J, Vector3D.ZERO);
509 }
510
511 @Test
512 public void testInverseCrossProductsFailures() {
513 checkInverseFailure(Vector3D.PLUS_K, Vector3D.ZERO, Vector3D.PLUS_J, Vector3D.PLUS_I, Vector3D.PLUS_K);
514 checkInverseFailure(Vector3D.PLUS_K, Vector3D.ZERO, Vector3D.ZERO, Vector3D.ZERO, Vector3D.PLUS_K);
515 checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.ZERO, Vector3D.MINUS_I, Vector3D.PLUS_K);
516 checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.ZERO, Vector3D.PLUS_J, Vector3D.PLUS_J);
517 checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.PLUS_J, Vector3D.ZERO);
518 checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.ZERO, Vector3D.PLUS_J);
519 }
520
521 @Test
522 public void testRandomInverseCrossProducts() {
523 RandomGenerator generator = new Well1024a(0x52b29d8f6ac2d64bl);
524 for (int i = 0; i < 10000; ++i) {
525 Vector3D omega = randomVector(generator, 10 * generator.nextDouble() + 1.0);
526 Vector3D v1 = randomVector(generator, 10 * generator.nextDouble() + 1.0);
527 Vector3D v2 = randomVector(generator, 10 * generator.nextDouble() + 1.0);
528 checkInverse(omega, v1, v2);
529 }
530 }
531
532 private void checkInverse(Vector3D omega, Vector3D v1, Vector3D v2) {
533 checkInverse(omega,
534 v1, Vector3D.crossProduct(omega, v1),
535 v2, Vector3D.crossProduct(omega, v2));
536 }
537
538 private void checkInverseFailure(Vector3D omega, Vector3D v1, Vector3D c1, Vector3D v2, Vector3D c2) {
539 try {
540 checkInverse(omega, v1, c1, v2, c2);
541 Assertions.fail("an exception should have been thrown");
542 } catch (MathIllegalArgumentException miae) {
543
544 }
545 }
546
547 private void checkInverse(Vector3D omega, Vector3D v1, Vector3D c1, Vector3D v2, Vector3D c2)
548 throws MathIllegalArgumentException {
549 try {
550 Method inverse;
551 inverse = AngularCoordinates.class.getDeclaredMethod("inverseCrossProducts",
552 Vector3D.class, Vector3D.class,
553 Vector3D.class, Vector3D.class,
554 double.class);
555 inverse.setAccessible(true);
556 Vector3D rebuilt = (Vector3D) inverse.invoke(null, v1, c1, v2, c2, 1.0e-9);
557 Assertions.assertEquals(0.0, Vector3D.distance(omega, rebuilt), 5.0e-12 * omega.getNorm());
558 } catch (NoSuchMethodException e) {
559 Assertions.fail(e.getLocalizedMessage());
560 } catch (SecurityException e) {
561 Assertions.fail(e.getLocalizedMessage());
562 } catch (IllegalAccessException e) {
563 Assertions.fail(e.getLocalizedMessage());
564 } catch (IllegalArgumentException e) {
565 Assertions.fail(e.getLocalizedMessage());
566 } catch (InvocationTargetException e) {
567 throw (MathIllegalArgumentException) e.getCause();
568 }
569 }
570
571 @Test
572 public void testRandomPVCoordinates() {
573 RandomGenerator generator = new Well1024a(0x49eb5b92d1f94b89l);
574 for (int i = 0; i < 100; ++i) {
575 Rotation r = randomRotation(generator);
576 Vector3D omega = randomVector(generator, 10 * generator.nextDouble() + 1.0);
577 Vector3D omegaDot = randomVector(generator, 0.1 * generator.nextDouble() + 0.01);
578 AngularCoordinates ref = new AngularCoordinates(r, omega, omegaDot);
579 AngularCoordinates inv = ref.revert();
580 for (int j = 0; j < 100; ++j) {
581 PVCoordinates v1 = randomPVCoordinates(generator, 1000, 1.0, 0.001);
582 PVCoordinates v2 = randomPVCoordinates(generator, 1000, 1.0, 0.0010);
583 PVCoordinates u1 = inv.applyTo(v1);
584 PVCoordinates u2 = inv.applyTo(v2);
585 AngularCoordinates rebuilt = new AngularCoordinates(u1, u2, v1, v2, 1.0e-9);
586 Assertions.assertEquals(0.0,
587 Rotation.distance(r, rebuilt.getRotation()),
588 4.0e-14);
589 Assertions.assertEquals(0.0,
590 Vector3D.distance(omega, rebuilt.getRotationRate()),
591 3.0e-12 * omega.getNorm());
592 Assertions.assertEquals(0.0,
593 Vector3D.distance(omegaDot, rebuilt.getRotationAcceleration()),
594 2.0e-6 * omegaDot.getNorm());
595 }
596 }
597 }
598
599 @Test
600 public void testCancellingDerivatives() {
601 PVCoordinates u1 = new PVCoordinates(new Vector3D(-0.4466591282528639, -0.009657376949231283, -0.894652087807798),
602 new Vector3D(-8.897296517803556E-4, 2.7825250920407674E-4, 4.411979658413134E-4),
603 new Vector3D( 4.753127475302486E-7, 1.0209400376727623E-8, 9.515403756524403E-7));
604 PVCoordinates u2 = new PVCoordinates(new Vector3D( 0.23723907259910096, 0.9628700806685033, -0.1288364474275361),
605 new Vector3D(-7.98741002062555E-24, 2.4979687659429984E-24, 3.9607863426704016E-24),
606 new Vector3D(-3.150541868418562E-23, 9.856329862034835E-24, 1.5648124883326986E-23));
607 PVCoordinates v1 = new PVCoordinates(Vector3D.PLUS_K, Vector3D.ZERO, Vector3D.ZERO);
608 PVCoordinates v2 = new PVCoordinates(Vector3D.MINUS_J, Vector3D.ZERO, Vector3D.ZERO);
609 AngularCoordinates ac = new AngularCoordinates(u1, u2, v1, v2, 1.0e-9);
610 PVCoordinates v1Computed = ac.applyTo(u1);
611 PVCoordinates v2Computed = ac.applyTo(u2);
612 Assertions.assertEquals(0, Vector3D.distance(v1.getPosition(), v1Computed.getPosition()), 1.0e-15);
613 Assertions.assertEquals(0, Vector3D.distance(v2.getPosition(), v2Computed.getPosition()), 1.0e-15);
614 Assertions.assertEquals(0, Vector3D.distance(v1.getVelocity(), v1Computed.getVelocity()), 1.0e-15);
615 Assertions.assertEquals(0, Vector3D.distance(v2.getVelocity(), v2Computed.getVelocity()), 1.0e-15);
616 Assertions.assertEquals(0, Vector3D.distance(v1.getAcceleration(), v1Computed.getAcceleration()), 1.0e-15);
617 Assertions.assertEquals(0, Vector3D.distance(v2.getAcceleration(), v2Computed.getAcceleration()), 1.0e-15);
618 }
619
620 private Vector3D randomVector(RandomGenerator random, double norm) {
621 double n = random.nextDouble() * norm;
622 double x = random.nextDouble();
623 double y = random.nextDouble();
624 double z = random.nextDouble();
625 return new Vector3D(n, new Vector3D(x, y, z).normalize());
626 }
627
628 private PVCoordinates randomPVCoordinates(RandomGenerator random,
629 double norm0, double norm1, double norm2) {
630 Vector3D p0 = randomVector(random, norm0);
631 Vector3D p1 = randomVector(random, norm1);
632 Vector3D p2 = randomVector(random, norm2);
633 return new PVCoordinates(p0, p1, p2);
634 }
635
636 private Rotation randomRotation(RandomGenerator random) {
637 double q0 = random.nextDouble() * 2 - 1;
638 double q1 = random.nextDouble() * 2 - 1;
639 double q2 = random.nextDouble() * 2 - 1;
640 double q3 = random.nextDouble() * 2 - 1;
641 double q = FastMath.sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
642 return new Rotation(q0 / q, q1 / q, q2 / q, q3 / q, false);
643 }
644
645 }
646