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23 package org.hipparchus.geometry.euclidean.threed;
24
25 import org.hipparchus.analysis.differentiation.DSFactory;
26 import org.hipparchus.analysis.differentiation.DerivativeStructure;
27 import org.hipparchus.exception.MathIllegalArgumentException;
28 import org.hipparchus.exception.MathIllegalStateException;
29 import org.hipparchus.exception.MathRuntimeException;
30 import org.hipparchus.geometry.LocalizedGeometryFormats;
31 import org.hipparchus.linear.MatrixUtils;
32 import org.hipparchus.linear.RealMatrix;
33 import org.hipparchus.random.UnitSphereRandomVectorGenerator;
34 import org.hipparchus.random.Well1024a;
35 import org.hipparchus.util.FastMath;
36 import org.hipparchus.util.MathUtils;
37 import org.junit.jupiter.api.Assertions;
38 import org.junit.jupiter.api.Test;
39
40 import static org.junit.jupiter.api.Assertions.assertEquals;
41 import static org.junit.jupiter.api.Assertions.assertTrue;
42 import static org.junit.jupiter.api.Assertions.fail;
43
44
45 class FieldRotationDSTest {
46
47 @Test
48 void testIdentity() {
49
50 FieldRotation<DerivativeStructure> r = createRotation(1, 0, 0, 0, false);
51 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
52 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
53 checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
54 checkAngle(r.getAngle(), 0);
55
56 r = createRotation(-1, 0, 0, 0, false);
57 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
58 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
59 checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
60 checkAngle(r.getAngle(), 0);
61
62 r = createRotation(42, 0, 0, 0, true);
63 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
64 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
65 checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
66 checkAngle(r.getAngle(), 0);
67
68 }
69
70 @Test
71 void testAxisAngleVectorOperator() throws MathIllegalArgumentException {
72
73 FieldRotation<DerivativeStructure> r = new FieldRotation<>(createAxis(10, 10, 10),
74 createAngle(2 * FastMath.PI / 3) ,
75 RotationConvention.VECTOR_OPERATOR);
76 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 1, 0));
77 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 0, 1));
78 checkVector(r.applyTo(createVector(0, 0, 1)), createVector(1, 0, 0));
79 double s = 1 / FastMath.sqrt(3);
80 checkVector(r.getAxis(RotationConvention.VECTOR_OPERATOR), createVector( s, s, s));
81 checkVector(r.getAxis(RotationConvention.FRAME_TRANSFORM), createVector(-s, -s, -s));
82 checkAngle(r.getAngle(), 2 * FastMath.PI / 3);
83
84 try {
85 new FieldRotation<>(createAxis(0, 0, 0), createAngle(2 * FastMath.PI / 3), RotationConvention.VECTOR_OPERATOR);
86 fail("an exception should have been thrown");
87 } catch (MathIllegalArgumentException e) {
88 Assertions.assertEquals(LocalizedGeometryFormats.ZERO_NORM_FOR_ROTATION_AXIS, e.getSpecifier());
89 }
90
91 r = new FieldRotation<>(createAxis(0, 0, 1),
92 createAngle(1.5 * FastMath.PI),
93 RotationConvention.VECTOR_OPERATOR);
94 checkVector(r.getAxis(RotationConvention.VECTOR_OPERATOR), createVector(0, 0, -1));
95 checkVector(r.getAxis(RotationConvention.FRAME_TRANSFORM), createVector(0, 0, +1));
96 checkAngle(r.getAngle(), MathUtils.SEMI_PI);
97
98 r = new FieldRotation<>(createAxis(0, 1, 0),
99 createAngle(FastMath.PI),
100 RotationConvention.VECTOR_OPERATOR);
101 checkVector(r.getAxis(RotationConvention.VECTOR_OPERATOR), createVector(0, +1, 0));
102 checkVector(r.getAxis(RotationConvention.FRAME_TRANSFORM), createVector(0, -1, 0));
103 checkAngle(r.getAngle(), FastMath.PI);
104
105 checkVector(createRotation(1, 0, 0, 0, false).getAxis(RotationConvention.VECTOR_OPERATOR), createVector(+1, 0, 0));
106 checkVector(createRotation(1, 0, 0, 0, false).getAxis(RotationConvention.FRAME_TRANSFORM), createVector(-1, 0, 0));
107
108 }
109
110 @Test
111 void testAxisAngleFrameTransform() throws MathIllegalArgumentException {
112
113 FieldRotation<DerivativeStructure> r = new FieldRotation<>(createAxis(10, 10, 10),
114 createAngle(2 * FastMath.PI / 3) ,
115 RotationConvention.FRAME_TRANSFORM);
116 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
117 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(1, 0, 0));
118 checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 1, 0));
119 double s = 1 / FastMath.sqrt(3);
120 checkVector(r.getAxis(RotationConvention.FRAME_TRANSFORM), createVector( s, s, s));
121 checkVector(r.getAxis(RotationConvention.VECTOR_OPERATOR), createVector(-s, -s, -s));
122 checkAngle(r.getAngle(), 2 * FastMath.PI / 3);
123
124 try {
125 new FieldRotation<>(createAxis(0, 0, 0),
126 createAngle(2 * FastMath.PI / 3),
127 RotationConvention.FRAME_TRANSFORM);
128 fail("an exception should have been thrown");
129 } catch (MathIllegalArgumentException e) {
130 Assertions.assertEquals(LocalizedGeometryFormats.ZERO_NORM_FOR_ROTATION_AXIS, e.getSpecifier());
131 }
132
133 r = new FieldRotation<>(createAxis(0, 0, 1),
134 createAngle(1.5 * FastMath.PI),
135 RotationConvention.FRAME_TRANSFORM);
136 checkVector(r.getAxis(RotationConvention.FRAME_TRANSFORM), createVector(0, 0, -1));
137 checkVector(r.getAxis(RotationConvention.VECTOR_OPERATOR), createVector(0, 0, +1));
138 checkAngle(r.getAngle(), MathUtils.SEMI_PI);
139
140 r = new FieldRotation<>(createAxis(0, 1, 0),
141 createAngle(FastMath.PI),
142 RotationConvention.FRAME_TRANSFORM);
143 checkVector(r.getAxis(RotationConvention.FRAME_TRANSFORM), createVector(0, +1, 0));
144 checkVector(r.getAxis(RotationConvention.VECTOR_OPERATOR), createVector(0, -1, 0));
145 checkAngle(r.getAngle(), FastMath.PI);
146
147 checkVector(createRotation(1, 0, 0, 0, false).getAxis(RotationConvention.FRAME_TRANSFORM), createVector(-1, 0, 0));
148 checkVector(createRotation(1, 0, 0, 0, false).getAxis(RotationConvention.VECTOR_OPERATOR), createVector(+1, 0, 0));
149
150 }
151
152 @Test
153 void testRevert() {
154 double a = 0.001;
155 double b = 0.36;
156 double c = 0.48;
157 double d = 0.8;
158 FieldRotation<DerivativeStructure> r = createRotation(a, b, c, d, true);
159 double a2 = a * a;
160 double b2 = b * b;
161 double c2 = c * c;
162 double d2 = d * d;
163 double den = (a2 + b2 + c2 + d2) * FastMath.sqrt(a2 + b2 + c2 + d2);
164 assertEquals((b2 + c2 + d2) / den, r.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
165 assertEquals(-a * b / den, r.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
166 assertEquals(-a * c / den, r.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
167 assertEquals(-a * d / den, r.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
168 assertEquals(-b * a / den, r.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
169 assertEquals((a2 + c2 + d2) / den, r.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
170 assertEquals(-b * c / den, r.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
171 assertEquals(-b * d / den, r.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
172 assertEquals(-c * a / den, r.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
173 assertEquals(-c * b / den, r.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
174 assertEquals((a2 + b2 + d2) / den, r.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
175 assertEquals(-c * d / den, r.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
176 assertEquals(-d * a / den, r.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
177 assertEquals(-d * b / den, r.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
178 assertEquals(-d * c / den, r.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
179 assertEquals((a2 + b2 + c2) / den, r.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
180 FieldRotation<DerivativeStructure> reverted = r.revert();
181 FieldRotation<DerivativeStructure> rrT = r.applyTo(reverted);
182 checkRotationDS(rrT, 1, 0, 0, 0);
183 assertEquals(0, rrT.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
184 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
185 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
186 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
187 assertEquals(0, rrT.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
188 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
189 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
190 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
191 assertEquals(0, rrT.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
192 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
193 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
194 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
195 assertEquals(0, rrT.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
196 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
197 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
198 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
199 FieldRotation<DerivativeStructure> rTr = reverted.applyTo(r);
200 checkRotationDS(rTr, 1, 0, 0, 0);
201 assertEquals(0, rTr.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
202 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
203 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
204 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
205 assertEquals(0, rTr.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
206 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
207 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
208 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
209 assertEquals(0, rTr.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
210 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
211 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
212 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
213 assertEquals(0, rTr.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
214 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
215 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
216 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
217 assertEquals(r.getAngle().getReal(), reverted.getAngle().getReal(), 1.0e-15);
218 assertEquals(-1,
219 FieldVector3D.dotProduct(r.getAxis(RotationConvention.VECTOR_OPERATOR),
220 reverted.getAxis(RotationConvention.VECTOR_OPERATOR)).getReal(),
221 1.0e-15);
222 }
223
224 @Test
225 void testRevertVectorOperator() {
226 double a = 0.001;
227 double b = 0.36;
228 double c = 0.48;
229 double d = 0.8;
230 FieldRotation<DerivativeStructure> r = createRotation(a, b, c, d, true);
231 double a2 = a * a;
232 double b2 = b * b;
233 double c2 = c * c;
234 double d2 = d * d;
235 double den = (a2 + b2 + c2 + d2) * FastMath.sqrt(a2 + b2 + c2 + d2);
236 assertEquals((b2 + c2 + d2) / den, r.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
237 assertEquals(-a * b / den, r.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
238 assertEquals(-a * c / den, r.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
239 assertEquals(-a * d / den, r.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
240 assertEquals(-b * a / den, r.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
241 assertEquals((a2 + c2 + d2) / den, r.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
242 assertEquals(-b * c / den, r.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
243 assertEquals(-b * d / den, r.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
244 assertEquals(-c * a / den, r.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
245 assertEquals(-c * b / den, r.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
246 assertEquals((a2 + b2 + d2) / den, r.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
247 assertEquals(-c * d / den, r.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
248 assertEquals(-d * a / den, r.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
249 assertEquals(-d * b / den, r.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
250 assertEquals(-d * c / den, r.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
251 assertEquals((a2 + b2 + c2) / den, r.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
252 FieldRotation<DerivativeStructure> reverted = r.revert();
253 FieldRotation<DerivativeStructure> rrT = r.compose(reverted, RotationConvention.VECTOR_OPERATOR);
254 checkRotationDS(rrT, 1, 0, 0, 0);
255 assertEquals(0, rrT.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
256 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
257 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
258 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
259 assertEquals(0, rrT.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
260 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
261 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
262 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
263 assertEquals(0, rrT.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
264 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
265 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
266 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
267 assertEquals(0, rrT.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
268 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
269 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
270 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
271 FieldRotation<DerivativeStructure> rTr = reverted.compose(r, RotationConvention.VECTOR_OPERATOR);
272 checkRotationDS(rTr, 1, 0, 0, 0);
273 assertEquals(0, rTr.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
274 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
275 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
276 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
277 assertEquals(0, rTr.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
278 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
279 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
280 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
281 assertEquals(0, rTr.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
282 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
283 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
284 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
285 assertEquals(0, rTr.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
286 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
287 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
288 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
289 assertEquals(r.getAngle().getReal(), reverted.getAngle().getReal(), 1.0e-15);
290 assertEquals(-1,
291 FieldVector3D.dotProduct(r.getAxis(RotationConvention.VECTOR_OPERATOR),
292 reverted.getAxis(RotationConvention.VECTOR_OPERATOR)).getReal(),
293 1.0e-15);
294 }
295
296 @Test
297 void testRevertFrameTransform() {
298 double a = 0.001;
299 double b = 0.36;
300 double c = 0.48;
301 double d = 0.8;
302 FieldRotation<DerivativeStructure> r = createRotation(a, b, c, d, true);
303 double a2 = a * a;
304 double b2 = b * b;
305 double c2 = c * c;
306 double d2 = d * d;
307 double den = (a2 + b2 + c2 + d2) * FastMath.sqrt(a2 + b2 + c2 + d2);
308 assertEquals((b2 + c2 + d2) / den, r.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
309 assertEquals(-a * b / den, r.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
310 assertEquals(-a * c / den, r.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
311 assertEquals(-a * d / den, r.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
312 assertEquals(-b * a / den, r.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
313 assertEquals((a2 + c2 + d2) / den, r.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
314 assertEquals(-b * c / den, r.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
315 assertEquals(-b * d / den, r.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
316 assertEquals(-c * a / den, r.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
317 assertEquals(-c * b / den, r.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
318 assertEquals((a2 + b2 + d2) / den, r.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
319 assertEquals(-c * d / den, r.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
320 assertEquals(-d * a / den, r.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
321 assertEquals(-d * b / den, r.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
322 assertEquals(-d * c / den, r.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
323 assertEquals((a2 + b2 + c2) / den, r.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
324 FieldRotation<DerivativeStructure> reverted = r.revert();
325 FieldRotation<DerivativeStructure> rrT = r.compose(reverted, RotationConvention.FRAME_TRANSFORM);
326 checkRotationDS(rrT, 1, 0, 0, 0);
327 assertEquals(0, rrT.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
328 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
329 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
330 assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
331 assertEquals(0, rrT.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
332 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
333 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
334 assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
335 assertEquals(0, rrT.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
336 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
337 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
338 assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
339 assertEquals(0, rrT.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
340 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
341 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
342 assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
343 FieldRotation<DerivativeStructure> rTr = reverted.compose(r, RotationConvention.FRAME_TRANSFORM);
344 checkRotationDS(rTr, 1, 0, 0, 0);
345 assertEquals(0, rTr.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
346 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
347 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
348 assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
349 assertEquals(0, rTr.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
350 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
351 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
352 assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
353 assertEquals(0, rTr.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
354 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
355 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
356 assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
357 assertEquals(0, rTr.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
358 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
359 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
360 assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
361 assertEquals(r.getAngle().getReal(), reverted.getAngle().getReal(), 1.0e-15);
362 assertEquals(-1,
363 FieldVector3D.dotProduct(r.getAxis(RotationConvention.FRAME_TRANSFORM),
364 reverted.getAxis(RotationConvention.FRAME_TRANSFORM)).getReal(),
365 1.0e-15);
366 }
367
368 @Test
369 void testVectorOnePair() throws MathRuntimeException {
370
371 FieldVector3D<DerivativeStructure> u = createVector(3, 2, 1);
372 FieldVector3D<DerivativeStructure> v = createVector(-4, 2, 2);
373 FieldRotation<DerivativeStructure> r = new FieldRotation<>(u, v);
374 checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));
375
376 checkAngle(new FieldRotation<>(u, u.negate()).getAngle(), FastMath.PI);
377
378 try {
379 new FieldRotation<>(u, createVector(0, 0, 0));
380 fail("an exception should have been thrown");
381 } catch (MathRuntimeException e) {
382
383 }
384
385 }
386
387 @Test
388 void testVectorTwoPairs() throws MathRuntimeException {
389
390 FieldVector3D<DerivativeStructure> u1 = createVector(3, 0, 0);
391 FieldVector3D<DerivativeStructure> u2 = createVector(0, 5, 0);
392 FieldVector3D<DerivativeStructure> v1 = createVector(0, 0, 2);
393 FieldVector3D<DerivativeStructure> v2 = createVector(-2, 0, 2);
394 FieldRotation<DerivativeStructure> r = new FieldRotation<>(u1, u2, v1, v2);
395 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
396 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(-1, 0, 0));
397
398 r = new FieldRotation<>(u1, u2, u1.negate(), u2.negate());
399 FieldVector3D<DerivativeStructure> axis = r.getAxis(RotationConvention.VECTOR_OPERATOR);
400 if (FieldVector3D.dotProduct(axis, createVector(0, 0, 1)).getReal() > 0) {
401 checkVector(axis, createVector(0, 0, 1));
402 } else {
403 checkVector(axis, createVector(0, 0, -1));
404 }
405 checkAngle(r.getAngle(), FastMath.PI);
406
407 double sqrt = FastMath.sqrt(2) / 2;
408 r = new FieldRotation<>(createVector(1, 0, 0), createVector(0, 1, 0),
409 createVector(0.5, 0.5, sqrt),
410 createVector(0.5, 0.5, -sqrt));
411 checkRotationDS(r, sqrt, 0.5, 0.5, 0);
412
413 r = new FieldRotation<>(u1, u2, u1, FieldVector3D.crossProduct(u1, u2));
414 checkRotationDS(r, sqrt, -sqrt, 0, 0);
415
416 checkRotationDS(new FieldRotation<>(u1, u2, u1, u2), 1, 0, 0, 0);
417
418 try {
419 new FieldRotation<>(u1, u2, createVector(0, 0, 0), v2);
420 fail("an exception should have been thrown");
421 } catch (MathRuntimeException e) {
422
423 }
424
425 }
426
427 @Test
428 void testMatrix()
429 throws MathIllegalArgumentException {
430
431 try {
432 createRotation(new double[][] {
433 { 0.0, 1.0, 0.0 },
434 { 1.0, 0.0, 0.0 }
435 }, 1.0e-7);
436 fail("Expecting MathIllegalArgumentException");
437 } catch (MathIllegalArgumentException nrme) {
438
439 }
440
441 try {
442 createRotation(new double[][] {
443 { 0.445888, 0.797184, -0.407040 },
444 { 0.821760, -0.184320, 0.539200 },
445 { -0.354816, 0.574912, 0.737280 }
446 }, 1.0e-7);
447 fail("Expecting MathIllegalArgumentException");
448 } catch (MathIllegalArgumentException nrme) {
449
450 }
451
452 try {
453 createRotation(new double[][] {
454 { 0.4, 0.8, -0.4 },
455 { -0.4, 0.6, 0.7 },
456 { 0.8, -0.2, 0.5 }
457 }, 1.0e-15);
458 fail("Expecting MathIllegalArgumentException");
459 } catch (MathIllegalArgumentException nrme) {
460
461 }
462
463 checkRotationDS(createRotation(new double[][] {
464 { 0.445888, 0.797184, -0.407040 },
465 { -0.354816, 0.574912, 0.737280 },
466 { 0.821760, -0.184320, 0.539200 }
467 }, 1.0e-10),
468 0.8, 0.288, 0.384, 0.36);
469
470 checkRotationDS(createRotation(new double[][] {
471 { 0.539200, 0.737280, 0.407040 },
472 { 0.184320, -0.574912, 0.797184 },
473 { 0.821760, -0.354816, -0.445888 }
474 }, 1.0e-10),
475 0.36, 0.8, 0.288, 0.384);
476
477 checkRotationDS(createRotation(new double[][] {
478 { -0.445888, 0.797184, -0.407040 },
479 { 0.354816, 0.574912, 0.737280 },
480 { 0.821760, 0.184320, -0.539200 }
481 }, 1.0e-10),
482 0.384, 0.36, 0.8, 0.288);
483
484 checkRotationDS(createRotation(new double[][] {
485 { -0.539200, 0.737280, 0.407040 },
486 { -0.184320, -0.574912, 0.797184 },
487 { 0.821760, 0.354816, 0.445888 }
488 }, 1.0e-10),
489 0.288, 0.384, 0.36, 0.8);
490
491 double[][] m1 = { { 0.0, 1.0, 0.0 },
492 { 0.0, 0.0, 1.0 },
493 { 1.0, 0.0, 0.0 } };
494 FieldRotation<DerivativeStructure> r = createRotation(m1, 1.0e-7);
495 checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
496 checkVector(r.applyTo(createVector(0, 1, 0)), createVector(1, 0, 0));
497 checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 1, 0));
498
499 double[][] m2 = { { 0.83203, -0.55012, -0.07139 },
500 { 0.48293, 0.78164, -0.39474 },
501 { 0.27296, 0.29396, 0.91602 } };
502 r = createRotation(m2, 1.0e-12);
503
504 DerivativeStructure[][] m3 = r.getMatrix();
505 double d00 = m2[0][0] - m3[0][0].getReal();
506 double d01 = m2[0][1] - m3[0][1].getReal();
507 double d02 = m2[0][2] - m3[0][2].getReal();
508 double d10 = m2[1][0] - m3[1][0].getReal();
509 double d11 = m2[1][1] - m3[1][1].getReal();
510 double d12 = m2[1][2] - m3[1][2].getReal();
511 double d20 = m2[2][0] - m3[2][0].getReal();
512 double d21 = m2[2][1] - m3[2][1].getReal();
513 double d22 = m2[2][2] - m3[2][2].getReal();
514
515 assertTrue(FastMath.abs(d00) < 6.0e-6);
516 assertTrue(FastMath.abs(d01) < 6.0e-6);
517 assertTrue(FastMath.abs(d02) < 6.0e-6);
518 assertTrue(FastMath.abs(d10) < 6.0e-6);
519 assertTrue(FastMath.abs(d11) < 6.0e-6);
520 assertTrue(FastMath.abs(d12) < 6.0e-6);
521 assertTrue(FastMath.abs(d20) < 6.0e-6);
522 assertTrue(FastMath.abs(d21) < 6.0e-6);
523 assertTrue(FastMath.abs(d22) < 6.0e-6);
524
525 assertTrue(FastMath.abs(d00) > 4.0e-7);
526 assertTrue(FastMath.abs(d01) > 4.0e-7);
527 assertTrue(FastMath.abs(d02) > 4.0e-7);
528 assertTrue(FastMath.abs(d10) > 4.0e-7);
529 assertTrue(FastMath.abs(d11) > 4.0e-7);
530 assertTrue(FastMath.abs(d12) > 4.0e-7);
531 assertTrue(FastMath.abs(d20) > 4.0e-7);
532 assertTrue(FastMath.abs(d21) > 4.0e-7);
533 assertTrue(FastMath.abs(d22) > 4.0e-7);
534
535 for (int i = 0; i < 3; ++i) {
536 for (int j = 0; j < 3; ++j) {
537 double m3tm3 = m3[i][0].getReal() * m3[j][0].getReal() +
538 m3[i][1].getReal() * m3[j][1].getReal() +
539 m3[i][2].getReal() * m3[j][2].getReal();
540 if (i == j) {
541 assertTrue(FastMath.abs(m3tm3 - 1.0) < 1.0e-10);
542 } else {
543 assertTrue(FastMath.abs(m3tm3) < 1.0e-10);
544 }
545 }
546 }
547
548 checkVector(r.applyTo(createVector(1, 0, 0)), new FieldVector3D<>(m3[0][0], m3[1][0], m3[2][0]));
549 checkVector(r.applyTo(createVector(0, 1, 0)), new FieldVector3D<>(m3[0][1], m3[1][1], m3[2][1]));
550 checkVector(r.applyTo(createVector(0, 0, 1)), new FieldVector3D<>(m3[0][2], m3[1][2], m3[2][2]));
551
552 double[][] m4 = { { 1.0, 0.0, 0.0 },
553 { 0.0, -1.0, 0.0 },
554 { 0.0, 0.0, -1.0 } };
555 r = createRotation(m4, 1.0e-7);
556 checkAngle(r.getAngle(), FastMath.PI);
557
558 try {
559 double[][] m5 = { { 0.0, 0.0, 1.0 },
560 { 0.0, 1.0, 0.0 },
561 { 1.0, 0.0, 0.0 } };
562 r = createRotation(m5, 1.0e-7);
563 fail("got " + r + ", should have caught an exception");
564 } catch (MathIllegalArgumentException e) {
565
566 }
567
568 }
569
570 @Test
571 void testAngles()
572 throws MathIllegalStateException {
573
574 DSFactory factory = new DSFactory(3, 1);
575 for (RotationConvention convention : RotationConvention.values()) {
576 RotationOrder[] CardanOrders = {
577 RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,
578 RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX
579 };
580
581 for (final RotationOrder cardanOrder : CardanOrders) {
582 for (double alpha1 = 0.1; alpha1 < 6.2; alpha1 += 0.3) {
583 for (double alpha2 = -1.55; alpha2 < 1.55; alpha2 += 0.3) {
584 for (double alpha3 = 0.1; alpha3 < 6.2; alpha3 += 0.3) {
585 FieldRotation<DerivativeStructure> r =
586 new FieldRotation<>(cardanOrder,
587 convention,
588 factory.variable(0, alpha1),
589 factory.variable(1, alpha2),
590 factory.variable(2, alpha3));
591 DerivativeStructure[] angles = r.getAngles(cardanOrder, convention);
592 checkAngle(angles[0], alpha1);
593 checkAngle(angles[1], alpha2);
594 checkAngle(angles[2], alpha3);
595 }
596 }
597 }
598 }
599
600 RotationOrder[] EulerOrders = {
601 RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,
602 RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ
603 };
604
605 for (final RotationOrder eulerOrder : EulerOrders) {
606 for (double alpha1 = 0.1; alpha1 < 6.2; alpha1 += 0.3) {
607 for (double alpha2 = 0.05; alpha2 < 3.1; alpha2 += 0.3) {
608 for (double alpha3 = 0.1; alpha3 < 6.2; alpha3 += 0.3) {
609 FieldRotation<DerivativeStructure> r =
610 new FieldRotation<>(eulerOrder,
611 convention,
612 factory.variable(0, alpha1),
613 factory.variable(1, alpha2),
614 factory.variable(2, alpha3));
615 DerivativeStructure[] angles = r.getAngles(eulerOrder, convention);
616 checkAngle(angles[0], alpha1);
617 checkAngle(angles[1], alpha2);
618 checkAngle(angles[2], alpha3);
619 }
620 }
621 }
622 }
623 }
624
625 }
626
627 @Test
628 void testSingularities() {
629
630 DSFactory factory = new DSFactory(3, 1);
631 for (RotationConvention convention : RotationConvention.values()) {
632 RotationOrder[] CardanOrders = {
633 RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,
634 RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX
635 };
636
637 double[] singularCardanAngle = {
638 -FastMath.PI / 2, -FastMath.PI / 2 + 1.0e-12, -FastMath.PI / 2 + 1.0e-10,
639 FastMath.PI / 2 - 1.0e-10, FastMath.PI / 2 - 1.0e-12, FastMath.PI / 2
640 };
641 for (final RotationOrder cardanOrder : CardanOrders) {
642 for (final double v : singularCardanAngle) {
643 FieldRotation<DerivativeStructure> r = new FieldRotation<>(cardanOrder,
644 convention,
645 factory.variable(0, 0.1),
646 factory.variable(1, v),
647 factory.variable(2, 0.3));
648 assertEquals(v, r.getAngles(cardanOrder, convention)[1].getReal(), 4.5e-16);
649 }
650 }
651
652 RotationOrder[] EulerOrders = {
653 RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,
654 RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ
655 };
656
657 double[] singularEulerAngle = { 0, 1.0e-12, 1.0e-10, FastMath.PI - 1.0e-10, FastMath.PI - 1.0e-12, FastMath.PI };
658 for (final RotationOrder eulerOrder : EulerOrders) {
659 for (final double v : singularEulerAngle) {
660 FieldRotation<DerivativeStructure> r = new FieldRotation<>(eulerOrder,
661 convention,
662 factory.variable(0, 0.1),
663 factory.variable(1, v),
664 factory.variable(2, 0.3));
665 r.getAngles(eulerOrder, convention);
666 assertEquals(v, r.getAngles(eulerOrder, convention)[1].getReal(), 1.0e-24);
667 }
668 }
669
670 }
671 }
672
673 @Test
674 void testQuaternion() throws MathIllegalArgumentException {
675
676 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
677 createAngle(1.7),
678 RotationConvention.VECTOR_OPERATOR);
679 double n = 23.5;
680 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(r1.getQ0().multiply(n), r1.getQ1().multiply(n),
681 r1.getQ2().multiply(n), r1.getQ3().multiply(n),
682 true);
683 for (double x = -0.9; x < 0.9; x += 0.2) {
684 for (double y = -0.9; y < 0.9; y += 0.2) {
685 for (double z = -0.9; z < 0.9; z += 0.2) {
686 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
687 checkVector(r2.applyTo(u), r1.applyTo(u));
688 }
689 }
690 }
691
692 r1 = createRotation(0.288, 0.384, 0.36, 0.8, false);
693 checkRotationDS(r1,
694 -r1.getQ0().getReal(), -r1.getQ1().getReal(),
695 -r1.getQ2().getReal(), -r1.getQ3().getReal());
696 assertEquals(0.288, r1.toRotation().getQ0(), 1.0e-15);
697 assertEquals(0.384, r1.toRotation().getQ1(), 1.0e-15);
698 assertEquals(0.36, r1.toRotation().getQ2(), 1.0e-15);
699 assertEquals(0.8, r1.toRotation().getQ3(), 1.0e-15);
700
701 }
702
703 @Test
704 void testApplyToRotation() throws MathIllegalArgumentException {
705
706 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
707 createAngle(1.7),
708 RotationConvention.VECTOR_OPERATOR);
709 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(-1, 3, 2),
710 createAngle(0.3),
711 RotationConvention.VECTOR_OPERATOR);
712 FieldRotation<DerivativeStructure> r3 = r2.applyTo(r1);
713 FieldRotation<DerivativeStructure> r3Double = r2.applyTo(new Rotation(r1.getQ0().getReal(),
714 r1.getQ1().getReal(),
715 r1.getQ2().getReal(),
716 r1.getQ3().getReal(),
717 false));
718
719 for (double x = -0.9; x < 0.9; x += 0.2) {
720 for (double y = -0.9; y < 0.9; y += 0.2) {
721 for (double z = -0.9; z < 0.9; z += 0.2) {
722 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
723 checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));
724 checkVector(r2.applyTo(r1.applyTo(u)), r3Double.applyTo(u));
725 }
726 }
727 }
728
729 }
730
731 @Test
732 void testComposeVectorOperator() throws MathIllegalArgumentException {
733
734 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
735 createAngle(1.7),
736 RotationConvention.VECTOR_OPERATOR);
737 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(-1, 3, 2),
738 createAngle(0.3),
739 RotationConvention.VECTOR_OPERATOR);
740 FieldRotation<DerivativeStructure> r3 = r2.compose(r1, RotationConvention.VECTOR_OPERATOR);
741 FieldRotation<DerivativeStructure> r3Double = r2.compose(new Rotation(r1.getQ0().getReal(),
742 r1.getQ1().getReal(),
743 r1.getQ2().getReal(),
744 r1.getQ3().getReal(),
745 false),
746 RotationConvention.VECTOR_OPERATOR);
747
748 for (double x = -0.9; x < 0.9; x += 0.2) {
749 for (double y = -0.9; y < 0.9; y += 0.2) {
750 for (double z = -0.9; z < 0.9; z += 0.2) {
751 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
752 checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));
753 checkVector(r2.applyTo(r1.applyTo(u)), r3Double.applyTo(u));
754 }
755 }
756 }
757
758 }
759
760 @Test
761 void testComposeFrameTransform() throws MathIllegalArgumentException {
762
763 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
764 createAngle(1.7),
765 RotationConvention.FRAME_TRANSFORM);
766 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(-1, 3, 2),
767 createAngle(0.3),
768 RotationConvention.FRAME_TRANSFORM);
769 FieldRotation<DerivativeStructure> r3 = r2.compose(r1, RotationConvention.FRAME_TRANSFORM);
770 FieldRotation<DerivativeStructure> r3Double = r2.compose(new Rotation(r1.getQ0().getReal(),
771 r1.getQ1().getReal(),
772 r1.getQ2().getReal(),
773 r1.getQ3().getReal(),
774 false),
775 RotationConvention.FRAME_TRANSFORM);
776
777 for (double x = -0.9; x < 0.9; x += 0.2) {
778 for (double y = -0.9; y < 0.9; y += 0.2) {
779 for (double z = -0.9; z < 0.9; z += 0.2) {
780 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
781 checkVector(r1.applyTo(r2.applyTo(u)), r3.applyTo(u));
782 checkVector(r1.applyTo(r2.applyTo(u)), r3Double.applyTo(u));
783 }
784 }
785 }
786
787 }
788
789 @Test
790 void testApplyInverseToRotation() throws MathIllegalArgumentException {
791
792 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
793 createAngle(1.7),
794 RotationConvention.VECTOR_OPERATOR);
795 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(-1, 3, 2),
796 createAngle(0.3),
797 RotationConvention.VECTOR_OPERATOR);
798 FieldRotation<DerivativeStructure> r3 = r2.applyInverseTo(r1);
799 FieldRotation<DerivativeStructure> r3Double = r2.applyInverseTo(new Rotation(r1.getQ0().getReal(),
800 r1.getQ1().getReal(),
801 r1.getQ2().getReal(),
802 r1.getQ3().getReal(),
803 false));
804
805 for (double x = -0.9; x < 0.9; x += 0.2) {
806 for (double y = -0.9; y < 0.9; y += 0.2) {
807 for (double z = -0.9; z < 0.9; z += 0.2) {
808 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
809 checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));
810 checkVector(r2.applyInverseTo(r1.applyTo(u)), r3Double.applyTo(u));
811 }
812 }
813 }
814
815 }
816
817 @Test
818 void testComposeInverseVectorOperator() throws MathIllegalArgumentException {
819
820 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
821 createAngle(1.7),
822 RotationConvention.VECTOR_OPERATOR);
823 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(-1, 3, 2),
824 createAngle(0.3),
825 RotationConvention.VECTOR_OPERATOR);
826 FieldRotation<DerivativeStructure> r3 = r2.composeInverse(r1, RotationConvention.VECTOR_OPERATOR);
827 FieldRotation<DerivativeStructure> r3Double = r2.composeInverse(new Rotation(r1.getQ0().getReal(),
828 r1.getQ1().getReal(),
829 r1.getQ2().getReal(),
830 r1.getQ3().getReal(),
831 false),
832 RotationConvention.VECTOR_OPERATOR);
833
834 for (double x = -0.9; x < 0.9; x += 0.2) {
835 for (double y = -0.9; y < 0.9; y += 0.2) {
836 for (double z = -0.9; z < 0.9; z += 0.2) {
837 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
838 checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));
839 checkVector(r2.applyInverseTo(r1.applyTo(u)), r3Double.applyTo(u));
840 }
841 }
842 }
843
844 }
845
846 @Test
847 void testComposeInverseframeTransform() throws MathIllegalArgumentException {
848
849 FieldRotation<DerivativeStructure> r1 = new FieldRotation<>(createVector(2, -3, 5),
850 createAngle(1.7),
851 RotationConvention.FRAME_TRANSFORM);
852 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(-1, 3, 2),
853 createAngle(0.3),
854 RotationConvention.FRAME_TRANSFORM);
855 FieldRotation<DerivativeStructure> r3 = r2.composeInverse(r1, RotationConvention.FRAME_TRANSFORM);
856 FieldRotation<DerivativeStructure> r3Double = r2.composeInverse(new Rotation(r1.getQ0().getReal(),
857 r1.getQ1().getReal(),
858 r1.getQ2().getReal(),
859 r1.getQ3().getReal(),
860 false),
861 RotationConvention.FRAME_TRANSFORM);
862
863 for (double x = -0.9; x < 0.9; x += 0.2) {
864 for (double y = -0.9; y < 0.9; y += 0.2) {
865 for (double z = -0.9; z < 0.9; z += 0.2) {
866 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
867 checkVector(r1.applyTo(r2.applyInverseTo(u)), r3.applyTo(u));
868 checkVector(r1.applyTo(r2.applyInverseTo(u)), r3Double.applyTo(u));
869 }
870 }
871 }
872
873 }
874
875 @Test
876 void testDoubleVectors() throws MathIllegalArgumentException {
877
878 Well1024a random = new Well1024a(0x180b41cfeeffaf67L);
879 UnitSphereRandomVectorGenerator g = new UnitSphereRandomVectorGenerator(3, random);
880 for (int i = 0; i < 10; ++i) {
881 double[] unit = g.nextVector();
882 FieldRotation<DerivativeStructure> r = new FieldRotation<>(createVector(unit[0], unit[1], unit[2]),
883 createAngle(random.nextDouble()),
884 RotationConvention.VECTOR_OPERATOR);
885
886 for (double x = -0.9; x < 0.9; x += 0.2) {
887 for (double y = -0.9; y < 0.9; y += 0.2) {
888 for (double z = -0.9; z < 0.9; z += 0.2) {
889 FieldVector3D<DerivativeStructure> uds = createVector(x, y, z);
890 FieldVector3D<DerivativeStructure> ruds = r.applyTo(uds);
891 FieldVector3D<DerivativeStructure> rIuds = r.applyInverseTo(uds);
892 Vector3D u = new Vector3D(x, y, z);
893 FieldVector3D<DerivativeStructure> ru = r.applyTo(u);
894 FieldVector3D<DerivativeStructure> rIu = r.applyInverseTo(u);
895 DerivativeStructure[] ruArray = new DerivativeStructure[3];
896 r.applyTo(new double[] { x, y, z}, ruArray);
897 DerivativeStructure[] rIuArray = new DerivativeStructure[3];
898 r.applyInverseTo(new double[] { x, y, z}, rIuArray);
899 checkVector(ruds, ru);
900 checkVector(ruds, new FieldVector3D<>(ruArray));
901 checkVector(rIuds, rIu);
902 checkVector(rIuds, new FieldVector3D<>(rIuArray));
903 }
904 }
905 }
906 }
907
908 }
909
910 @Test
911 void testDoubleRotations() throws MathIllegalArgumentException {
912
913 Well1024a random = new Well1024a(0x180b41cfeeffaf67L);
914 UnitSphereRandomVectorGenerator g = new UnitSphereRandomVectorGenerator(3, random);
915 DSFactory factory = new DSFactory(4, 1);
916 for (int i = 0; i < 10; ++i) {
917 double[] unit1 = g.nextVector();
918 Rotation r1 = new Rotation(new Vector3D(unit1[0], unit1[1], unit1[2]),
919 random.nextDouble(), RotationConvention.VECTOR_OPERATOR);
920 FieldRotation<DerivativeStructure> r1Prime = new FieldRotation<>(factory.variable(0, r1.getQ0()),
921 factory.variable(1, r1.getQ1()),
922 factory.variable(2, r1.getQ2()),
923 factory.variable(3, r1.getQ3()),
924 false);
925 double[] unit2 = g.nextVector();
926 FieldRotation<DerivativeStructure> r2 = new FieldRotation<>(createVector(unit2[0], unit2[1], unit2[2]),
927 createAngle(random.nextDouble()),
928 RotationConvention.VECTOR_OPERATOR);
929
930 FieldRotation<DerivativeStructure> rA = FieldRotation.applyTo(r1, r2);
931 FieldRotation<DerivativeStructure> rB = r1Prime.compose(r2, RotationConvention.VECTOR_OPERATOR);
932 FieldRotation<DerivativeStructure> rC = FieldRotation.applyInverseTo(r1, r2);
933 FieldRotation<DerivativeStructure> rD = r1Prime.composeInverse(r2, RotationConvention.VECTOR_OPERATOR);
934
935 for (double x = -0.9; x < 0.9; x += 0.2) {
936 for (double y = -0.9; y < 0.9; y += 0.2) {
937 for (double z = -0.9; z < 0.9; z += 0.2) {
938
939 FieldVector3D<DerivativeStructure> uds = createVector(x, y, z);
940 checkVector(r1Prime.applyTo(uds), FieldRotation.applyTo(r1, uds));
941 checkVector(r1Prime.applyInverseTo(uds), FieldRotation.applyInverseTo(r1, uds));
942 checkVector(rA.applyTo(uds), rB.applyTo(uds));
943 checkVector(rA.applyInverseTo(uds), rB.applyInverseTo(uds));
944 checkVector(rC.applyTo(uds), rD.applyTo(uds));
945 checkVector(rC.applyInverseTo(uds), rD.applyInverseTo(uds));
946
947 }
948 }
949 }
950 }
951
952 }
953
954 @Test
955 void testDerivatives() {
956
957 double eps = 7.e-16;
958 double kx = 2;
959 double ky = -3;
960 double kz = 5;
961 double n2 = kx * kx + ky * ky + kz * kz;
962 double n = FastMath.sqrt(n2);
963 double theta = 1.7;
964 double cosTheta = FastMath.cos(theta);
965 double sinTheta = FastMath.sin(theta);
966 FieldRotation<DerivativeStructure> r = new FieldRotation<>(createAxis(kx, ky, kz),
967 createAngle(theta),
968 RotationConvention.VECTOR_OPERATOR);
969 Vector3D a = new Vector3D(kx / n, ky / n, kz / n);
970
971
972 RealMatrix dadk = MatrixUtils.createRealMatrix(new double[][] {
973 { (ky * ky + kz * kz) / ( n * n2), -kx * ky / ( n * n2), -kx * kz / ( n * n2) },
974 { -kx * ky / ( n * n2), (kx * kx + kz * kz) / ( n * n2), -ky * kz / ( n * n2) },
975 { -kx * kz / ( n * n2), -ky * kz / ( n * n2), (kx * kx + ky * ky) / ( n * n2) }
976 });
977
978 for (double x = -0.9; x < 0.9; x += 0.2) {
979 for (double y = -0.9; y < 0.9; y += 0.2) {
980 for (double z = -0.9; z < 0.9; z += 0.2) {
981 Vector3D u = new Vector3D(x, y, z);
982 FieldVector3D<DerivativeStructure> v = r.applyTo(createVector(x, y, z));
983
984
985 double dot = Vector3D.dotProduct(u, a);
986 Vector3D cross = Vector3D.crossProduct(a, u);
987 double c1 = 1 - cosTheta;
988 double c2 = c1 * dot;
989 Vector3D rt = new Vector3D(cosTheta, u, c2, a, sinTheta, cross);
990 assertEquals(rt.getX(), v.getX().getReal(), eps);
991 assertEquals(rt.getY(), v.getY().getReal(), eps);
992 assertEquals(rt.getZ(), v.getZ().getReal(), eps);
993
994
995
996 RealMatrix dvda = MatrixUtils.createRealMatrix(new double[][] {
997 { c1 * x * a.getX() + c2, c1 * y * a.getX() + sinTheta * z, c1 * z * a.getX() - sinTheta * y },
998 { c1 * x * a.getY() - sinTheta * z, c1 * y * a.getY() + c2, c1 * z * a.getY() + sinTheta * x },
999 { c1 * x * a.getZ() + sinTheta * y, c1 * y * a.getZ() - sinTheta * x, c1 * z * a.getZ() + c2 }
1000 });
1001
1002
1003 RealMatrix dvdk = dvda.multiply(dadk);
1004
1005
1006 assertEquals(dvdk.getEntry(0, 0), v.getX().getPartialDerivative(1, 0, 0, 0), eps);
1007 assertEquals(dvdk.getEntry(0, 1), v.getX().getPartialDerivative(0, 1, 0, 0), eps);
1008 assertEquals(dvdk.getEntry(0, 2), v.getX().getPartialDerivative(0, 0, 1, 0), eps);
1009 assertEquals(dvdk.getEntry(1, 0), v.getY().getPartialDerivative(1, 0, 0, 0), eps);
1010 assertEquals(dvdk.getEntry(1, 1), v.getY().getPartialDerivative(0, 1, 0, 0), eps);
1011 assertEquals(dvdk.getEntry(1, 2), v.getY().getPartialDerivative(0, 0, 1, 0), eps);
1012 assertEquals(dvdk.getEntry(2, 0), v.getZ().getPartialDerivative(1, 0, 0, 0), eps);
1013 assertEquals(dvdk.getEntry(2, 1), v.getZ().getPartialDerivative(0, 1, 0, 0), eps);
1014 assertEquals(dvdk.getEntry(2, 2), v.getZ().getPartialDerivative(0, 0, 1, 0), eps);
1015
1016
1017
1018 Vector3D dvdTheta =
1019 new Vector3D(-sinTheta, u, sinTheta * dot, a, cosTheta, cross);
1020 assertEquals(dvdTheta.getX(), v.getX().getPartialDerivative(0, 0, 0, 1), eps);
1021 assertEquals(dvdTheta.getY(), v.getY().getPartialDerivative(0, 0, 0, 1), eps);
1022 assertEquals(dvdTheta.getZ(), v.getZ().getPartialDerivative(0, 0, 0, 1), eps);
1023
1024 }
1025 }
1026 }
1027 }
1028
1029 @Test
1030 void testArray() throws MathIllegalArgumentException {
1031
1032 FieldRotation<DerivativeStructure> r = new FieldRotation<>(createAxis(2, -3, 5),
1033 createAngle(1.7),
1034 RotationConvention.VECTOR_OPERATOR);
1035
1036 for (double x = -0.9; x < 0.9; x += 0.2) {
1037 for (double y = -0.9; y < 0.9; y += 0.2) {
1038 for (double z = -0.9; z < 0.9; z += 0.2) {
1039 FieldVector3D<DerivativeStructure> u = createVector(x, y, z);
1040 FieldVector3D<DerivativeStructure> v = r.applyTo(u);
1041 DerivativeStructure[] out = new DerivativeStructure[3];
1042 r.applyTo(new DerivativeStructure[] { u.getX(), u.getY(), u.getZ() }, out);
1043 assertEquals(v.getX().getReal(), out[0].getReal(), 1.0e-10);
1044 assertEquals(v.getY().getReal(), out[1].getReal(), 1.0e-10);
1045 assertEquals(v.getZ().getReal(), out[2].getReal(), 1.0e-10);
1046 r.applyInverseTo(out, out);
1047 assertEquals(u.getX().getReal(), out[0].getReal(), 1.0e-10);
1048 assertEquals(u.getY().getReal(), out[1].getReal(), 1.0e-10);
1049 assertEquals(u.getZ().getReal(), out[2].getReal(), 1.0e-10);
1050 }
1051 }
1052 }
1053
1054 }
1055
1056 @Test
1057 void testApplyInverseTo() throws MathIllegalArgumentException {
1058
1059 DerivativeStructure[] in = new DerivativeStructure[3];
1060 DerivativeStructure[] out = new DerivativeStructure[3];
1061 DerivativeStructure[] rebuilt = new DerivativeStructure[3];
1062 FieldRotation<DerivativeStructure> r = new FieldRotation<>(createVector(2, -3, 5),
1063 createAngle(1.7),
1064 RotationConvention.VECTOR_OPERATOR);
1065 for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
1066 for (double phi = -1.55; phi < 1.55; phi += 0.2) {
1067 FieldVector3D<DerivativeStructure> u = createVector(FastMath.cos(lambda) * FastMath.cos(phi),
1068 FastMath.sin(lambda) * FastMath.cos(phi),
1069 FastMath.sin(phi));
1070 r.applyInverseTo(r.applyTo(u));
1071 checkVector(u, r.applyInverseTo(r.applyTo(u)));
1072 checkVector(u, r.applyTo(r.applyInverseTo(u)));
1073 in[0] = u.getX();
1074 in[1] = u.getY();
1075 in[2] = u.getZ();
1076 r.applyTo(in, out);
1077 r.applyInverseTo(out, rebuilt);
1078 assertEquals(in[0].getReal(), rebuilt[0].getReal(), 1.0e-12);
1079 assertEquals(in[1].getReal(), rebuilt[1].getReal(), 1.0e-12);
1080 assertEquals(in[2].getReal(), rebuilt[2].getReal(), 1.0e-12);
1081 }
1082 }
1083
1084 r = createRotation(1, 0, 0, 0, false);
1085 for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
1086 for (double phi = -1.55; phi < 1.55; phi += 0.2) {
1087 FieldVector3D<DerivativeStructure> u = createVector(FastMath.cos(lambda) * FastMath.cos(phi),
1088 FastMath.sin(lambda) * FastMath.cos(phi),
1089 FastMath.sin(phi));
1090 checkVector(u, r.applyInverseTo(r.applyTo(u)));
1091 checkVector(u, r.applyTo(r.applyInverseTo(u)));
1092 }
1093 }
1094
1095 r = new FieldRotation<>(createVector(0, 0, 1), createAngle(FastMath.PI), RotationConvention.VECTOR_OPERATOR);
1096 for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
1097 for (double phi = -1.55; phi < 1.55; phi += 0.2) {
1098 FieldVector3D<DerivativeStructure> u = createVector(FastMath.cos(lambda) * FastMath.cos(phi),
1099 FastMath.sin(lambda) * FastMath.cos(phi),
1100 FastMath.sin(phi));
1101 checkVector(u, r.applyInverseTo(r.applyTo(u)));
1102 checkVector(u, r.applyTo(r.applyInverseTo(u)));
1103 }
1104 }
1105
1106 }
1107
1108 @Test
1109 void testIssue639() throws MathRuntimeException{
1110 FieldVector3D<DerivativeStructure> u1 = createVector(-1321008684645961.0 / 268435456.0,
1111 -5774608829631843.0 / 268435456.0,
1112 -3822921525525679.0 / 4294967296.0);
1113 FieldVector3D<DerivativeStructure> u2 =createVector( -5712344449280879.0 / 2097152.0,
1114 -2275058564560979.0 / 1048576.0,
1115 4423475992255071.0 / 65536.0);
1116 FieldRotation<DerivativeStructure> rot = new FieldRotation<>(u1, u2, createVector(1, 0, 0),createVector(0, 0, 1));
1117 assertEquals( 0.6228370359608200639829222, rot.getQ0().getReal(), 1.0e-15);
1118 assertEquals( 0.0257707621456498790029987, rot.getQ1().getReal(), 1.0e-15);
1119 assertEquals(-0.0000000002503012255839931, rot.getQ2().getReal(), 1.0e-15);
1120 assertEquals(-0.7819270390861109450724902, rot.getQ3().getReal(), 1.0e-15);
1121 }
1122
1123 @Test
1124 void testIssue801() throws MathRuntimeException {
1125 FieldVector3D<DerivativeStructure> u1 = createVector(0.9999988431610581, -0.0015210774290851095, 0.0);
1126 FieldVector3D<DerivativeStructure> u2 = createVector(0.0, 0.0, 1.0);
1127
1128 FieldVector3D<DerivativeStructure> v1 = createVector(0.9999999999999999, 0.0, 0.0);
1129 FieldVector3D<DerivativeStructure> v2 = createVector(0.0, 0.0, -1.0);
1130
1131 FieldRotation<DerivativeStructure> quat = new FieldRotation<>(u1, u2, v1, v2);
1132 double q2 = quat.getQ0().getReal() * quat.getQ0().getReal() +
1133 quat.getQ1().getReal() * quat.getQ1().getReal() +
1134 quat.getQ2().getReal() * quat.getQ2().getReal() +
1135 quat.getQ3().getReal() * quat.getQ3().getReal();
1136 assertEquals(1.0, q2, 1.0e-14);
1137 assertEquals(0.0, FieldVector3D.angle(v1, quat.applyTo(u1)).getReal(), 1.0e-14);
1138 assertEquals(0.0, FieldVector3D.angle(v2, quat.applyTo(u2)).getReal(), 1.0e-14);
1139
1140 }
1141
1142 private void checkAngle(DerivativeStructure a1, double a2) {
1143 assertEquals(a1.getReal(), MathUtils.normalizeAngle(a2, a1.getReal()), 1.0e-10);
1144 }
1145
1146 private void checkRotationDS(FieldRotation<DerivativeStructure> r, double q0, double q1, double q2, double q3) {
1147 FieldRotation<DerivativeStructure> rPrime = createRotation(q0, q1, q2, q3, false);
1148 assertEquals(0, FieldRotation.distance(r, rPrime).getReal(), 1.0e-12);
1149 }
1150
1151 private FieldRotation<DerivativeStructure> createRotation(double q0, double q1, double q2, double q3,
1152 boolean needsNormalization) {
1153 DSFactory factory = new DSFactory(4, 1);
1154 return new FieldRotation<>(factory.variable(0, q0),
1155 factory.variable(1, q1),
1156 factory.variable(2, q2),
1157 factory.variable(3, q3),
1158 needsNormalization);
1159 }
1160
1161 private FieldRotation<DerivativeStructure> createRotation(double[][] m, double threshold) {
1162 DSFactory factory = new DSFactory(4, 1);
1163 DerivativeStructure[][] mds = new DerivativeStructure[m.length][m[0].length];
1164 int index = 0;
1165 for (int i = 0; i < m.length; ++i) {
1166 for (int j = 0; j < m[i].length; ++j) {
1167 mds[i][j] = factory.variable(index, m[i][j]);
1168 index = (index + 1) % 4;
1169 }
1170 }
1171 return new FieldRotation<>(mds, threshold);
1172 }
1173
1174 private FieldVector3D<DerivativeStructure> createVector(double x, double y, double z) {
1175 DSFactory factory = new DSFactory(4, 1);
1176 return new FieldVector3D<>(factory.constant(x), factory.constant(y), factory.constant(z));
1177 }
1178
1179 private FieldVector3D<DerivativeStructure> createAxis(double x, double y, double z) {
1180 DSFactory factory = new DSFactory(4, 1);
1181 return new FieldVector3D<>(factory.variable(0, x), factory.variable(1, y), factory.variable(2, z));
1182 }
1183
1184 private DerivativeStructure createAngle(double alpha) {
1185 DSFactory factory = new DSFactory(4, 1);
1186 return factory.variable(3, alpha);
1187 }
1188
1189 private void checkVector(FieldVector3D<DerivativeStructure> u, FieldVector3D<DerivativeStructure> v) {
1190 assertEquals(u.getX().getReal(), v.getX().getReal(), 1.0e-12);
1191 assertEquals(u.getY().getReal(), v.getY().getReal(), 1.0e-12);
1192 assertEquals(u.getZ().getReal(), v.getZ().getReal(), 1.0e-12);
1193 }
1194
1195 }