1 /* Copyright 2002-2023 CS GROUP
2 * Licensed to CS GROUP (CS) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * CS licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.orekit.frames;
18
19 import java.io.Serializable;
20 import java.util.ArrayList;
21 import java.util.Arrays;
22 import java.util.Collection;
23 import java.util.List;
24 import java.util.stream.Collectors;
25 import java.util.stream.Stream;
26
27 import org.hipparchus.CalculusFieldElement;
28 import org.hipparchus.geometry.euclidean.threed.Line;
29 import org.hipparchus.geometry.euclidean.threed.Rotation;
30 import org.hipparchus.geometry.euclidean.threed.Vector3D;
31 import org.orekit.time.AbsoluteDate;
32 import org.orekit.time.TimeInterpolator;
33 import org.orekit.time.TimeShiftable;
34 import org.orekit.utils.AngularCoordinates;
35 import org.orekit.utils.AngularDerivativesFilter;
36 import org.orekit.utils.CartesianDerivativesFilter;
37 import org.orekit.utils.FieldPVCoordinates;
38 import org.orekit.utils.PVCoordinates;
39 import org.orekit.utils.TimeStampedAngularCoordinates;
40 import org.orekit.utils.TimeStampedAngularCoordinatesHermiteInterpolator;
41 import org.orekit.utils.TimeStampedFieldPVCoordinates;
42 import org.orekit.utils.TimeStampedPVCoordinates;
43 import org.orekit.utils.TimeStampedPVCoordinatesHermiteInterpolator;
44
45
46 /** Transformation class in three dimensional space.
47 *
48 * <p>This class represents the transformation engine between {@link Frame frames}.
49 * It is used both to define the relationship between each frame and its
50 * parent frame and to gather all individual transforms into one
51 * operation when converting between frames far away from each other.</p>
52 * <p> The convention used in OREKIT is vectorial transformation. It means
53 * that a transformation is defined as a transform to apply to the
54 * coordinates of a vector expressed in the old frame to obtain the
55 * same vector expressed in the new frame.
56 *
57 * <p>Instances of this class are guaranteed to be immutable.</p>
58 *
59 * <h2> Examples </h2>
60 *
61 * <h3> Example of translation from R<sub>A</sub> to R<sub>B</sub> </h3>
62 *
63 * <p> We want to transform the {@link PVCoordinates} PV<sub>A</sub> to
64 * PV<sub>B</sub> with :
65 * <p> PV<sub>A</sub> = ({1, 0, 0}, {2, 0, 0}, {3, 0, 0}); <br>
66 * PV<sub>B</sub> = ({0, 0, 0}, {0, 0, 0}, {0, 0, 0});
67 *
68 * <p> The transform to apply then is defined as follows :
69 *
70 * <pre><code>
71 * Vector3D translation = new Vector3D(-1, 0, 0);
72 * Vector3D velocity = new Vector3D(-2, 0, 0);
73 * Vector3D acceleration = new Vector3D(-3, 0, 0);
74 *
75 * Transform R1toR2 = new Transform(date, translation, velocity, acceleration);
76 *
77 * PVB = R1toR2.transformPVCoordinates(PVA);
78 * </code></pre>
79 *
80 * <h3> Example of rotation from R<sub>A</sub> to R<sub>B</sub> </h3>
81 * <p> We want to transform the {@link PVCoordinates} PV<sub>A</sub> to
82 * PV<sub>B</sub> with
83 *
84 * <p> PV<sub>A</sub> = ({1, 0, 0}, { 1, 0, 0}); <br>
85 * PV<sub>B</sub> = ({0, 1, 0}, {-2, 1, 0});
86 *
87 * <p> The transform to apply then is defined as follows :
88 *
89 * <pre><code>
90 * Rotation rotation = new Rotation(Vector3D.PLUS_K, FastMath.PI / 2);
91 * Vector3D rotationRate = new Vector3D(0, 0, -2);
92 *
93 * Transform R1toR2 = new Transform(rotation, rotationRate);
94 *
95 * PVB = R1toR2.transformPVCoordinates(PVA);
96 * </code></pre>
97 *
98 * @author Luc Maisonobe
99 * @author Fabien Maussion
100 */
101 public class Transform implements
102 TimeShiftable<Transform>,
103 Serializable,
104 StaticTransform {
105
106 /** Identity transform. */
107 public static final Transform IDENTITY = new IdentityTransform();
108
109 /** Serializable UID. */
110 private static final long serialVersionUID = 210140410L;
111
112 /** Date of the transform. */
113 private final AbsoluteDate date;
114
115 /** Cartesian coordinates of the target frame with respect to the original frame. */
116 private final PVCoordinates cartesian;
117
118 /** Angular coordinates of the target frame with respect to the original frame. */
119 private final AngularCoordinates angular;
120
121 /** Build a transform from its primitive operations.
122 * @param date date of the transform
123 * @param cartesian Cartesian coordinates of the target frame with respect to the original frame
124 * @param angular angular coordinates of the target frame with respect to the original frame
125 */
126 public Transform(final AbsoluteDate date, final PVCoordinates cartesian, final AngularCoordinates angular) {
127 this.date = date;
128 this.cartesian = cartesian;
129 this.angular = angular;
130 }
131
132 /** Build a translation transform.
133 * @param date date of the transform
134 * @param translation translation to apply (i.e. coordinates of
135 * the transformed origin, or coordinates of the origin of the
136 * old frame in the new frame)
137 */
138 public Transform(final AbsoluteDate date, final Vector3D translation) {
139 this(date,
140 new PVCoordinates(translation),
141 AngularCoordinates.IDENTITY);
142 }
143
144 /** Build a rotation transform.
145 * @param date date of the transform
146 * @param rotation rotation to apply ( i.e. rotation to apply to the
147 * coordinates of a vector expressed in the old frame to obtain the
148 * same vector expressed in the new frame )
149 */
150 public Transform(final AbsoluteDate date, final Rotation rotation) {
151 this(date,
152 PVCoordinates.ZERO,
153 new AngularCoordinates(rotation));
154 }
155
156 /** Build a translation transform, with its first time derivative.
157 * @param date date of the transform
158 * @param translation translation to apply (i.e. coordinates of
159 * the transformed origin, or coordinates of the origin of the
160 * old frame in the new frame)
161 * @param velocity the velocity of the translation (i.e. origin
162 * of the old frame velocity in the new frame)
163 */
164 public Transform(final AbsoluteDate date, final Vector3D translation,
165 final Vector3D velocity) {
166 this(date,
167 new PVCoordinates(translation, velocity, Vector3D.ZERO),
168 AngularCoordinates.IDENTITY);
169 }
170
171 /** Build a translation transform, with its first and second time derivatives.
172 * @param date date of the transform
173 * @param translation translation to apply (i.e. coordinates of
174 * the transformed origin, or coordinates of the origin of the
175 * old frame in the new frame)
176 * @param velocity the velocity of the translation (i.e. origin
177 * of the old frame velocity in the new frame)
178 * @param acceleration the acceleration of the translation (i.e. origin
179 * of the old frame acceleration in the new frame)
180 */
181 public Transform(final AbsoluteDate date, final Vector3D translation,
182 final Vector3D velocity, final Vector3D acceleration) {
183 this(date,
184 new PVCoordinates(translation, velocity, acceleration),
185 AngularCoordinates.IDENTITY);
186 }
187
188 /** Build a translation transform, with its first time derivative.
189 * @param date date of the transform
190 * @param cartesian Cartesian part of the transformation to apply (i.e. coordinates of
191 * the transformed origin, or coordinates of the origin of the
192 * old frame in the new frame, with their derivatives)
193 */
194 public Transform(final AbsoluteDate date, final PVCoordinates cartesian) {
195 this(date,
196 cartesian,
197 AngularCoordinates.IDENTITY);
198 }
199
200 /** Build a rotation transform.
201 * @param date date of the transform
202 * @param rotation rotation to apply ( i.e. rotation to apply to the
203 * coordinates of a vector expressed in the old frame to obtain the
204 * same vector expressed in the new frame )
205 * @param rotationRate the axis of the instant rotation
206 * expressed in the new frame. (norm representing angular rate)
207 */
208 public Transform(final AbsoluteDate date, final Rotation rotation, final Vector3D rotationRate) {
209 this(date,
210 PVCoordinates.ZERO,
211 new AngularCoordinates(rotation, rotationRate, Vector3D.ZERO));
212 }
213
214 /** Build a rotation transform.
215 * @param date date of the transform
216 * @param rotation rotation to apply ( i.e. rotation to apply to the
217 * coordinates of a vector expressed in the old frame to obtain the
218 * same vector expressed in the new frame )
219 * @param rotationRate the axis of the instant rotation
220 * @param rotationAcceleration the axis of the instant rotation
221 * expressed in the new frame. (norm representing angular rate)
222 */
223 public Transform(final AbsoluteDate date, final Rotation rotation, final Vector3D rotationRate,
224 final Vector3D rotationAcceleration) {
225 this(date,
226 PVCoordinates.ZERO,
227 new AngularCoordinates(rotation, rotationRate, rotationAcceleration));
228 }
229
230 /** Build a rotation transform.
231 * @param date date of the transform
232 * @param angular angular part of the transformation to apply (i.e. rotation to
233 * apply to the coordinates of a vector expressed in the old frame to obtain the
234 * same vector expressed in the new frame, with its rotation rate)
235 */
236 public Transform(final AbsoluteDate date, final AngularCoordinates angular) {
237 this(date, PVCoordinates.ZERO, angular);
238 }
239
240 /** Build a transform by combining two existing ones.
241 * <p>
242 * Note that the dates of the two existing transformed are <em>ignored</em>,
243 * and the combined transform date is set to the date supplied in this constructor
244 * without any attempt to shift the raw transforms. This is a design choice allowing
245 * user full control of the combination.
246 * </p>
247 * @param date date of the transform
248 * @param first first transform applied
249 * @param second second transform applied
250 */
251 public Transform(final AbsoluteDate date, final Transform first, final Transform second) {
252 this(date,
253 new PVCoordinates(StaticTransform.compositeTranslation(first, second),
254 compositeVelocity(first, second),
255 compositeAcceleration(first, second)),
256 new AngularCoordinates(StaticTransform.compositeRotation(first, second),
257 compositeRotationRate(first, second),
258 compositeRotationAcceleration(first, second)));
259 }
260
261 /** Compute a composite velocity.
262 * @param first first applied transform
263 * @param second second applied transform
264 * @return velocity part of the composite transform
265 */
266 private static Vector3D compositeVelocity(final Transform first, final Transform second) {
267
268 final Vector3D v1 = first.cartesian.getVelocity();
269 final Rotation r1 = first.angular.getRotation();
270 final Vector3D o1 = first.angular.getRotationRate();
271 final Vector3D p2 = second.cartesian.getPosition();
272 final Vector3D v2 = second.cartesian.getVelocity();
273
274 final Vector3D crossP = Vector3D.crossProduct(o1, p2);
275
276 return v1.add(r1.applyInverseTo(v2.add(crossP)));
277
278 }
279
280 /** Compute a composite acceleration.
281 * @param first first applied transform
282 * @param second second applied transform
283 * @return acceleration part of the composite transform
284 */
285 private static Vector3D compositeAcceleration(final Transform first, final Transform second) {
286
287 final Vector3D a1 = first.cartesian.getAcceleration();
288 final Rotation r1 = first.angular.getRotation();
289 final Vector3D o1 = first.angular.getRotationRate();
290 final Vector3D oDot1 = first.angular.getRotationAcceleration();
291 final Vector3D p2 = second.cartesian.getPosition();
292 final Vector3D v2 = second.cartesian.getVelocity();
293 final Vector3D a2 = second.cartesian.getAcceleration();
294
295 final Vector3D crossCrossP = Vector3D.crossProduct(o1, Vector3D.crossProduct(o1, p2));
296 final Vector3D crossV = Vector3D.crossProduct(o1, v2);
297 final Vector3D crossDotP = Vector3D.crossProduct(oDot1, p2);
298
299 return a1.add(r1.applyInverseTo(new Vector3D(1, a2, 2, crossV, 1, crossCrossP, 1, crossDotP)));
300
301 }
302
303 /** Compute a composite rotation rate.
304 * @param first first applied transform
305 * @param second second applied transform
306 * @return rotation rate part of the composite transform
307 */
308 private static Vector3D compositeRotationRate(final Transform first, final Transform second) {
309
310 final Vector3D o1 = first.angular.getRotationRate();
311 final Rotation r2 = second.angular.getRotation();
312 final Vector3D o2 = second.angular.getRotationRate();
313
314 return o2.add(r2.applyTo(o1));
315
316 }
317
318 /** Compute a composite rotation acceleration.
319 * @param first first applied transform
320 * @param second second applied transform
321 * @return rotation acceleration part of the composite transform
322 */
323 private static Vector3D compositeRotationAcceleration(final Transform first, final Transform second) {
324
325 final Vector3D o1 = first.angular.getRotationRate();
326 final Vector3D oDot1 = first.angular.getRotationAcceleration();
327 final Rotation r2 = second.angular.getRotation();
328 final Vector3D o2 = second.angular.getRotationRate();
329 final Vector3D oDot2 = second.angular.getRotationAcceleration();
330
331 return new Vector3D( 1, oDot2,
332 1, r2.applyTo(oDot1),
333 -1, Vector3D.crossProduct(o2, r2.applyTo(o1)));
334
335 }
336
337 /** {@inheritDoc} */
338 public AbsoluteDate getDate() {
339 return date;
340 }
341
342 /** {@inheritDoc} */
343 public Transform shiftedBy(final double dt) {
344 return new Transform(date.shiftedBy(dt), cartesian.shiftedBy(dt), angular.shiftedBy(dt));
345 }
346
347 /**
348 * Shift the transform in time considering all rates, then return only the
349 * translation and rotation portion of the transform.
350 *
351 * @param dt time shift in seconds.
352 * @return shifted transform as a static transform. It is static in the
353 * sense that it can only be used to transform directions and positions, but
354 * not velocities or accelerations.
355 * @see #shiftedBy(double)
356 */
357 public StaticTransform staticShiftedBy(final double dt) {
358 return StaticTransform.of(
359 date.shiftedBy(dt),
360 cartesian.positionShiftedBy(dt),
361 angular.rotationShiftedBy(dt));
362 }
363
364 /**
365 * Create a so-called static transform from the instance.
366 *
367 * @return static part of the transform. It is static in the
368 * sense that it can only be used to transform directions and positions, but
369 * not velocities or accelerations.
370 * @see StaticTransform
371 */
372 public StaticTransform toStaticTransform() {
373 return StaticTransform.of(date, cartesian.getPosition(), angular.getRotation());
374 }
375
376 /** Interpolate a transform from a sample set of existing transforms.
377 * <p>
378 * Calling this method is equivalent to call {@link #interpolate(AbsoluteDate,
379 * CartesianDerivativesFilter, AngularDerivativesFilter, Collection)} with {@code cFilter}
380 * set to {@link CartesianDerivativesFilter#USE_PVA} and {@code aFilter} set to
381 * {@link AngularDerivativesFilter#USE_RRA}
382 * set to true.
383 * </p>
384 * @param interpolationDate interpolation date
385 * @param sample sample points on which interpolation should be done
386 * @return a new instance, interpolated at specified date
387 */
388 public Transform interpolate(final AbsoluteDate interpolationDate, final Stream<Transform> sample) {
389 return interpolate(interpolationDate,
390 CartesianDerivativesFilter.USE_PVA, AngularDerivativesFilter.USE_RRA,
391 sample.collect(Collectors.toList()));
392 }
393
394 /** Interpolate a transform from a sample set of existing transforms.
395 * <p>
396 * Note that even if first time derivatives (velocities and rotation rates)
397 * from sample can be ignored, the interpolated instance always includes
398 * interpolated derivatives. This feature can be used explicitly to
399 * compute these derivatives when it would be too complex to compute them
400 * from an analytical formula: just compute a few sample points from the
401 * explicit formula and set the derivatives to zero in these sample points,
402 * then use interpolation to add derivatives consistent with the positions
403 * and rotations.
404 * </p>
405 * <p>
406 * As this implementation of interpolation is polynomial, it should be used only
407 * with small samples (about 10-20 points) in order to avoid <a
408 * href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
409 * and numerical problems (including NaN appearing).
410 * </p>
411 * @param date interpolation date
412 * @param cFilter filter for derivatives from the sample to use in interpolation
413 * @param aFilter filter for derivatives from the sample to use in interpolation
414 * @param sample sample points on which interpolation should be done
415 * @return a new instance, interpolated at specified date
416 * @since 7.0
417 */
418 public static Transform interpolate(final AbsoluteDate date,
419 final CartesianDerivativesFilter cFilter,
420 final AngularDerivativesFilter aFilter,
421 final Collection<Transform> sample) {
422
423 // Create samples
424 final List<TimeStampedPVCoordinates> datedPV = new ArrayList<>(sample.size());
425 final List<TimeStampedAngularCoordinates> datedAC = new ArrayList<>(sample.size());
426 for (final Transform t : sample) {
427 datedPV.add(new TimeStampedPVCoordinates(t.getDate(), t.getTranslation(), t.getVelocity(), t.getAcceleration()));
428 datedAC.add(new TimeStampedAngularCoordinates(t.getDate(), t.getRotation(), t.getRotationRate(), t.getRotationAcceleration()));
429 }
430
431 // Create interpolators
432 final TimeInterpolator<TimeStampedPVCoordinates> pvInterpolator =
433 new TimeStampedPVCoordinatesHermiteInterpolator(datedPV.size(), cFilter);
434
435 final TimeInterpolator<TimeStampedAngularCoordinates> angularInterpolator =
436 new TimeStampedAngularCoordinatesHermiteInterpolator(datedPV.size(), aFilter);
437
438 // Interpolate
439 final TimeStampedPVCoordinates interpolatedPV = pvInterpolator.interpolate(date, datedPV);
440 final TimeStampedAngularCoordinates interpolatedAC = angularInterpolator.interpolate(date, datedAC);
441 return new Transform(date, interpolatedPV, interpolatedAC);
442 }
443
444 /** Get the inverse transform of the instance.
445 * @return inverse transform of the instance
446 */
447 @Override
448 public Transform getInverse() {
449
450 final Rotation r = angular.getRotation();
451 final Vector3D o = angular.getRotationRate();
452 final Vector3D oDot = angular.getRotationAcceleration();
453 final Vector3D rp = r.applyTo(cartesian.getPosition());
454 final Vector3D rv = r.applyTo(cartesian.getVelocity());
455 final Vector3D ra = r.applyTo(cartesian.getAcceleration());
456
457 final Vector3D pInv = rp.negate();
458 final Vector3D crossP = Vector3D.crossProduct(o, rp);
459 final Vector3D vInv = crossP.subtract(rv);
460 final Vector3D crossV = Vector3D.crossProduct(o, rv);
461 final Vector3D crossDotP = Vector3D.crossProduct(oDot, rp);
462 final Vector3D crossCrossP = Vector3D.crossProduct(o, crossP);
463 final Vector3D aInv = new Vector3D(-1, ra,
464 2, crossV,
465 1, crossDotP,
466 -1, crossCrossP);
467
468 return new Transform(getDate(), new PVCoordinates(pInv, vInv, aInv), angular.revert());
469
470 }
471
472 /** Get a frozen transform.
473 * <p>
474 * This method creates a copy of the instance but frozen in time,
475 * i.e. with velocity, acceleration and rotation rate forced to zero.
476 * </p>
477 * @return a new transform, without any time-dependent parts
478 */
479 public Transform freeze() {
480 return new Transform(date,
481 new PVCoordinates(cartesian.getPosition(), Vector3D.ZERO, Vector3D.ZERO),
482 new AngularCoordinates(angular.getRotation(), Vector3D.ZERO, Vector3D.ZERO));
483 }
484
485 /** Transform {@link PVCoordinates} including kinematic effects.
486 * @param pva the position-velocity-acceleration triplet to transform.
487 * @return transformed position-velocity-acceleration
488 */
489 public PVCoordinates transformPVCoordinates(final PVCoordinates pva) {
490 return angular.applyTo(new PVCoordinates(1, pva, 1, cartesian));
491 }
492
493 /** Transform {@link TimeStampedPVCoordinates} including kinematic effects.
494 * <p>
495 * In order to allow the user more flexibility, this method does <em>not</em> check for
496 * consistency between the transform {@link #getDate() date} and the time-stamped
497 * position-velocity {@link TimeStampedPVCoordinates#getDate() date}. The returned
498 * value will always have the same {@link TimeStampedPVCoordinates#getDate() date} as
499 * the input argument, regardless of the instance {@link #getDate() date}.
500 * </p>
501 * @param pv time-stamped position-velocity to transform.
502 * @return transformed time-stamped position-velocity
503 * @since 7.0
504 */
505 public TimeStampedPVCoordinates transformPVCoordinates(final TimeStampedPVCoordinates pv) {
506 return angular.applyTo(new TimeStampedPVCoordinates(pv.getDate(), 1, pv, 1, cartesian));
507 }
508
509 /** Transform {@link FieldPVCoordinates} including kinematic effects.
510 * @param pv position-velocity to transform.
511 * @param <T> type of the field elements
512 * @return transformed position-velocity
513 */
514 public <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> transformPVCoordinates(final FieldPVCoordinates<T> pv) {
515 return angular.applyTo(new FieldPVCoordinates<>(pv.getPosition().add(cartesian.getPosition()),
516 pv.getVelocity().add(cartesian.getVelocity()),
517 pv.getAcceleration().add(cartesian.getAcceleration())));
518 }
519
520 /** Transform {@link TimeStampedFieldPVCoordinates} including kinematic effects.
521 * <p>
522 * In order to allow the user more flexibility, this method does <em>not</em> check for
523 * consistency between the transform {@link #getDate() date} and the time-stamped
524 * position-velocity {@link TimeStampedFieldPVCoordinates#getDate() date}. The returned
525 * value will always have the same {@link TimeStampedFieldPVCoordinates#getDate() date} as
526 * the input argument, regardless of the instance {@link #getDate() date}.
527 * </p>
528 * @param pv time-stamped position-velocity to transform.
529 * @param <T> type of the field elements
530 * @return transformed time-stamped position-velocity
531 * @since 7.0
532 */
533 public <T extends CalculusFieldElement<T>> TimeStampedFieldPVCoordinates<T> transformPVCoordinates(final TimeStampedFieldPVCoordinates<T> pv) {
534 return angular.applyTo(new TimeStampedFieldPVCoordinates<>(pv.getDate(),
535 pv.getPosition().add(cartesian.getPosition()),
536 pv.getVelocity().add(cartesian.getVelocity()),
537 pv.getAcceleration().add(cartesian.getAcceleration())));
538 }
539
540 /** Compute the Jacobian of the {@link #transformPVCoordinates(PVCoordinates)}
541 * method of the transform.
542 * <p>
543 * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i
544 * of the transformed {@link PVCoordinates} with respect to Cartesian coordinate j
545 * of the input {@link PVCoordinates} in method {@link #transformPVCoordinates(PVCoordinates)}.
546 * </p>
547 * <p>
548 * This definition implies that if we define position-velocity coordinates
549 * <pre>
550 * PV₁ = transform.transformPVCoordinates(PV₀), then
551 * </pre>
552 * <p> their differentials dPV₁ and dPV₀ will obey the following relation
553 * where J is the matrix computed by this method:
554 * <pre>
555 * dPV₁ = J × dPV₀
556 * </pre>
557 *
558 * @param selector selector specifying the size of the upper left corner that must be filled
559 * (either 3x3 for positions only, 6x6 for positions and velocities, 9x9 for positions,
560 * velocities and accelerations)
561 * @param jacobian placeholder matrix whose upper-left corner is to be filled with
562 * the Jacobian, the rest of the matrix remaining untouched
563 */
564 public void getJacobian(final CartesianDerivativesFilter selector, final double[][] jacobian) {
565
566 // elementary matrix for rotation
567 final double[][] mData = angular.getRotation().getMatrix();
568
569 // dP1/dP0
570 System.arraycopy(mData[0], 0, jacobian[0], 0, 3);
571 System.arraycopy(mData[1], 0, jacobian[1], 0, 3);
572 System.arraycopy(mData[2], 0, jacobian[2], 0, 3);
573
574 if (selector.getMaxOrder() >= 1) {
575
576 // dP1/dV0
577 Arrays.fill(jacobian[0], 3, 6, 0.0);
578 Arrays.fill(jacobian[1], 3, 6, 0.0);
579 Arrays.fill(jacobian[2], 3, 6, 0.0);
580
581 // dV1/dP0
582 final Vector3D o = angular.getRotationRate();
583 final double ox = o.getX();
584 final double oy = o.getY();
585 final double oz = o.getZ();
586 for (int i = 0; i < 3; ++i) {
587 jacobian[3][i] = -(oy * mData[2][i] - oz * mData[1][i]);
588 jacobian[4][i] = -(oz * mData[0][i] - ox * mData[2][i]);
589 jacobian[5][i] = -(ox * mData[1][i] - oy * mData[0][i]);
590 }
591
592 // dV1/dV0
593 System.arraycopy(mData[0], 0, jacobian[3], 3, 3);
594 System.arraycopy(mData[1], 0, jacobian[4], 3, 3);
595 System.arraycopy(mData[2], 0, jacobian[5], 3, 3);
596
597 if (selector.getMaxOrder() >= 2) {
598
599 // dP1/dA0
600 Arrays.fill(jacobian[0], 6, 9, 0.0);
601 Arrays.fill(jacobian[1], 6, 9, 0.0);
602 Arrays.fill(jacobian[2], 6, 9, 0.0);
603
604 // dV1/dA0
605 Arrays.fill(jacobian[3], 6, 9, 0.0);
606 Arrays.fill(jacobian[4], 6, 9, 0.0);
607 Arrays.fill(jacobian[5], 6, 9, 0.0);
608
609 // dA1/dP0
610 final Vector3D oDot = angular.getRotationAcceleration();
611 final double oDotx = oDot.getX();
612 final double oDoty = oDot.getY();
613 final double oDotz = oDot.getZ();
614 for (int i = 0; i < 3; ++i) {
615 jacobian[6][i] = -(oDoty * mData[2][i] - oDotz * mData[1][i]) - (oy * jacobian[5][i] - oz * jacobian[4][i]);
616 jacobian[7][i] = -(oDotz * mData[0][i] - oDotx * mData[2][i]) - (oz * jacobian[3][i] - ox * jacobian[5][i]);
617 jacobian[8][i] = -(oDotx * mData[1][i] - oDoty * mData[0][i]) - (ox * jacobian[4][i] - oy * jacobian[3][i]);
618 }
619
620 // dA1/dV0
621 for (int i = 0; i < 3; ++i) {
622 jacobian[6][i + 3] = -2 * (oy * mData[2][i] - oz * mData[1][i]);
623 jacobian[7][i + 3] = -2 * (oz * mData[0][i] - ox * mData[2][i]);
624 jacobian[8][i + 3] = -2 * (ox * mData[1][i] - oy * mData[0][i]);
625 }
626
627 // dA1/dA0
628 System.arraycopy(mData[0], 0, jacobian[6], 6, 3);
629 System.arraycopy(mData[1], 0, jacobian[7], 6, 3);
630 System.arraycopy(mData[2], 0, jacobian[8], 6, 3);
631
632 }
633
634 }
635
636 }
637
638 /** Get the underlying elementary Cartesian part.
639 * <p>A transform can be uniquely represented as an elementary
640 * translation followed by an elementary rotation. This method
641 * returns this unique elementary translation with its derivative.</p>
642 * @return underlying elementary Cartesian part
643 * @see #getTranslation()
644 * @see #getVelocity()
645 */
646 public PVCoordinates getCartesian() {
647 return cartesian;
648 }
649
650 /** Get the underlying elementary translation.
651 * <p>A transform can be uniquely represented as an elementary
652 * translation followed by an elementary rotation. This method
653 * returns this unique elementary translation.</p>
654 * @return underlying elementary translation
655 * @see #getCartesian()
656 * @see #getVelocity()
657 * @see #getAcceleration()
658 */
659 public Vector3D getTranslation() {
660 return cartesian.getPosition();
661 }
662
663 /** Get the first time derivative of the translation.
664 * @return first time derivative of the translation
665 * @see #getCartesian()
666 * @see #getTranslation()
667 * @see #getAcceleration()
668 */
669 public Vector3D getVelocity() {
670 return cartesian.getVelocity();
671 }
672
673 /** Get the second time derivative of the translation.
674 * @return second time derivative of the translation
675 * @see #getCartesian()
676 * @see #getTranslation()
677 * @see #getVelocity()
678 */
679 public Vector3D getAcceleration() {
680 return cartesian.getAcceleration();
681 }
682
683 /** Get the underlying elementary angular part.
684 * <p>A transform can be uniquely represented as an elementary
685 * translation followed by an elementary rotation. This method
686 * returns this unique elementary rotation with its derivative.</p>
687 * @return underlying elementary angular part
688 * @see #getRotation()
689 * @see #getRotationRate()
690 * @see #getRotationAcceleration()
691 */
692 public AngularCoordinates getAngular() {
693 return angular;
694 }
695
696 /** Get the underlying elementary rotation.
697 * <p>A transform can be uniquely represented as an elementary
698 * translation followed by an elementary rotation. This method
699 * returns this unique elementary rotation.</p>
700 * @return underlying elementary rotation
701 * @see #getAngular()
702 * @see #getRotationRate()
703 * @see #getRotationAcceleration()
704 */
705 public Rotation getRotation() {
706 return angular.getRotation();
707 }
708
709 /** Get the first time derivative of the rotation.
710 * <p>The norm represents the angular rate.</p>
711 * @return First time derivative of the rotation
712 * @see #getAngular()
713 * @see #getRotation()
714 * @see #getRotationAcceleration()
715 */
716 public Vector3D getRotationRate() {
717 return angular.getRotationRate();
718 }
719
720 /** Get the second time derivative of the rotation.
721 * @return Second time derivative of the rotation
722 * @see #getAngular()
723 * @see #getRotation()
724 * @see #getRotationRate()
725 */
726 public Vector3D getRotationAcceleration() {
727 return angular.getRotationAcceleration();
728 }
729
730 /** Specialized class for identity transform. */
731 private static class IdentityTransform extends Transform {
732
733 /** Serializable UID. */
734 private static final long serialVersionUID = -9042082036141830517L;
735
736 /** Simple constructor. */
737 IdentityTransform() {
738 super(AbsoluteDate.ARBITRARY_EPOCH, PVCoordinates.ZERO, AngularCoordinates.IDENTITY);
739 }
740
741 /** {@inheritDoc} */
742 @Override
743 public Transform shiftedBy(final double dt) {
744 return this;
745 }
746
747 /** {@inheritDoc} */
748 @Override
749 public Transform getInverse() {
750 return this;
751 }
752
753 /** {@inheritDoc} */
754 @Override
755 public Vector3D transformPosition(final Vector3D position) {
756 return position;
757 }
758
759 /** {@inheritDoc} */
760 @Override
761 public Vector3D transformVector(final Vector3D vector) {
762 return vector;
763 }
764
765 /** {@inheritDoc} */
766 @Override
767 public Line transformLine(final Line line) {
768 return line;
769 }
770
771 /** {@inheritDoc} */
772 @Override
773 public PVCoordinates transformPVCoordinates(final PVCoordinates pv) {
774 return pv;
775 }
776
777 @Override
778 public Transform freeze() {
779 return this;
780 }
781
782 @Override
783 public TimeStampedPVCoordinates transformPVCoordinates(
784 final TimeStampedPVCoordinates pv) {
785 return pv;
786 }
787
788 @Override
789 public <T extends CalculusFieldElement<T>> FieldPVCoordinates<T>
790 transformPVCoordinates(final FieldPVCoordinates<T> pv) {
791 return pv;
792 }
793
794 @Override
795 public <T extends CalculusFieldElement<T>>
796 TimeStampedFieldPVCoordinates<T> transformPVCoordinates(
797 final TimeStampedFieldPVCoordinates<T> pv) {
798 return pv;
799 }
800
801 /** {@inheritDoc} */
802 @Override
803 public void getJacobian(final CartesianDerivativesFilter selector, final double[][] jacobian) {
804 final int n = 3 * (selector.getMaxOrder() + 1);
805 for (int i = 0; i < n; ++i) {
806 Arrays.fill(jacobian[i], 0, n, 0.0);
807 jacobian[i][i] = 1.0;
808 }
809 }
810
811 }
812
813 }