Transform.java

  1. /* Copyright 2002-2024 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;

  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;

  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;


  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.         KinematicTransform {

  106.     /** Identity transform. */
  107.     public static final Transform IDENTITY = new IdentityTransform();

  109.     /** Serializable UID. */
  110.     private static final long serialVersionUID = 210140410L;

  112.     /** Date of the transform. */
  113.     private final AbsoluteDate date;

  115.     /** Cartesian coordinates of the target frame with respect to the original frame. */
  116.     private final PVCoordinates cartesian;

  118.     /** Angular coordinates of the target frame with respect to the original frame. */
  119.     private final AngularCoordinates angular;

  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.     }

  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.     }

  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.     }

  156.     /** Build a combined translation and rotation transform.
  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 rotation rotation to apply ( i.e. rotation to apply to the
  162.      * coordinates of a vector expressed in the old frame to obtain the
  163.      * same vector expressed in the new frame )
  164.      * @since 12.1
  165.      */
  166.     public Transform(final AbsoluteDate date, final Vector3D translation, final Rotation rotation) {
  167.         this(date, new PVCoordinates(translation), new AngularCoordinates(rotation));
  168.     }

  170.     /** Build a translation transform, with its first time derivative.
  171.      * @param date date of the transform
  172.      * @param translation translation to apply (i.e. coordinates of
  173.      * the transformed origin, or coordinates of the origin of the
  174.      * old frame in the new frame)
  175.      * @param velocity the velocity of the translation (i.e. origin
  176.      * of the old frame velocity in the new frame)
  177.      */
  178.     public Transform(final AbsoluteDate date, final Vector3D translation,
  179.                      final Vector3D velocity) {
  180.         this(date,
  181.              new PVCoordinates(translation, velocity, Vector3D.ZERO),
  182.              AngularCoordinates.IDENTITY);
  183.     }

  185.     /** Build a translation transform, with its first and second time derivatives.
  186.      * @param date date of the transform
  187.      * @param translation translation to apply (i.e. coordinates of
  188.      * the transformed origin, or coordinates of the origin of the
  189.      * old frame in the new frame)
  190.      * @param velocity the velocity of the translation (i.e. origin
  191.      * of the old frame velocity in the new frame)
  192.      * @param acceleration the acceleration of the translation (i.e. origin
  193.      * of the old frame acceleration in the new frame)
  194.      */
  195.     public Transform(final AbsoluteDate date, final Vector3D translation,
  196.                      final Vector3D velocity, final Vector3D acceleration) {
  197.         this(date,
  198.              new PVCoordinates(translation, velocity, acceleration),
  199.              AngularCoordinates.IDENTITY);
  200.     }

  202.     /** Build a translation transform, with its first time derivative.
  203.      * @param date date of the transform
  204.      * @param cartesian Cartesian part of the transformation to apply (i.e. coordinates of
  205.      * the transformed origin, or coordinates of the origin of the
  206.      * old frame in the new frame, with their derivatives)
  207.      */
  208.     public Transform(final AbsoluteDate date, final PVCoordinates cartesian) {
  209.         this(date,
  210.              cartesian,
  211.              AngularCoordinates.IDENTITY);
  212.     }

  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.      * expressed in the new frame. (norm representing angular rate)
  221.      */
  222.     public Transform(final AbsoluteDate date, final Rotation rotation, final Vector3D rotationRate) {
  223.         this(date,
  224.              PVCoordinates.ZERO,
  225.              new AngularCoordinates(rotation, rotationRate, Vector3D.ZERO));
  226.     }

  228.     /** Build a rotation transform.
  229.      * @param date date of the transform
  230.      * @param rotation rotation to apply ( i.e. rotation to apply to the
  231.      * coordinates of a vector expressed in the old frame to obtain the
  232.      * same vector expressed in the new frame )
  233.      * @param rotationRate the axis of the instant rotation
  234.      * @param rotationAcceleration the axis of the instant rotation
  235.      * expressed in the new frame. (norm representing angular rate)
  236.      */
  237.     public Transform(final AbsoluteDate date, final Rotation rotation, final Vector3D rotationRate,
  238.                      final Vector3D rotationAcceleration) {
  239.         this(date,
  240.              PVCoordinates.ZERO,
  241.              new AngularCoordinates(rotation, rotationRate, rotationAcceleration));
  242.     }

  244.     /** Build a rotation transform.
  245.      * @param date date of the transform
  246.      * @param angular angular part of the transformation to apply (i.e. rotation to
  247.      * apply to the coordinates of a vector expressed in the old frame to obtain the
  248.      * same vector expressed in the new frame, with its rotation rate)
  249.      */
  250.     public Transform(final AbsoluteDate date, final AngularCoordinates angular) {
  251.         this(date, PVCoordinates.ZERO, angular);
  252.     }

  254.     /** Build a transform by combining two existing ones.
  255.      * <p>
  256.      * Note that the dates of the two existing transformed are <em>ignored</em>,
  257.      * and the combined transform date is set to the date supplied in this constructor
  258.      * without any attempt to shift the raw transforms. This is a design choice allowing
  259.      * user full control of the combination.
  260.      * </p>
  261.      * @param date date of the transform
  262.      * @param first first transform applied
  263.      * @param second second transform applied
  264.      */
  265.     public Transform(final AbsoluteDate date, final Transform first, final Transform second) {
  266.         this(date,
  267.              new PVCoordinates(StaticTransform.compositeTranslation(first, second),
  268.                                KinematicTransform.compositeVelocity(first, second),
  269.                                compositeAcceleration(first, second)),
  270.              new AngularCoordinates(StaticTransform.compositeRotation(first, second),
  271.                                     KinematicTransform.compositeRotationRate(first, second),
  272.                                     compositeRotationAcceleration(first, second)));
  273.     }

  275.     /** Compute a composite acceleration.
  276.      * @param first first applied transform
  277.      * @param second second applied transform
  278.      * @return acceleration part of the composite transform
  279.      */
  280.     private static Vector3D compositeAcceleration(final Transform first, final Transform second) {

  282.         final Vector3D a1    = first.cartesian.getAcceleration();
  283.         final Rotation r1    = first.angular.getRotation();
  284.         final Vector3D o1    = first.angular.getRotationRate();
  285.         final Vector3D oDot1 = first.angular.getRotationAcceleration();
  286.         final Vector3D p2    = second.cartesian.getPosition();
  287.         final Vector3D v2    = second.cartesian.getVelocity();
  288.         final Vector3D a2    = second.cartesian.getAcceleration();

  290.         final Vector3D crossCrossP = Vector3D.crossProduct(o1,    Vector3D.crossProduct(o1, p2));
  291.         final Vector3D crossV      = Vector3D.crossProduct(o1,    v2);
  292.         final Vector3D crossDotP   = Vector3D.crossProduct(oDot1, p2);

  294.         return a1.add(r1.applyInverseTo(new Vector3D(1, a2, 2, crossV, 1, crossCrossP, 1, crossDotP)));

  296.     }

  298.     /** Compute a composite rotation acceleration.
  299.      * @param first first applied transform
  300.      * @param second second applied transform
  301.      * @return rotation acceleration part of the composite transform
  302.      */
  303.     private static Vector3D compositeRotationAcceleration(final Transform first, final Transform second) {

  305.         final Vector3D o1    = first.angular.getRotationRate();
  306.         final Vector3D oDot1 = first.angular.getRotationAcceleration();
  307.         final Rotation r2    = second.angular.getRotation();
  308.         final Vector3D o2    = second.angular.getRotationRate();
  309.         final Vector3D oDot2 = second.angular.getRotationAcceleration();

  311.         return new Vector3D( 1, oDot2,
  312.                              1, r2.applyTo(oDot1),
  313.                             -1, Vector3D.crossProduct(o2, r2.applyTo(o1)));

  315.     }

  317.     /** {@inheritDoc} */
  318.     public AbsoluteDate getDate() {
  319.         return date;
  320.     }

  322.     /** {@inheritDoc} */
  323.     public Transform shiftedBy(final double dt) {
  324.         return new Transform(date.shiftedBy(dt), cartesian.shiftedBy(dt), angular.shiftedBy(dt));
  325.     }

  327.     /**
  328.      * Shift the transform in time considering all rates, then return only the
  329.      * translation and rotation portion of the transform.
  330.      *
  331.      * @param dt time shift in seconds.
  332.      * @return shifted transform as a static transform. It is static in the
  333.      * sense that it can only be used to transform directions and positions, but
  334.      * not velocities or accelerations.
  335.      * @see #shiftedBy(double)
  336.      */
  337.     public StaticTransform staticShiftedBy(final double dt) {
  338.         return StaticTransform.of(
  339.                 date.shiftedBy(dt),
  340.                 cartesian.positionShiftedBy(dt),
  341.                 angular.rotationShiftedBy(dt));
  342.     }

  344.     /**
  345.      * Create a so-called static transform from the instance.
  346.      *
  347.      * @return static part of the transform. It is static in the
  348.      * sense that it can only be used to transform directions and positions, but
  349.      * not velocities or accelerations.
  350.      * @see StaticTransform
  351.      */
  352.     public StaticTransform toStaticTransform() {
  353.         return StaticTransform.of(date, cartesian.getPosition(), angular.getRotation());
  354.     }

  356.     /** Interpolate a transform from a sample set of existing transforms.
  357.      * <p>
  358.      * Calling this method is equivalent to call {@link #interpolate(AbsoluteDate,
  359.      * CartesianDerivativesFilter, AngularDerivativesFilter, Collection)} with {@code cFilter}
  360.      * set to {@link CartesianDerivativesFilter#USE_PVA} and {@code aFilter} set to
  361.      * {@link AngularDerivativesFilter#USE_RRA}
  362.      * set to true.
  363.      * </p>
  364.      * @param interpolationDate interpolation date
  365.      * @param sample sample points on which interpolation should be done
  366.      * @return a new instance, interpolated at specified date
  367.      */
  368.     public Transform interpolate(final AbsoluteDate interpolationDate, final Stream<Transform> sample) {
  369.         return interpolate(interpolationDate,
  370.                            CartesianDerivativesFilter.USE_PVA, AngularDerivativesFilter.USE_RRA,
  371.                            sample.collect(Collectors.toList()));
  372.     }

  374.     /** Interpolate a transform from a sample set of existing transforms.
  375.      * <p>
  376.      * Note that even if first time derivatives (velocities and rotation rates)
  377.      * from sample can be ignored, the interpolated instance always includes
  378.      * interpolated derivatives. This feature can be used explicitly to
  379.      * compute these derivatives when it would be too complex to compute them
  380.      * from an analytical formula: just compute a few sample points from the
  381.      * explicit formula and set the derivatives to zero in these sample points,
  382.      * then use interpolation to add derivatives consistent with the positions
  383.      * and rotations.
  384.      * </p>
  385.      * <p>
  386.      * As this implementation of interpolation is polynomial, it should be used only
  387.      * with small samples (about 10-20 points) in order to avoid <a
  388.      * href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
  389.      * and numerical problems (including NaN appearing).
  390.      * </p>
  391.      * @param date interpolation date
  392.      * @param cFilter filter for derivatives from the sample to use in interpolation
  393.      * @param aFilter filter for derivatives from the sample to use in interpolation
  394.      * @param sample sample points on which interpolation should be done
  395.      * @return a new instance, interpolated at specified date
  396.      * @since 7.0
  397.      */
  398.     public static Transform interpolate(final AbsoluteDate date,
  399.                                         final CartesianDerivativesFilter cFilter,
  400.                                         final AngularDerivativesFilter aFilter,
  401.                                         final Collection<Transform> sample) {

  403.         // Create samples
  404.         final List<TimeStampedPVCoordinates>      datedPV = new ArrayList<>(sample.size());
  405.         final List<TimeStampedAngularCoordinates> datedAC = new ArrayList<>(sample.size());
  406.         for (final Transform t : sample) {
  407.             datedPV.add(new TimeStampedPVCoordinates(t.getDate(), t.getTranslation(), t.getVelocity(), t.getAcceleration()));
  408.             datedAC.add(new TimeStampedAngularCoordinates(t.getDate(), t.getRotation(), t.getRotationRate(), t.getRotationAcceleration()));
  409.         }

  411.         // Create interpolators
  412.         final TimeInterpolator<TimeStampedPVCoordinates> pvInterpolator =
  413.                 new TimeStampedPVCoordinatesHermiteInterpolator(datedPV.size(), cFilter);

  415.         final TimeInterpolator<TimeStampedAngularCoordinates> angularInterpolator =
  416.                 new TimeStampedAngularCoordinatesHermiteInterpolator(datedPV.size(), aFilter);

  418.         // Interpolate
  419.         final TimeStampedPVCoordinates      interpolatedPV = pvInterpolator.interpolate(date, datedPV);
  420.         final TimeStampedAngularCoordinates interpolatedAC = angularInterpolator.interpolate(date, datedAC);
  421.         return new Transform(date, interpolatedPV, interpolatedAC);
  422.     }

  424.     /** Get the inverse transform of the instance.
  425.      * @return inverse transform of the instance
  426.      */
  427.     @Override
  428.     public Transform getInverse() {

  430.         final Rotation r    = angular.getRotation();
  431.         final Vector3D o    = angular.getRotationRate();
  432.         final Vector3D oDot = angular.getRotationAcceleration();
  433.         final Vector3D rp   = r.applyTo(cartesian.getPosition());
  434.         final Vector3D rv   = r.applyTo(cartesian.getVelocity());
  435.         final Vector3D ra   = r.applyTo(cartesian.getAcceleration());

  437.         final Vector3D pInv        = rp.negate();
  438.         final Vector3D crossP      = Vector3D.crossProduct(o, rp);
  439.         final Vector3D vInv        = crossP.subtract(rv);
  440.         final Vector3D crossV      = Vector3D.crossProduct(o, rv);
  441.         final Vector3D crossDotP   = Vector3D.crossProduct(oDot, rp);
  442.         final Vector3D crossCrossP = Vector3D.crossProduct(o, crossP);
  443.         final Vector3D aInv        = new Vector3D(-1, ra,
  444.                                                    2, crossV,
  445.                                                    1, crossDotP,
  446.                                                   -1, crossCrossP);

  448.         return new Transform(getDate(), new PVCoordinates(pInv, vInv, aInv), angular.revert());

  450.     }

  452.     /** Get a frozen transform.
  453.      * <p>
  454.      * This method creates a copy of the instance but frozen in time,
  455.      * i.e. with velocity, acceleration and rotation rate forced to zero.
  456.      * </p>
  457.      * @return a new transform, without any time-dependent parts
  458.      */
  459.     public Transform freeze() {
  460.         return new Transform(date,
  461.                              new PVCoordinates(cartesian.getPosition(), Vector3D.ZERO, Vector3D.ZERO),
  462.                              new AngularCoordinates(angular.getRotation(), Vector3D.ZERO, Vector3D.ZERO));
  463.     }

  465.     /** Transform {@link PVCoordinates} including kinematic effects.
  466.      * @param pva the position-velocity-acceleration triplet to transform.
  467.      * @return transformed position-velocity-acceleration
  468.      */
  469.     public PVCoordinates transformPVCoordinates(final PVCoordinates pva) {
  470.         return angular.applyTo(new PVCoordinates(1, pva, 1, cartesian));
  471.     }

  473.     /** Transform {@link TimeStampedPVCoordinates} including kinematic effects.
  474.      * <p>
  475.      * In order to allow the user more flexibility, this method does <em>not</em> check for
  476.      * consistency between the transform {@link #getDate() date} and the time-stamped
  477.      * position-velocity {@link TimeStampedPVCoordinates#getDate() date}. The returned
  478.      * value will always have the same {@link TimeStampedPVCoordinates#getDate() date} as
  479.      * the input argument, regardless of the instance {@link #getDate() date}.
  480.      * </p>
  481.      * @param pv time-stamped  position-velocity to transform.
  482.      * @return transformed time-stamped position-velocity
  483.      * @since 7.0
  484.      */
  485.     public TimeStampedPVCoordinates transformPVCoordinates(final TimeStampedPVCoordinates pv) {
  486.         return angular.applyTo(new TimeStampedPVCoordinates(pv.getDate(), 1, pv, 1, cartesian));
  487.     }

  489.     /** Transform {@link FieldPVCoordinates} including kinematic effects.
  490.      * @param pv position-velocity to transform.
  491.      * @param <T> type of the field elements
  492.      * @return transformed position-velocity
  493.      */
  494.     public <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> transformPVCoordinates(final FieldPVCoordinates<T> pv) {
  495.         return angular.applyTo(new FieldPVCoordinates<>(pv.getPosition().add(cartesian.getPosition()),
  496.                                                         pv.getVelocity().add(cartesian.getVelocity()),
  497.                                                         pv.getAcceleration().add(cartesian.getAcceleration())));
  498.     }

  500.     /** Transform {@link TimeStampedFieldPVCoordinates} including kinematic effects.
  501.      * <p>
  502.      * In order to allow the user more flexibility, this method does <em>not</em> check for
  503.      * consistency between the transform {@link #getDate() date} and the time-stamped
  504.      * position-velocity {@link TimeStampedFieldPVCoordinates#getDate() date}. The returned
  505.      * value will always have the same {@link TimeStampedFieldPVCoordinates#getDate() date} as
  506.      * the input argument, regardless of the instance {@link #getDate() date}.
  507.      * </p>
  508.      * @param pv time-stamped position-velocity to transform.
  509.      * @param <T> type of the field elements
  510.      * @return transformed time-stamped position-velocity
  511.      * @since 7.0
  512.      */
  513.     public <T extends CalculusFieldElement<T>> TimeStampedFieldPVCoordinates<T> transformPVCoordinates(final TimeStampedFieldPVCoordinates<T> pv) {
  514.         return angular.applyTo(new TimeStampedFieldPVCoordinates<>(pv.getDate(),
  515.                                                                    pv.getPosition().add(cartesian.getPosition()),
  516.                                                                    pv.getVelocity().add(cartesian.getVelocity()),
  517.                                                                    pv.getAcceleration().add(cartesian.getAcceleration())));
  518.     }

  520.     /** Compute the Jacobian of the {@link #transformPVCoordinates(PVCoordinates)}
  521.      * method of the transform.
  522.      * <p>
  523.      * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i
  524.      * of the transformed {@link PVCoordinates} with respect to Cartesian coordinate j
  525.      * of the input {@link PVCoordinates} in method {@link #transformPVCoordinates(PVCoordinates)}.
  526.      * </p>
  527.      * <p>
  528.      * This definition implies that if we define position-velocity coordinates
  529.      * <pre>
  530.      * PV₁ = transform.transformPVCoordinates(PV₀), then
  531.      * </pre>
  532.      * <p> their differentials dPV₁ and dPV₀ will obey the following relation
  533.      * where J is the matrix computed by this method:
  534.      * <pre>
  535.      * dPV₁ = J &times; dPV₀
  536.      * </pre>
  537.      *
  538.      * @param selector selector specifying the size of the upper left corner that must be filled
  539.      * (either 3x3 for positions only, 6x6 for positions and velocities, 9x9 for positions,
  540.      * velocities and accelerations)
  541.      * @param jacobian placeholder matrix whose upper-left corner is to be filled with
  542.      * the Jacobian, the rest of the matrix remaining untouched
  543.      */
  544.     public void getJacobian(final CartesianDerivativesFilter selector, final double[][] jacobian) {

  546.         // elementary matrix for rotation
  547.         final double[][] mData = angular.getRotation().getMatrix();

  549.         // dP1/dP0
  550.         System.arraycopy(mData[0], 0, jacobian[0], 0, 3);
  551.         System.arraycopy(mData[1], 0, jacobian[1], 0, 3);
  552.         System.arraycopy(mData[2], 0, jacobian[2], 0, 3);

  554.         if (selector.getMaxOrder() >= 1) {

  556.             // dP1/dV0
  557.             Arrays.fill(jacobian[0], 3, 6, 0.0);
  558.             Arrays.fill(jacobian[1], 3, 6, 0.0);
  559.             Arrays.fill(jacobian[2], 3, 6, 0.0);

  561.             // dV1/dP0
  562.             final Vector3D o = angular.getRotationRate();
  563.             final double ox = o.getX();
  564.             final double oy = o.getY();
  565.             final double oz = o.getZ();
  566.             for (int i = 0; i < 3; ++i) {
  567.                 jacobian[3][i] = -(oy * mData[2][i] - oz * mData[1][i]);
  568.                 jacobian[4][i] = -(oz * mData[0][i] - ox * mData[2][i]);
  569.                 jacobian[5][i] = -(ox * mData[1][i] - oy * mData[0][i]);
  570.             }

  572.             // dV1/dV0
  573.             System.arraycopy(mData[0], 0, jacobian[3], 3, 3);
  574.             System.arraycopy(mData[1], 0, jacobian[4], 3, 3);
  575.             System.arraycopy(mData[2], 0, jacobian[5], 3, 3);

  577.             if (selector.getMaxOrder() >= 2) {

  579.                 // dP1/dA0
  580.                 Arrays.fill(jacobian[0], 6, 9, 0.0);
  581.                 Arrays.fill(jacobian[1], 6, 9, 0.0);
  582.                 Arrays.fill(jacobian[2], 6, 9, 0.0);

  584.                 // dV1/dA0
  585.                 Arrays.fill(jacobian[3], 6, 9, 0.0);
  586.                 Arrays.fill(jacobian[4], 6, 9, 0.0);
  587.                 Arrays.fill(jacobian[5], 6, 9, 0.0);

  589.                 // dA1/dP0
  590.                 final Vector3D oDot = angular.getRotationAcceleration();
  591.                 final double oDotx  = oDot.getX();
  592.                 final double oDoty  = oDot.getY();
  593.                 final double oDotz  = oDot.getZ();
  594.                 for (int i = 0; i < 3; ++i) {
  595.                     jacobian[6][i] = -(oDoty * mData[2][i] - oDotz * mData[1][i]) - (oy * jacobian[5][i] - oz * jacobian[4][i]);
  596.                     jacobian[7][i] = -(oDotz * mData[0][i] - oDotx * mData[2][i]) - (oz * jacobian[3][i] - ox * jacobian[5][i]);
  597.                     jacobian[8][i] = -(oDotx * mData[1][i] - oDoty * mData[0][i]) - (ox * jacobian[4][i] - oy * jacobian[3][i]);
  598.                 }

  600.                 // dA1/dV0
  601.                 for (int i = 0; i < 3; ++i) {
  602.                     jacobian[6][i + 3] = -2 * (oy * mData[2][i] - oz * mData[1][i]);
  603.                     jacobian[7][i + 3] = -2 * (oz * mData[0][i] - ox * mData[2][i]);
  604.                     jacobian[8][i + 3] = -2 * (ox * mData[1][i] - oy * mData[0][i]);
  605.                 }

  607.                 // dA1/dA0
  608.                 System.arraycopy(mData[0], 0, jacobian[6], 6, 3);
  609.                 System.arraycopy(mData[1], 0, jacobian[7], 6, 3);
  610.                 System.arraycopy(mData[2], 0, jacobian[8], 6, 3);

  612.             }

  614.         }

  616.     }

  618.     /** Get the underlying elementary Cartesian part.
  619.      * <p>A transform can be uniquely represented as an elementary
  620.      * translation followed by an elementary rotation. This method
  621.      * returns this unique elementary translation with its derivative.</p>
  622.      * @return underlying elementary Cartesian part
  623.      * @see #getTranslation()
  624.      * @see #getVelocity()
  625.      */
  626.     public PVCoordinates getCartesian() {
  627.         return cartesian;
  628.     }

  630.     /** Get the underlying elementary translation.
  631.      * <p>A transform can be uniquely represented as an elementary
  632.      * translation followed by an elementary rotation. This method
  633.      * returns this unique elementary translation.</p>
  634.      * @return underlying elementary translation
  635.      * @see #getCartesian()
  636.      * @see #getVelocity()
  637.      * @see #getAcceleration()
  638.      */
  639.     public Vector3D getTranslation() {
  640.         return cartesian.getPosition();
  641.     }

  643.     /** Get the first time derivative of the translation.
  644.      * @return first time derivative of the translation
  645.      * @see #getCartesian()
  646.      * @see #getTranslation()
  647.      * @see #getAcceleration()
  648.      */
  649.     public Vector3D getVelocity() {
  650.         return cartesian.getVelocity();
  651.     }

  653.     /** Get the second time derivative of the translation.
  654.      * @return second time derivative of the translation
  655.      * @see #getCartesian()
  656.      * @see #getTranslation()
  657.      * @see #getVelocity()
  658.      */
  659.     public Vector3D getAcceleration() {
  660.         return cartesian.getAcceleration();
  661.     }

  663.     /** Get the underlying elementary angular part.
  664.      * <p>A transform can be uniquely represented as an elementary
  665.      * translation followed by an elementary rotation. This method
  666.      * returns this unique elementary rotation with its derivative.</p>
  667.      * @return underlying elementary angular part
  668.      * @see #getRotation()
  669.      * @see #getRotationRate()
  670.      * @see #getRotationAcceleration()
  671.      */
  672.     public AngularCoordinates getAngular() {
  673.         return angular;
  674.     }

  676.     /** Get the underlying elementary rotation.
  677.      * <p>A transform can be uniquely represented as an elementary
  678.      * translation followed by an elementary rotation. This method
  679.      * returns this unique elementary rotation.</p>
  680.      * @return underlying elementary rotation
  681.      * @see #getAngular()
  682.      * @see #getRotationRate()
  683.      * @see #getRotationAcceleration()
  684.      */
  685.     public Rotation getRotation() {
  686.         return angular.getRotation();
  687.     }

  689.     /** Get the first time derivative of the rotation.
  690.      * <p>The norm represents the angular rate.</p>
  691.      * @return First time derivative of the rotation
  692.      * @see #getAngular()
  693.      * @see #getRotation()
  694.      * @see #getRotationAcceleration()
  695.      */
  696.     public Vector3D getRotationRate() {
  697.         return angular.getRotationRate();
  698.     }

  700.     /** Get the second time derivative of the rotation.
  701.      * @return Second time derivative of the rotation
  702.      * @see #getAngular()
  703.      * @see #getRotation()
  704.      * @see #getRotationRate()
  705.      */
  706.     public Vector3D getRotationAcceleration() {
  707.         return angular.getRotationAcceleration();
  708.     }

  710.     /** Specialized class for identity transform. */
  711.     private static class IdentityTransform extends Transform {

  713.         /** Serializable UID. */
  714.         private static final long serialVersionUID = -9042082036141830517L;

  716.         /** Simple constructor. */
  717.         IdentityTransform() {
  718.             super(AbsoluteDate.ARBITRARY_EPOCH, PVCoordinates.ZERO, AngularCoordinates.IDENTITY);
  719.         }

  721.         /** {@inheritDoc} */
  722.         @Override
  723.         public Transform shiftedBy(final double dt) {
  724.             return this;
  725.         }

  727.         /** {@inheritDoc} */
  728.         @Override
  729.         public Transform getInverse() {
  730.             return this;
  731.         }

  733.         /** {@inheritDoc} */
  734.         @Override
  735.         public Vector3D transformPosition(final Vector3D position) {
  736.             return position;
  737.         }

  739.         /** {@inheritDoc} */
  740.         @Override
  741.         public Vector3D transformVector(final Vector3D vector) {
  742.             return vector;
  743.         }

  745.         /** {@inheritDoc} */
  746.         @Override
  747.         public Line transformLine(final Line line) {
  748.             return line;
  749.         }

  751.         /** {@inheritDoc} */
  752.         @Override
  753.         public PVCoordinates transformPVCoordinates(final PVCoordinates pv) {
  754.             return pv;
  755.         }

  757.         @Override
  758.         public Transform freeze() {
  759.             return this;
  760.         }

  762.         @Override
  763.         public TimeStampedPVCoordinates transformPVCoordinates(
  764.                 final TimeStampedPVCoordinates pv) {
  765.             return pv;
  766.         }

  768.         @Override
  769.         public <T extends CalculusFieldElement<T>> FieldPVCoordinates<T>
  770.             transformPVCoordinates(final FieldPVCoordinates<T> pv) {
  771.             return pv;
  772.         }

  774.         @Override
  775.         public <T extends CalculusFieldElement<T>>
  776.             TimeStampedFieldPVCoordinates<T> transformPVCoordinates(
  777.                     final TimeStampedFieldPVCoordinates<T> pv) {
  778.             return pv;
  779.         }

  781.         /** {@inheritDoc} */
  782.         @Override
  783.         public void getJacobian(final CartesianDerivativesFilter selector, final double[][] jacobian) {
  784.             final int n = 3 * (selector.getMaxOrder() + 1);
  785.             for (int i = 0; i < n; ++i) {
  786.                 Arrays.fill(jacobian[i], 0, n, 0.0);
  787.                 jacobian[i][i] = 1.0;
  788.             }
  789.         }

  791.     }

  793. }
Created with JaCoCo 0.8.12.202403310830