Transform.java

  1. /* Copyright 2002-2019 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (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.RealFieldElement;
  28. import org.hipparchus.geometry.euclidean.threed.FieldRotation;
  29. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  30. import org.hipparchus.geometry.euclidean.threed.Line;
  31. import org.hipparchus.geometry.euclidean.threed.Rotation;
  32. import org.hipparchus.geometry.euclidean.threed.RotationConvention;
  33. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  34. import org.orekit.time.AbsoluteDate;
  35. import org.orekit.time.TimeInterpolable;
  36. import org.orekit.time.TimeShiftable;
  37. import org.orekit.time.TimeStamped;
  38. import org.orekit.utils.AngularCoordinates;
  39. import org.orekit.utils.AngularDerivativesFilter;
  40. import org.orekit.utils.CartesianDerivativesFilter;
  41. import org.orekit.utils.FieldPVCoordinates;
  42. import org.orekit.utils.PVCoordinates;
  43. import org.orekit.utils.TimeStampedAngularCoordinates;
  44. import org.orekit.utils.TimeStampedFieldPVCoordinates;
  45. import org.orekit.utils.TimeStampedPVCoordinates;


  48. /** Transformation class in three dimensional space.
  49.  *
  50.  * <p>This class represents the transformation engine between {@link Frame frames}.
  51.  * It is used both to define the relationship between each frame and its
  52.  * parent frame and to gather all individual transforms into one
  53.  * operation when converting between frames far away from each other.</p>
  54.  * <p> The convention used in OREKIT is vectorial transformation. It means
  55.  * that a transformation is defined as a transform to apply to the
  56.  * coordinates of a vector expressed in the old frame to obtain the
  57.  * same vector expressed in the new frame.
  58.  *
  59.  * <p>Instances of this class are guaranteed to be immutable.</p>
  60.  *
  61.  * <h1> Examples </h1>
  62.  *
  63.  * <h2> Example of translation from R<sub>A</sub> to R<sub>B</sub> </h2>
  64.  *
  65.  * <p> We want to transform the {@link PVCoordinates} PV<sub>A</sub> to
  66.  * PV<sub>B</sub> with :
  67.  * <p> PV<sub>A</sub> = ({1, 0, 0}, {2, 0, 0}, {3, 0, 0}); <br>
  68.  *     PV<sub>B</sub> = ({0, 0, 0}, {0, 0, 0}, {0, 0, 0});
  69.  *
  70.  * <p> The transform to apply then is defined as follows :
  71.  *
  72.  * <pre><code>
  73.  * Vector3D translation  = new Vector3D(-1, 0, 0);
  74.  * Vector3D velocity     = new Vector3D(-2, 0, 0);
  75.  * Vector3D acceleration = new Vector3D(-3, 0, 0);
  76.  *
  77.  * Transform R1toR2 = new Transform(date, translation, velocity, acceleration);
  78.  *
  79.  * PVB = R1toR2.transformPVCoordinates(PVA);
  80.  * </code></pre>
  81.  *
  82.  * <h2> Example of rotation from R<sub>A</sub> to R<sub>B</sub> </h2>
  83.  * <p> We want to transform the {@link PVCoordinates} PV<sub>A</sub> to
  84.  * PV<sub>B</sub> with
  85.  *
  86.  * <p> PV<sub>A</sub> = ({1, 0, 0}, { 1, 0, 0}); <br>
  87.  *     PV<sub>B</sub> = ({0, 1, 0}, {-2, 1, 0});
  88.  *
  89.  * <p> The transform to apply then is defined as follows :
  90.  *
  91.  * <pre><code>
  92.  * Rotation rotation = new Rotation(Vector3D.PLUS_K, FastMath.PI / 2);
  93.  * Vector3D rotationRate = new Vector3D(0, 0, -2);
  94.  *
  95.  * Transform R1toR2 = new Transform(rotation, rotationRate);
  96.  *
  97.  * PVB = R1toR2.transformPVCoordinates(PVA);
  98.  * </code></pre>
  99.  *
  100.  * @author Luc Maisonobe
  101.  * @author Fabien Maussion
  102.  */
  103. public class Transform
  104.     implements TimeStamped, TimeShiftable<Transform>, TimeInterpolable<Transform>, Serializable {

  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.     private Transform(final AbsoluteDate date,
  127.                       final PVCoordinates cartesian, final AngularCoordinates angular) {
  128.         this.date      = date;
  129.         this.cartesian = cartesian;
  130.         this.angular   = angular;
  131.     }

  133.     /** Build a translation transform.
  134.      * @param date date of the transform
  135.      * @param translation translation to apply (i.e. coordinates of
  136.      * the transformed origin, or coordinates of the origin of the
  137.      * old frame in the new frame)
  138.      */
  139.     public Transform(final AbsoluteDate date, final Vector3D translation) {
  140.         this(date,
  141.              new PVCoordinates(translation, Vector3D.ZERO, Vector3D.ZERO),
  142.              AngularCoordinates.IDENTITY);
  143.     }

  145.     /** Build a rotation transform.
  146.      * @param date date of the transform
  147.      * @param rotation rotation to apply ( i.e. rotation to apply to the
  148.      * coordinates of a vector expressed in the old frame to obtain the
  149.      * same vector expressed in the new frame )
  150.      */
  151.     public Transform(final AbsoluteDate date, final Rotation rotation) {
  152.         this(date,
  153.              PVCoordinates.ZERO,
  154.              new AngularCoordinates(rotation, Vector3D.ZERO));
  155.     }

  157.     /** Build a translation transform, with its first time derivative.
  158.      * @param date date of the transform
  159.      * @param translation translation to apply (i.e. coordinates of
  160.      * the transformed origin, or coordinates of the origin of the
  161.      * old frame in the new frame)
  162.      * @param velocity the velocity of the translation (i.e. origin
  163.      * of the old frame velocity in the new frame)
  164.      */
  165.     public Transform(final AbsoluteDate date, final Vector3D translation,
  166.                      final Vector3D velocity) {
  167.         this(date,
  168.              new PVCoordinates(translation, velocity, Vector3D.ZERO),
  169.              AngularCoordinates.IDENTITY);
  170.     }

  172.     /** Build a translation transform, with its first and second time derivatives.
  173.      * @param date date of the transform
  174.      * @param translation translation to apply (i.e. coordinates of
  175.      * the transformed origin, or coordinates of the origin of the
  176.      * old frame in the new frame)
  177.      * @param velocity the velocity of the translation (i.e. origin
  178.      * of the old frame velocity in the new frame)
  179.      * @param acceleration the acceleration of the translation (i.e. origin
  180.      * of the old frame acceleration in the new frame)
  181.      */
  182.     public Transform(final AbsoluteDate date, final Vector3D translation,
  183.                      final Vector3D velocity, final Vector3D acceleration) {
  184.         this(date,
  185.              new PVCoordinates(translation, velocity, acceleration),
  186.              AngularCoordinates.IDENTITY);
  187.     }

  189.     /** Build a translation transform, with its first time derivative.
  190.      * @param date date of the transform
  191.      * @param cartesian Cartesian part of the transformation to apply (i.e. coordinates of
  192.      * the transformed origin, or coordinates of the origin of the
  193.      * old frame in the new frame, with their derivatives)
  194.      */
  195.     public Transform(final AbsoluteDate date, final PVCoordinates cartesian) {
  196.         this(date,
  197.              cartesian,
  198.              AngularCoordinates.IDENTITY);
  199.     }

  201.     /** Build a rotation transform.
  202.      * @param date date of the transform
  203.      * @param rotation rotation to apply ( i.e. rotation to apply to the
  204.      * coordinates of a vector expressed in the old frame to obtain the
  205.      * same vector expressed in the new frame )
  206.      * @param rotationRate the axis of the instant rotation
  207.      * expressed in the new frame. (norm representing angular rate)
  208.      */
  209.     public Transform(final AbsoluteDate date, final Rotation rotation, final Vector3D rotationRate) {
  210.         this(date,
  211.              PVCoordinates.ZERO,
  212.              new AngularCoordinates(rotation, rotationRate, Vector3D.ZERO));
  213.     }

  215.     /** Build a rotation transform.
  216.      * @param date date of the transform
  217.      * @param rotation rotation to apply ( i.e. rotation to apply to the
  218.      * coordinates of a vector expressed in the old frame to obtain the
  219.      * same vector expressed in the new frame )
  220.      * @param rotationRate the axis of the instant rotation
  221.      * @param rotationAcceleration the axis of the instant rotation
  222.      * expressed in the new frame. (norm representing angular rate)
  223.      */
  224.     public Transform(final AbsoluteDate date, final Rotation rotation, final Vector3D rotationRate,
  225.                      final Vector3D rotationAcceleration) {
  226.         this(date,
  227.              PVCoordinates.ZERO,
  228.              new AngularCoordinates(rotation, rotationRate, rotationAcceleration));
  229.     }

  231.     /** Build a rotation transform.
  232.      * @param date date of the transform
  233.      * @param angular angular part of the transformation to apply (i.e. rotation to
  234.      * apply to the coordinates of a vector expressed in the old frame to obtain the
  235.      * same vector expressed in the new frame, with its rotation rate)
  236.      */
  237.     public Transform(final AbsoluteDate date, final AngularCoordinates angular) {
  238.         this(date, PVCoordinates.ZERO, angular);
  239.     }

  241.     /** Build a transform by combining two existing ones.
  242.      * <p>
  243.      * Note that the dates of the two existing transformed are <em>ignored</em>,
  244.      * and the combined transform date is set to the date supplied in this constructor
  245.      * without any attempt to shift the raw transforms. This is a design choice allowing
  246.      * user full control of the combination.
  247.      * </p>
  248.      * @param date date of the transform
  249.      * @param first first transform applied
  250.      * @param second second transform applied
  251.      */
  252.     public Transform(final AbsoluteDate date, final Transform first, final Transform second) {
  253.         this(date,
  254.              new PVCoordinates(compositeTranslation(first, second),
  255.                                compositeVelocity(first, second),
  256.                                compositeAcceleration(first, second)),
  257.              new AngularCoordinates(compositeRotation(first, second),
  258.                                     compositeRotationRate(first, second),
  259.                                     compositeRotationAcceleration(first, second)));
  260.     }

  262.     /** Compute a composite translation.
  263.      * @param first first applied transform
  264.      * @param second second applied transform
  265.      * @return translation part of the composite transform
  266.      */
  267.     private static Vector3D compositeTranslation(final Transform first, final Transform second) {

  269.         final Vector3D p1 = first.cartesian.getPosition();
  270.         final Rotation r1 = first.angular.getRotation();
  271.         final Vector3D p2 = second.cartesian.getPosition();

  273.         return p1.add(r1.applyInverseTo(p2));

  275.     }

  277.     /** Compute a composite velocity.
  278.      * @param first first applied transform
  279.      * @param second second applied transform
  280.      * @return velocity part of the composite transform
  281.      */
  282.     private static Vector3D compositeVelocity(final Transform first, final Transform second) {

  284.         final Vector3D v1 = first.cartesian.getVelocity();
  285.         final Rotation r1 = first.angular.getRotation();
  286.         final Vector3D o1 = first.angular.getRotationRate();
  287.         final Vector3D p2 = second.cartesian.getPosition();
  288.         final Vector3D v2 = second.cartesian.getVelocity();

  290.         final Vector3D crossP = Vector3D.crossProduct(o1, p2);

  292.         return v1.add(r1.applyInverseTo(v2.add(crossP)));

  294.     }

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

  303.         final Vector3D a1    = first.cartesian.getAcceleration();
  304.         final Rotation r1    = first.angular.getRotation();
  305.         final Vector3D o1    = first.angular.getRotationRate();
  306.         final Vector3D oDot1 = first.angular.getRotationAcceleration();
  307.         final Vector3D p2    = second.cartesian.getPosition();
  308.         final Vector3D v2    = second.cartesian.getVelocity();
  309.         final Vector3D a2    = second.cartesian.getAcceleration();

  311.         final Vector3D crossCrossP = Vector3D.crossProduct(o1,    Vector3D.crossProduct(o1, p2));
  312.         final Vector3D crossV      = Vector3D.crossProduct(o1,    v2);
  313.         final Vector3D crossDotP   = Vector3D.crossProduct(oDot1, p2);

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

  317.     }

  319.     /** Compute a composite rotation.
  320.      * @param first first applied transform
  321.      * @param second second applied transform
  322.      * @return rotation part of the composite transform
  323.      */
  324.     private static Rotation compositeRotation(final Transform first, final Transform second) {

  326.         final Rotation r1 = first.angular.getRotation();
  327.         final Rotation r2 = second.angular.getRotation();

  329.         return r1.compose(r2, RotationConvention.FRAME_TRANSFORM);

  331.     }

  333.     /** Compute a composite rotation rate.
  334.      * @param first first applied transform
  335.      * @param second second applied transform
  336.      * @return rotation rate part of the composite transform
  337.      */
  338.     private static Vector3D compositeRotationRate(final Transform first, final Transform second) {

  340.         final Vector3D o1 = first.angular.getRotationRate();
  341.         final Rotation r2 = second.angular.getRotation();
  342.         final Vector3D o2 = second.angular.getRotationRate();

  344.         return o2.add(r2.applyTo(o1));

  346.     }

  348.     /** Compute a composite rotation acceleration.
  349.      * @param first first applied transform
  350.      * @param second second applied transform
  351.      * @return rotation acceleration part of the composite transform
  352.      */
  353.     private static Vector3D compositeRotationAcceleration(final Transform first, final Transform second) {

  355.         final Vector3D o1    = first.angular.getRotationRate();
  356.         final Vector3D oDot1 = first.angular.getRotationAcceleration();
  357.         final Rotation r2    = second.angular.getRotation();
  358.         final Vector3D o2    = second.angular.getRotationRate();
  359.         final Vector3D oDot2 = second.angular.getRotationAcceleration();

  361.         return new Vector3D( 1, oDot2,
  362.                              1, r2.applyTo(oDot1),
  363.                             -1, Vector3D.crossProduct(o2, r2.applyTo(o1)));

  365.     }

  367.     /** {@inheritDoc} */
  368.     public AbsoluteDate getDate() {
  369.         return date;
  370.     }

  372.     /** {@inheritDoc} */
  373.     public Transform shiftedBy(final double dt) {
  374.         return new Transform(date.shiftedBy(dt), cartesian.shiftedBy(dt), angular.shiftedBy(dt));
  375.     }

  377.     /** {@inheritDoc}
  378.      * <p>
  379.      * Calling this method is equivalent to call {@link #interpolate(AbsoluteDate,
  380.      * CartesianDerivativesFilter, AngularDerivativesFilter, Collection)} with {@code cFilter}
  381.      * set to {@link CartesianDerivativesFilter#USE_PVA} and {@code aFilter} set to
  382.      * {@link AngularDerivativesFilter#USE_RRA}
  383.      * set to true.
  384.      * </p>
  385.      */
  386.     public Transform interpolate(final AbsoluteDate interpolationDate, final Stream<Transform> sample) {
  387.         return interpolate(interpolationDate,
  388.                            CartesianDerivativesFilter.USE_PVA, AngularDerivativesFilter.USE_RRA,
  389.                            sample.collect(Collectors.toList()));
  390.     }

  392.     /** Interpolate a transform from a sample set of existing transforms.
  393.      * <p>
  394.      * Note that even if first time derivatives (velocities and rotation rates)
  395.      * from sample can be ignored, the interpolated instance always includes
  396.      * interpolated derivatives. This feature can be used explicitly to
  397.      * compute these derivatives when it would be too complex to compute them
  398.      * from an analytical formula: just compute a few sample points from the
  399.      * explicit formula and set the derivatives to zero in these sample points,
  400.      * then use interpolation to add derivatives consistent with the positions
  401.      * and rotations.
  402.      * </p>
  403.      * <p>
  404.      * As this implementation of interpolation is polynomial, it should be used only
  405.      * with small samples (about 10-20 points) in order to avoid <a
  406.      * href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
  407.      * and numerical problems (including NaN appearing).
  408.      * </p>
  409.      * @param date interpolation date
  410.      * @param cFilter filter for derivatives from the sample to use in interpolation
  411.      * @param aFilter filter for derivatives from the sample to use in interpolation
  412.      * @param sample sample points on which interpolation should be done
  413.      * @return a new instance, interpolated at specified date
  414.           * @since 7.0
  415.      */
  416.     public static Transform interpolate(final AbsoluteDate date,
  417.                                         final CartesianDerivativesFilter cFilter,
  418.                                         final AngularDerivativesFilter aFilter,
  419.                                         final Collection<Transform> sample) {
  420.         final List<TimeStampedPVCoordinates>      datedPV = new ArrayList<TimeStampedPVCoordinates>(sample.size());
  421.         final List<TimeStampedAngularCoordinates> datedAC = new ArrayList<TimeStampedAngularCoordinates>(sample.size());
  422.         for (final Transform t : sample) {
  423.             datedPV.add(new TimeStampedPVCoordinates(t.getDate(), t.getTranslation(), t.getVelocity(), t.getAcceleration()));
  424.             datedAC.add(new TimeStampedAngularCoordinates(t.getDate(), t.getRotation(), t.getRotationRate(), t.getRotationAcceleration()));
  425.         }
  426.         final TimeStampedPVCoordinates      interpolatedPV = TimeStampedPVCoordinates.interpolate(date, cFilter, datedPV);
  427.         final TimeStampedAngularCoordinates interpolatedAC = TimeStampedAngularCoordinates.interpolate(date, aFilter, datedAC);
  428.         return new Transform(date, interpolatedPV, interpolatedAC);
  429.     }

  431.     /** Get the inverse transform of the instance.
  432.      * @return inverse transform of the instance
  433.      */
  434.     public Transform getInverse() {

  436.         final Rotation r    = angular.getRotation();
  437.         final Vector3D o    = angular.getRotationRate();
  438.         final Vector3D oDot = angular.getRotationAcceleration();
  439.         final Vector3D rp   = r.applyTo(cartesian.getPosition());
  440.         final Vector3D rv   = r.applyTo(cartesian.getVelocity());
  441.         final Vector3D ra   = r.applyTo(cartesian.getAcceleration());

  443.         final Vector3D pInv        = rp.negate();
  444.         final Vector3D crossP      = Vector3D.crossProduct(o, rp);
  445.         final Vector3D vInv        = crossP.subtract(rv);
  446.         final Vector3D crossV      = Vector3D.crossProduct(o, rv);
  447.         final Vector3D crossDotP   = Vector3D.crossProduct(oDot, rp);
  448.         final Vector3D crossCrossP = Vector3D.crossProduct(o, crossP);
  449.         final Vector3D aInv        = new Vector3D(-1, ra,
  450.                                                    2, crossV,
  451.                                                    1, crossDotP,
  452.                                                   -1, crossCrossP);

  454.         return new Transform(date, new PVCoordinates(pInv, vInv, aInv), angular.revert());

  456.     }

  458.     /** Get a frozen transform.
  459.      * <p>
  460.      * This method creates a copy of the instance but frozen in time,
  461.      * i.e. with velocity, acceleration and rotation rate forced to zero.
  462.      * </p>
  463.      * @return a new transform, without any time-dependent parts
  464.      */
  465.     public Transform freeze() {
  466.         return new Transform(date,
  467.                              new PVCoordinates(cartesian.getPosition(), Vector3D.ZERO, Vector3D.ZERO),
  468.                              new AngularCoordinates(angular.getRotation(), Vector3D.ZERO, Vector3D.ZERO));
  469.     }

  471.     /** Transform a position vector (including translation effects).
  472.      * @param position vector to transform
  473.      * @return transformed position
  474.      */
  475.     public Vector3D transformPosition(final Vector3D position) {
  476.         return angular.getRotation().applyTo(cartesian.getPosition().add(position));
  477.     }

  479.     /** Transform a position vector (including translation effects).
  480.      * @param position vector to transform
  481.      * @param <T> the type of the field elements
  482.      * @return transformed position
  483.      */
  484.     public <T extends RealFieldElement<T>> FieldVector3D<T> transformPosition(final FieldVector3D<T> position) {
  485.         return FieldRotation.applyTo(angular.getRotation(), position.add(cartesian.getPosition()));
  486.     }

  488.     /** Transform a vector (ignoring translation effects).
  489.      * @param vector vector to transform
  490.      * @return transformed vector
  491.      */
  492.     public Vector3D transformVector(final Vector3D vector) {
  493.         return angular.getRotation().applyTo(vector);
  494.     }

  496.     /** Transform a vector (ignoring translation effects).
  497.      * @param vector vector to transform
  498.      * @param <T> the type of the field elements
  499.      * @return transformed vector
  500.      */
  501.     public <T extends RealFieldElement<T>> FieldVector3D<T> transformVector(final FieldVector3D<T> vector) {
  502.         return FieldRotation.applyTo(angular.getRotation(), vector);
  503.     }

  505.     /** Transform a line.
  506.      * @param line to transform
  507.      * @return transformed line
  508.      */
  509.     public Line transformLine(final Line line) {
  510.         final Vector3D transformedP0 = transformPosition(line.getOrigin());
  511.         final Vector3D transformedP1 = transformPosition(line.pointAt(1.0e6));
  512.         return new Line(transformedP0, transformedP1, 1.0e-10);
  513.     }

  515.     /** Transform {@link PVCoordinates} including kinematic effects.
  516.      * @param pva the position-velocity-acceleration triplet to transform.
  517.      * @return transformed position-velocity-acceleration
  518.      */
  519.     public PVCoordinates transformPVCoordinates(final PVCoordinates pva) {
  520.         return angular.applyTo(new PVCoordinates(1, pva, 1, cartesian));
  521.     }

  523.     /** Transform {@link TimeStampedPVCoordinates} including kinematic effects.
  524.      * <p>
  525.      * In order to allow the user more flexibility, this method does <em>not</em> check for
  526.      * consistency between the transform {@link #getDate() date} and the time-stamped
  527.      * position-velocity {@link TimeStampedPVCoordinates#getDate() date}. The returned
  528.      * value will always have the same {@link TimeStampedPVCoordinates#getDate() date} as
  529.      * the input argument, regardless of the instance {@link #getDate() date}.
  530.      * </p>
  531.      * @param pv time-stamped  position-velocity to transform.
  532.      * @return transformed time-stamped position-velocity
  533.      * @since 7.0
  534.      */
  535.     public TimeStampedPVCoordinates transformPVCoordinates(final TimeStampedPVCoordinates pv) {
  536.         return angular.applyTo(new TimeStampedPVCoordinates(pv.getDate(), 1, pv, 1, cartesian));
  537.     }

  539.     /** Transform {@link FieldPVCoordinates} including kinematic effects.
  540.      * @param pv position-velocity to transform.
  541.      * @param <T> type of the field elements
  542.      * @return transformed position-velocity
  543.      */
  544.     public <T extends RealFieldElement<T>> FieldPVCoordinates<T> transformPVCoordinates(final FieldPVCoordinates<T> pv) {
  545.         return angular.applyTo(new FieldPVCoordinates<>(pv.getPosition().add(cartesian.getPosition()),
  546.                                                         pv.getVelocity().add(cartesian.getVelocity()),
  547.                                                         pv.getAcceleration().add(cartesian.getAcceleration())));
  548.     }

  550.     /** Transform {@link TimeStampedFieldPVCoordinates} including kinematic effects.
  551.      * <p>
  552.      * In order to allow the user more flexibility, this method does <em>not</em> check for
  553.      * consistency between the transform {@link #getDate() date} and the time-stamped
  554.      * position-velocity {@link TimeStampedFieldPVCoordinates#getDate() date}. The returned
  555.      * value will always have the same {@link TimeStampedFieldPVCoordinates#getDate() date} as
  556.      * the input argument, regardless of the instance {@link #getDate() date}.
  557.      * </p>
  558.      * @param pv time-stamped position-velocity to transform.
  559.      * @param <T> type of the field elements
  560.      * @return transformed time-stamped position-velocity
  561.      * @since 7.0
  562.      */
  563.     public <T extends RealFieldElement<T>> TimeStampedFieldPVCoordinates<T> transformPVCoordinates(final TimeStampedFieldPVCoordinates<T> pv) {
  564.         return angular.applyTo(new TimeStampedFieldPVCoordinates<>(pv.getDate(),
  565.                                                                    pv.getPosition().add(cartesian.getPosition()),
  566.                                                                    pv.getVelocity().add(cartesian.getVelocity()),
  567.                                                                    pv.getAcceleration().add(cartesian.getAcceleration())));
  568.     }

  570.     /** Compute the Jacobian of the {@link #transformPVCoordinates(PVCoordinates)}
  571.      * method of the transform.
  572.      * <p>
  573.      * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i
  574.      * of the transformed {@link PVCoordinates} with respect to Cartesian coordinate j
  575.      * of the input {@link PVCoordinates} in method {@link #transformPVCoordinates(PVCoordinates)}.
  576.      * </p>
  577.      * <p>
  578.      * This definition implies that if we define position-velocity coordinates
  579.      * <pre>
  580.      * PV₁ = transform.transformPVCoordinates(PV₀), then
  581.      * </pre>
  582.      * <p> their differentials dPV₁ and dPV₀ will obey the following relation
  583.      * where J is the matrix computed by this method:
  584.      * <pre>
  585.      * dPV₁ = J &times; dPV₀
  586.      * </pre>
  587.      *
  588.      * @param selector selector specifying the size of the upper left corner that must be filled
  589.      * (either 3x3 for positions only, 6x6 for positions and velocities, 9x9 for positions,
  590.      * velocities and accelerations)
  591.      * @param jacobian placeholder matrix whose upper-left corner is to be filled with
  592.      * the Jacobian, the rest of the matrix remaining untouched
  593.      */
  594.     public void getJacobian(final CartesianDerivativesFilter selector, final double[][] jacobian) {

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

  599.         // dP1/dP0
  600.         System.arraycopy(mData[0], 0, jacobian[0], 0, 3);
  601.         System.arraycopy(mData[1], 0, jacobian[1], 0, 3);
  602.         System.arraycopy(mData[2], 0, jacobian[2], 0, 3);

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

  606.             // dP1/dV0
  607.             Arrays.fill(jacobian[0], 3, 6, 0.0);
  608.             Arrays.fill(jacobian[1], 3, 6, 0.0);
  609.             Arrays.fill(jacobian[2], 3, 6, 0.0);

  611.             // dV1/dP0
  612.             final Vector3D o = angular.getRotationRate();
  613.             final double ox = o.getX();
  614.             final double oy = o.getY();
  615.             final double oz = o.getZ();
  616.             for (int i = 0; i < 3; ++i) {
  617.                 jacobian[3][i] = -(oy * mData[2][i] - oz * mData[1][i]);
  618.                 jacobian[4][i] = -(oz * mData[0][i] - ox * mData[2][i]);
  619.                 jacobian[5][i] = -(ox * mData[1][i] - oy * mData[0][i]);
  620.             }

  622.             // dV1/dV0
  623.             System.arraycopy(mData[0], 0, jacobian[3], 3, 3);
  624.             System.arraycopy(mData[1], 0, jacobian[4], 3, 3);
  625.             System.arraycopy(mData[2], 0, jacobian[5], 3, 3);

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

  629.                 // dP1/dA0
  630.                 Arrays.fill(jacobian[0], 6, 9, 0.0);
  631.                 Arrays.fill(jacobian[1], 6, 9, 0.0);
  632.                 Arrays.fill(jacobian[2], 6, 9, 0.0);

  634.                 // dV1/dA0
  635.                 Arrays.fill(jacobian[3], 6, 9, 0.0);
  636.                 Arrays.fill(jacobian[4], 6, 9, 0.0);
  637.                 Arrays.fill(jacobian[5], 6, 9, 0.0);

  639.                 // dA1/dP0
  640.                 final Vector3D oDot = angular.getRotationAcceleration();
  641.                 final double oDotx  = oDot.getX();
  642.                 final double oDoty  = oDot.getY();
  643.                 final double oDotz  = oDot.getZ();
  644.                 for (int i = 0; i < 3; ++i) {
  645.                     jacobian[6][i] = -(oDoty * mData[2][i] - oDotz * mData[1][i]) - (oy * jacobian[5][i] - oz * jacobian[4][i]);
  646.                     jacobian[7][i] = -(oDotz * mData[0][i] - oDotx * mData[2][i]) - (oz * jacobian[3][i] - ox * jacobian[5][i]);
  647.                     jacobian[8][i] = -(oDotx * mData[1][i] - oDoty * mData[0][i]) - (ox * jacobian[4][i] - oy * jacobian[3][i]);
  648.                 }

  650.                 // dA1/dV0
  651.                 for (int i = 0; i < 3; ++i) {
  652.                     jacobian[6][i + 3] = -2 * (oy * mData[2][i] - oz * mData[1][i]);
  653.                     jacobian[7][i + 3] = -2 * (oz * mData[0][i] - ox * mData[2][i]);
  654.                     jacobian[8][i + 3] = -2 * (ox * mData[1][i] - oy * mData[0][i]);
  655.                 }

  657.                 // dA1/dA0
  658.                 System.arraycopy(mData[0], 0, jacobian[6], 6, 3);
  659.                 System.arraycopy(mData[1], 0, jacobian[7], 6, 3);
  660.                 System.arraycopy(mData[2], 0, jacobian[8], 6, 3);

  662.             }

  664.         }

  666.     }

  668.     /** Get the underlying elementary Cartesian part.
  669.      * <p>A transform can be uniquely represented as an elementary
  670.      * translation followed by an elementary rotation. This method
  671.      * returns this unique elementary translation with its derivative.</p>
  672.      * @return underlying elementary Cartesian part
  673.      * @see #getTranslation()
  674.      * @see #getVelocity()
  675.      */
  676.     public PVCoordinates getCartesian() {
  677.         return cartesian;
  678.     }

  680.     /** Get the underlying elementary translation.
  681.      * <p>A transform can be uniquely represented as an elementary
  682.      * translation followed by an elementary rotation. This method
  683.      * returns this unique elementary translation.</p>
  684.      * @return underlying elementary translation
  685.      * @see #getCartesian()
  686.      * @see #getVelocity()
  687.      * @see #getAcceleration()
  688.      */
  689.     public Vector3D getTranslation() {
  690.         return cartesian.getPosition();
  691.     }

  693.     /** Get the first time derivative of the translation.
  694.      * @return first time derivative of the translation
  695.      * @see #getCartesian()
  696.      * @see #getTranslation()
  697.      * @see #getAcceleration()
  698.      */
  699.     public Vector3D getVelocity() {
  700.         return cartesian.getVelocity();
  701.     }

  703.     /** Get the second time derivative of the translation.
  704.      * @return second time derivative of the translation
  705.      * @see #getCartesian()
  706.      * @see #getTranslation()
  707.      * @see #getVelocity()
  708.      */
  709.     public Vector3D getAcceleration() {
  710.         return cartesian.getAcceleration();
  711.     }

  713.     /** Get the underlying elementary angular part.
  714.      * <p>A transform can be uniquely represented as an elementary
  715.      * translation followed by an elementary rotation. This method
  716.      * returns this unique elementary rotation with its derivative.</p>
  717.      * @return underlying elementary angular part
  718.      * @see #getRotation()
  719.      * @see #getRotationRate()
  720.      * @see #getRotationAcceleration()
  721.      */
  722.     public AngularCoordinates getAngular() {
  723.         return angular;
  724.     }

  726.     /** Get the underlying elementary rotation.
  727.      * <p>A transform can be uniquely represented as an elementary
  728.      * translation followed by an elementary rotation. This method
  729.      * returns this unique elementary rotation.</p>
  730.      * @return underlying elementary rotation
  731.      * @see #getAngular()
  732.      * @see #getRotationRate()
  733.      * @see #getRotationAcceleration()
  734.      */
  735.     public Rotation getRotation() {
  736.         return angular.getRotation();
  737.     }

  739.     /** Get the first time derivative of the rotation.
  740.      * <p>The norm represents the angular rate.</p>
  741.      * @return First time derivative of the rotation
  742.      * @see #getAngular()
  743.      * @see #getRotation()
  744.      * @see #getRotationAcceleration()
  745.      */
  746.     public Vector3D getRotationRate() {
  747.         return angular.getRotationRate();
  748.     }

  750.     /** Get the second time derivative of the rotation.
  751.      * @return Second time derivative of the rotation
  752.      * @see #getAngular()
  753.      * @see #getRotation()
  754.      * @see #getRotationRate()
  755.      */
  756.     public Vector3D getRotationAcceleration() {
  757.         return angular.getRotationAcceleration();
  758.     }

  760.     /** Specialized class for identity transform. */
  761.     private static class IdentityTransform extends Transform {

  763.         /** Serializable UID. */
  764.         private static final long serialVersionUID = -9042082036141830517L;

  766.         /** Simple constructor. */
  767.         IdentityTransform() {
  768.             super(AbsoluteDate.J2000_EPOCH, PVCoordinates.ZERO, AngularCoordinates.IDENTITY);
  769.         }

  771.         /** {@inheritDoc} */
  772.         @Override
  773.         public Transform shiftedBy(final double dt) {
  774.             return this;
  775.         }

  777.         /** {@inheritDoc} */
  778.         @Override
  779.         public Transform getInverse() {
  780.             return this;
  781.         }

  783.         /** {@inheritDoc} */
  784.         @Override
  785.         public Vector3D transformPosition(final Vector3D position) {
  786.             return position;
  787.         }

  789.         /** {@inheritDoc} */
  790.         @Override
  791.         public Vector3D transformVector(final Vector3D vector) {
  792.             return vector;
  793.         }

  795.         /** {@inheritDoc} */
  796.         @Override
  797.         public Line transformLine(final Line line) {
  798.             return line;
  799.         }

  801.         /** {@inheritDoc} */
  802.         @Override
  803.         public PVCoordinates transformPVCoordinates(final PVCoordinates pv) {
  804.             return pv;
  805.         }

  807.         /** {@inheritDoc} */
  808.         @Override
  809.         public void getJacobian(final CartesianDerivativesFilter selector, final double[][] jacobian) {
  810.             final int n = 3 * (selector.getMaxOrder() + 1);
  811.             for (int i = 0; i < n; ++i) {
  812.                 Arrays.fill(jacobian[i], 0, n, 0.0);
  813.                 jacobian[i][i] = 1.0;
  814.             }
  815.         }

  817.     }

  819. }
Created with JaCoCo 0.8.2.201808211720