Orbit.java

  1. /* Copyright 2002-2016 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.orbits;

  19. import java.io.Serializable;

  21. import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
  22. import org.apache.commons.math3.linear.DecompositionSolver;
  23. import org.apache.commons.math3.linear.MatrixUtils;
  24. import org.apache.commons.math3.linear.QRDecomposition;
  25. import org.apache.commons.math3.linear.RealMatrix;
  26. import org.apache.commons.math3.util.FastMath;
  27. import org.orekit.errors.OrekitIllegalArgumentException;
  28. import org.orekit.errors.OrekitException;
  29. import org.orekit.errors.OrekitInternalError;
  30. import org.orekit.errors.OrekitMessages;
  31. import org.orekit.frames.Frame;
  32. import org.orekit.frames.Transform;
  33. import org.orekit.time.AbsoluteDate;
  34. import org.orekit.time.TimeInterpolable;
  35. import org.orekit.time.TimeShiftable;
  36. import org.orekit.time.TimeStamped;
  37. import org.orekit.utils.PVCoordinatesProvider;
  38. import org.orekit.utils.TimeStampedPVCoordinates;

  40. /**
  41.  * This class handles orbital parameters.

  43.  * <p>
  44.  * For user convenience, both the Cartesian and the equinoctial elements
  45.  * are provided by this class, regardless of the canonical representation
  46.  * implemented in the derived class (which may be classical keplerian
  47.  * elements for example).
  48.  * </p>
  49.  * <p>
  50.  * The parameters are defined in a frame specified by the user. It is important
  51.  * to make sure this frame is consistent: it probably is inertial and centered
  52.  * on the central body. This information is used for example by some
  53.  * force models.
  54.  * </p>
  55.  * <p>
  56.  * The object <code>OrbitalParameters</code> is guaranteed to be immutable.
  57.  * </p>
  58.  * @author Luc Maisonobe
  59.  * @author Guylaine Prat
  60.  * @author Fabien Maussion
  61.  * @author V&eacute;ronique Pommier-Maurussane
  62.  */
  63. public abstract class Orbit
  64.     implements TimeStamped, TimeShiftable<Orbit>, TimeInterpolable<Orbit>,
  65.                Serializable, PVCoordinatesProvider {

  67.     /** Serializable UID. */
  68.     private static final long serialVersionUID = 438733454597999578L;

  70.     /** Frame in which are defined the orbital parameters. */
  71.     private final Frame frame;

  73.     /** Date of the orbital parameters. */
  74.     private final AbsoluteDate date;

  76.     /** Value of mu used to compute position and velocity (m³/s²). */
  77.     private final double mu;

  79.     /** Computed PVCoordinates. */
  80.     private transient TimeStampedPVCoordinates pvCoordinates;

  82.     /** Jacobian of the orbital parameters with mean angle with respect to the Cartesian coordinates. */
  83.     private transient double[][] jacobianMeanWrtCartesian;

  85.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with mean angle. */
  86.     private transient double[][] jacobianWrtParametersMean;

  88.     /** Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian coordinates. */
  89.     private transient double[][] jacobianEccentricWrtCartesian;

  91.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with eccentric angle. */
  92.     private transient double[][] jacobianWrtParametersEccentric;

  94.     /** Jacobian of the orbital parameters with true angle with respect to the Cartesian coordinates. */
  95.     private transient double[][] jacobianTrueWrtCartesian;

  97.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with true angle. */
  98.     private transient double[][] jacobianWrtParametersTrue;

  100.     /** Default constructor.
  101.      * Build a new instance with arbitrary default elements.
  102.      * @param frame the frame in which the parameters are defined
  103.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  104.      * @param date date of the orbital parameters
  105.      * @param mu central attraction coefficient (m^3/s^2)
  106.      * @exception IllegalArgumentException if frame is not a {@link
  107.      * Frame#isPseudoInertial pseudo-inertial frame}
  108.      */
  109.     protected Orbit(final Frame frame, final AbsoluteDate date, final double mu)
  110.         throws IllegalArgumentException {
  111.         ensurePseudoInertialFrame(frame);
  112.         this.date                      = date;
  113.         this.mu                        = mu;
  114.         this.pvCoordinates             = null;
  115.         this.frame                     = frame;
  116.         jacobianMeanWrtCartesian       = null;
  117.         jacobianWrtParametersMean      = null;
  118.         jacobianEccentricWrtCartesian  = null;
  119.         jacobianWrtParametersEccentric = null;
  120.         jacobianTrueWrtCartesian       = null;
  121.         jacobianWrtParametersTrue      = null;
  122.     }

  124.     /** Set the orbit from Cartesian parameters.
  125.      *
  126.      * <p> The acceleration provided in {@code pvCoordinates} is accessible using
  127.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  128.      * use {@code mu} and the position to compute the acceleration, including
  129.      * {@link #shiftedBy(double)} and {@link #getPVCoordinates(AbsoluteDate, Frame)}.
  130.      *
  131.      * @param pvCoordinates the position and velocity in the inertial frame
  132.      * @param frame the frame in which the {@link TimeStampedPVCoordinates} are defined
  133.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  134.      * @param mu central attraction coefficient (m^3/s^2)
  135.      * @exception IllegalArgumentException if frame is not a {@link
  136.      * Frame#isPseudoInertial pseudo-inertial frame}
  137.      */
  138.     protected Orbit(final TimeStampedPVCoordinates pvCoordinates, final Frame frame, final double mu)
  139.         throws IllegalArgumentException {
  140.         ensurePseudoInertialFrame(frame);
  141.         this.date = pvCoordinates.getDate();
  142.         this.mu = mu;
  143.         if (pvCoordinates.getAcceleration().getNormSq() == 0) {
  144.             // the acceleration was not provided,
  145.             // compute it from Newtonian attraction
  146.             final double r2 = pvCoordinates.getPosition().getNormSq();
  147.             final double r3 = r2 * FastMath.sqrt(r2);
  148.             this.pvCoordinates = new TimeStampedPVCoordinates(pvCoordinates.getDate(),
  149.                                                               pvCoordinates.getPosition(),
  150.                                                               pvCoordinates.getVelocity(),
  151.                                                               new Vector3D(-mu / r3, pvCoordinates.getPosition()));
  152.         } else {
  153.             this.pvCoordinates = pvCoordinates;
  154.         }
  155.         this.frame = frame;
  156.     }

  158.     /** Get the orbit type.
  159.      * @return orbit type
  160.      */
  161.     public abstract OrbitType getType();

  163.     /** Ensure the defining frame is a pseudo-inertial frame.
  164.      * @param frame frame to check
  165.      * @exception IllegalArgumentException if frame is not a {@link
  166.      * Frame#isPseudoInertial pseudo-inertial frame}
  167.      */
  168.     private static void ensurePseudoInertialFrame(final Frame frame)
  169.         throws IllegalArgumentException {
  170.         if (!frame.isPseudoInertial()) {
  171.             throw new OrekitIllegalArgumentException(OrekitMessages.NON_PSEUDO_INERTIAL_FRAME,
  172.                                                      frame.getName());
  173.         }
  174.     }

  176.     /** Get the frame in which the orbital parameters are defined.
  177.      * @return frame in which the orbital parameters are defined
  178.      */
  179.     public Frame getFrame() {
  180.         return frame;
  181.     }

  183.     /** Get the semi-major axis.
  184.      * <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
  185.      * @return semi-major axis (m)
  186.      */
  187.     public abstract double getA();

  189.     /** Get the first component of the equinoctial eccentricity vector.
  190.      * @return first component of the equinoctial eccentricity vector
  191.      */
  192.     public abstract double getEquinoctialEx();

  194.     /** Get the second component of the equinoctial eccentricity vector.
  195.      * @return second component of the equinoctial eccentricity vector
  196.      */
  197.     public abstract double getEquinoctialEy();

  199.     /** Get the first component of the inclination vector.
  200.      * @return first component of the inclination vector
  201.      */
  202.     public abstract double getHx();

  204.     /** Get the second component of the inclination vector.
  205.      * @return second component of the inclination vector
  206.      */
  207.     public abstract double getHy();

  209.     /** Get the eccentric longitude argument.
  210.      * @return E + ω + Ω eccentric longitude argument (rad)
  211.      */
  212.     public abstract double getLE();

  214.     /** Get the true longitude argument.
  215.      * @return v + ω + Ω true longitude argument (rad)
  216.      */
  217.     public abstract double getLv();

  219.     /** Get the mean longitude argument.
  220.      * @return M + ω + Ω mean longitude argument (rad)
  221.      */
  222.     public abstract double getLM();

  224.     // Additional orbital elements

  226.     /** Get the eccentricity.
  227.      * @return eccentricity
  228.      */
  229.     public abstract double getE();

  231.     /** Get the inclination.
  232.      * @return inclination (rad)
  233.      */
  234.     public abstract double getI();

  236.     /** Get the central acceleration constant.
  237.      * @return central acceleration constant
  238.      */
  239.     public double getMu() {
  240.         return mu;
  241.     }

  243.     /** Get the keplerian period.
  244.      * <p>The keplerian period is computed directly from semi major axis
  245.      * and central acceleration constant.</p>
  246.      * @return keplerian period in seconds, or positive infinity for hyperbolic orbits
  247.      */
  248.     public double getKeplerianPeriod() {
  249.         final double a = getA();
  250.         return (a < 0) ? Double.POSITIVE_INFINITY : 2.0 * FastMath.PI * a * FastMath.sqrt(a / mu);
  251.     }

  253.     /** Get the keplerian mean motion.
  254.      * <p>The keplerian mean motion is computed directly from semi major axis
  255.      * and central acceleration constant.</p>
  256.      * @return keplerian mean motion in radians per second
  257.      */
  258.     public double getKeplerianMeanMotion() {
  259.         final double absA = FastMath.abs(getA());
  260.         return FastMath.sqrt(mu / absA) / absA;
  261.     }

  263.     /** Get the date of orbital parameters.
  264.      * @return date of the orbital parameters
  265.      */
  266.     public AbsoluteDate getDate() {
  267.         return date;
  268.     }

  270.     /** Get the {@link TimeStampedPVCoordinates} in a specified frame.
  271.      * @param outputFrame frame in which the position/velocity coordinates shall be computed
  272.      * @return pvCoordinates in the specified output frame
  273.      * @exception OrekitException if transformation between frames cannot be computed
  274.      * @see #getPVCoordinates()
  275.      */
  276.     public TimeStampedPVCoordinates getPVCoordinates(final Frame outputFrame)
  277.         throws OrekitException {
  278.         if (pvCoordinates == null) {
  279.             pvCoordinates = initPVCoordinates();
  280.         }

  282.         // If output frame requested is the same as definition frame,
  283.         // PV coordinates are returned directly
  284.         if (outputFrame == frame) {
  285.             return pvCoordinates;
  286.         }

  288.         // Else, PV coordinates are transformed to output frame
  289.         final Transform t = frame.getTransformTo(outputFrame, date);
  290.         return t.transformPVCoordinates(pvCoordinates);
  291.     }

  293.     /** {@inheritDoc} */
  294.     public TimeStampedPVCoordinates getPVCoordinates(final AbsoluteDate otherDate, final Frame otherFrame)
  295.         throws OrekitException {
  296.         return shiftedBy(otherDate.durationFrom(getDate())).getPVCoordinates(otherFrame);
  297.     }


  300.     /** Get the {@link TimeStampedPVCoordinates} in definition frame.
  301.      * @return pvCoordinates in the definition frame
  302.      * @see #getPVCoordinates(Frame)
  303.      */
  304.     public TimeStampedPVCoordinates getPVCoordinates() {
  305.         if (pvCoordinates == null) {
  306.             pvCoordinates = initPVCoordinates();
  307.         }
  308.         return pvCoordinates;
  309.     }

  311.     /** Compute the position/velocity coordinates from the canonical parameters.
  312.      * @return computed position/velocity coordinates
  313.      */
  314.     protected abstract TimeStampedPVCoordinates initPVCoordinates();

  316.     /** Get a time-shifted orbit.
  317.      * <p>
  318.      * The orbit can be slightly shifted to close dates. This shift is based on
  319.      * a simple keplerian model. It is <em>not</em> intended as a replacement
  320.      * for proper orbit and attitude propagation but should be sufficient for
  321.      * small time shifts or coarse accuracy.
  322.      * </p>
  323.      * @param dt time shift in seconds
  324.      * @return a new orbit, shifted with respect to the instance (which is immutable)
  325.      */
  326.     public abstract Orbit shiftedBy(final double dt);

  328.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  329.      * <p>
  330.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  331.      * respect to Cartesian coordinate j. This means each row corresponds to one orbital parameter
  332.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  333.      * </p>
  334.      * @param type type of the position angle to use
  335.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  336.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  337.      */
  338.     public void getJacobianWrtCartesian(final PositionAngle type, final double[][] jacobian) {

  340.         final double[][] cachedJacobian;
  341.         synchronized (this) {
  342.             switch (type) {
  343.                 case MEAN :
  344.                     if (jacobianMeanWrtCartesian == null) {
  345.                         // first call, we need to compute the jacobian and cache it
  346.                         jacobianMeanWrtCartesian = computeJacobianMeanWrtCartesian();
  347.                     }
  348.                     cachedJacobian = jacobianMeanWrtCartesian;
  349.                     break;
  350.                 case ECCENTRIC :
  351.                     if (jacobianEccentricWrtCartesian == null) {
  352.                         // first call, we need to compute the jacobian and cache it
  353.                         jacobianEccentricWrtCartesian = computeJacobianEccentricWrtCartesian();
  354.                     }
  355.                     cachedJacobian = jacobianEccentricWrtCartesian;
  356.                     break;
  357.                 case TRUE :
  358.                     if (jacobianTrueWrtCartesian == null) {
  359.                         // first call, we need to compute the jacobian and cache it
  360.                         jacobianTrueWrtCartesian = computeJacobianTrueWrtCartesian();
  361.                     }
  362.                     cachedJacobian = jacobianTrueWrtCartesian;
  363.                     break;
  364.                 default :
  365.                     throw new OrekitInternalError(null);
  366.             }
  367.         }

  369.         // fill the user provided array
  370.         for (int i = 0; i < cachedJacobian.length; ++i) {
  371.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  372.         }

  374.     }

  376.     /** Compute the Jacobian of the Cartesian parameters with respect to the orbital parameters.
  377.      * <p>
  378.      * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i of the orbit with
  379.      * respect to orbital parameter j. This means each row corresponds to one Cartesian coordinate
  380.      * x, y, z, xdot, ydot, zdot whereas columns 0 to 5 correspond to the orbital parameters.
  381.      * </p>
  382.      * @param type type of the position angle to use
  383.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  384.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  385.      */
  386.     public void getJacobianWrtParameters(final PositionAngle type, final double[][] jacobian) {

  388.         final double[][] cachedJacobian;
  389.         synchronized (this) {
  390.             switch (type) {
  391.                 case MEAN :
  392.                     if (jacobianWrtParametersMean == null) {
  393.                         // first call, we need to compute the jacobian and cache it
  394.                         jacobianWrtParametersMean = createInverseJacobian(type);
  395.                     }
  396.                     cachedJacobian = jacobianWrtParametersMean;
  397.                     break;
  398.                 case ECCENTRIC :
  399.                     if (jacobianWrtParametersEccentric == null) {
  400.                         // first call, we need to compute the jacobian and cache it
  401.                         jacobianWrtParametersEccentric = createInverseJacobian(type);
  402.                     }
  403.                     cachedJacobian = jacobianWrtParametersEccentric;
  404.                     break;
  405.                 case TRUE :
  406.                     if (jacobianWrtParametersTrue == null) {
  407.                         // first call, we need to compute the jacobian and cache it
  408.                         jacobianWrtParametersTrue = createInverseJacobian(type);
  409.                     }
  410.                     cachedJacobian = jacobianWrtParametersTrue;
  411.                     break;
  412.                 default :
  413.                     throw new OrekitInternalError(null);
  414.             }
  415.         }

  417.         // fill the user-provided array
  418.         for (int i = 0; i < cachedJacobian.length; ++i) {
  419.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  420.         }

  422.     }

  424.     /** Create an inverse Jacobian.
  425.      * @param type type of the position angle to use
  426.      * @return inverse Jacobian
  427.      */
  428.     private double[][] createInverseJacobian(final PositionAngle type) {

  430.         // get the direct Jacobian
  431.         final double[][] directJacobian = new double[6][6];
  432.         getJacobianWrtCartesian(type, directJacobian);

  434.         // invert the direct Jacobian
  435.         final RealMatrix matrix = MatrixUtils.createRealMatrix(directJacobian);
  436.         final DecompositionSolver solver = new QRDecomposition(matrix).getSolver();
  437.         return solver.getInverse().getData();

  439.     }

  441.     /** Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.
  442.      * <p>
  443.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  444.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  445.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  446.      * </p>
  447.      * @return 6x6 Jacobian matrix
  448.      * @see #computeJacobianEccentricWrtCartesian()
  449.      * @see #computeJacobianTrueWrtCartesian()
  450.      */
  451.     protected abstract double[][] computeJacobianMeanWrtCartesian();

  453.     /** Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
  454.      * <p>
  455.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  456.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  457.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  458.      * </p>
  459.      * @return 6x6 Jacobian matrix
  460.      * @see #computeJacobianMeanWrtCartesian()
  461.      * @see #computeJacobianTrueWrtCartesian()
  462.      */
  463.     protected abstract double[][] computeJacobianEccentricWrtCartesian();

  465.     /** Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
  466.      * <p>
  467.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  468.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  469.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  470.      * </p>
  471.      * @return 6x6 Jacobian matrix
  472.      * @see #computeJacobianMeanWrtCartesian()
  473.      * @see #computeJacobianEccentricWrtCartesian()
  474.      */
  475.     protected abstract double[][] computeJacobianTrueWrtCartesian();

  477.     /** Add the contribution of the Keplerian motion to parameters derivatives
  478.      * <p>
  479.      * This method is used by integration-based propagators to evaluate the part of Keplerian
  480.      * motion to evolution of the orbital state.
  481.      * </p>
  482.      * @param type type of the position angle in the state
  483.      * @param gm attraction coefficient to use
  484.      * @param pDot array containing orbital state derivatives to update (the Keplerian
  485.      * part must be <em>added</em> to the array components, as the array may already
  486.      * contain some non-zero elements corresponding to non-Keplerian parts)
  487.      */
  488.     public abstract void addKeplerContribution(final PositionAngle type, final double gm, double[] pDot);

  490.         /** Fill a Jacobian half row with a single vector.
  491.      * @param a coefficient of the vector
  492.      * @param v vector
  493.      * @param row Jacobian matrix row
  494.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  495.      */
  496.     protected static void fillHalfRow(final double a, final Vector3D v, final double[] row, final int j) {
  497.         row[j]     = a * v.getX();
  498.         row[j + 1] = a * v.getY();
  499.         row[j + 2] = a * v.getZ();
  500.     }

  502.     /** Fill a Jacobian half row with a linear combination of vectors.
  503.      * @param a1 coefficient of the first vector
  504.      * @param v1 first vector
  505.      * @param a2 coefficient of the second vector
  506.      * @param v2 second vector
  507.      * @param row Jacobian matrix row
  508.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  509.      */
  510.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  511.                                       final double[] row, final int j) {
  512.         row[j]     = a1 * v1.getX() + a2 * v2.getX();
  513.         row[j + 1] = a1 * v1.getY() + a2 * v2.getY();
  514.         row[j + 2] = a1 * v1.getZ() + a2 * v2.getZ();
  515.     }

  517.     /** Fill a Jacobian half row with a linear combination of vectors.
  518.      * @param a1 coefficient of the first vector
  519.      * @param v1 first vector
  520.      * @param a2 coefficient of the second vector
  521.      * @param v2 second vector
  522.      * @param a3 coefficient of the third vector
  523.      * @param v3 third vector
  524.      * @param row Jacobian matrix row
  525.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  526.      */
  527.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  528.                                       final double a3, final Vector3D v3,
  529.                                       final double[] row, final int j) {
  530.         row[j]     = a1 * v1.getX() + a2 * v2.getX() + a3 * v3.getX();
  531.         row[j + 1] = a1 * v1.getY() + a2 * v2.getY() + a3 * v3.getY();
  532.         row[j + 2] = a1 * v1.getZ() + a2 * v2.getZ() + a3 * v3.getZ();
  533.     }

  535.     /** Fill a Jacobian half row with a linear combination of vectors.
  536.      * @param a1 coefficient of the first vector
  537.      * @param v1 first vector
  538.      * @param a2 coefficient of the second vector
  539.      * @param v2 second vector
  540.      * @param a3 coefficient of the third vector
  541.      * @param v3 third vector
  542.      * @param a4 coefficient of the fourth vector
  543.      * @param v4 fourth vector
  544.      * @param row Jacobian matrix row
  545.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  546.      */
  547.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  548.                                       final double a3, final Vector3D v3, final double a4, final Vector3D v4,
  549.                                       final double[] row, final int j) {
  550.         row[j]     = a1 * v1.getX() + a2 * v2.getX() + a3 * v3.getX() + a4 * v4.getX();
  551.         row[j + 1] = a1 * v1.getY() + a2 * v2.getY() + a3 * v3.getY() + a4 * v4.getY();
  552.         row[j + 2] = a1 * v1.getZ() + a2 * v2.getZ() + a3 * v3.getZ() + a4 * v4.getZ();
  553.     }

  555.     /** Fill a Jacobian half row with a linear combination of vectors.
  556.      * @param a1 coefficient of the first vector
  557.      * @param v1 first vector
  558.      * @param a2 coefficient of the second vector
  559.      * @param v2 second vector
  560.      * @param a3 coefficient of the third vector
  561.      * @param v3 third vector
  562.      * @param a4 coefficient of the fourth vector
  563.      * @param v4 fourth vector
  564.      * @param a5 coefficient of the fifth vector
  565.      * @param v5 fifth vector
  566.      * @param row Jacobian matrix row
  567.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  568.      */
  569.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  570.                                       final double a3, final Vector3D v3, final double a4, final Vector3D v4,
  571.                                       final double a5, final Vector3D v5,
  572.                                       final double[] row, final int j) {
  573.         row[j]     = a1 * v1.getX() + a2 * v2.getX() + a3 * v3.getX() + a4 * v4.getX() + a5 * v5.getX();
  574.         row[j + 1] = a1 * v1.getY() + a2 * v2.getY() + a3 * v3.getY() + a4 * v4.getY() + a5 * v5.getY();
  575.         row[j + 2] = a1 * v1.getZ() + a2 * v2.getZ() + a3 * v3.getZ() + a4 * v4.getZ() + a5 * v5.getZ();
  576.     }

  578.     /** Fill a Jacobian half row with a linear combination of vectors.
  579.      * @param a1 coefficient of the first vector
  580.      * @param v1 first vector
  581.      * @param a2 coefficient of the second vector
  582.      * @param v2 second vector
  583.      * @param a3 coefficient of the third vector
  584.      * @param v3 third vector
  585.      * @param a4 coefficient of the fourth vector
  586.      * @param v4 fourth vector
  587.      * @param a5 coefficient of the fifth vector
  588.      * @param v5 fifth vector
  589.      * @param a6 coefficient of the sixth vector
  590.      * @param v6 sixth vector
  591.      * @param row Jacobian matrix row
  592.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  593.      */
  594.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  595.                                       final double a3, final Vector3D v3, final double a4, final Vector3D v4,
  596.                                       final double a5, final Vector3D v5, final double a6, final Vector3D v6,
  597.                                       final double[] row, final int j) {
  598.         row[j]     = a1 * v1.getX() + a2 * v2.getX() + a3 * v3.getX() + a4 * v4.getX() + a5 * v5.getX() + a6 * v6.getX();
  599.         row[j + 1] = a1 * v1.getY() + a2 * v2.getY() + a3 * v3.getY() + a4 * v4.getY() + a5 * v5.getY() + a6 * v6.getY();
  600.         row[j + 2] = a1 * v1.getZ() + a2 * v2.getZ() + a3 * v3.getZ() + a4 * v4.getZ() + a5 * v5.getZ() + a6 * v6.getZ();
  601.     }

  603. }
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