TopocentricFrame.java

  1. /* Copyright 2002-2020 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 org.hipparchus.Field;
  20. import org.hipparchus.RealFieldElement;
  21. import org.hipparchus.analysis.UnivariateFunction;
  22. import org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver;
  23. import org.hipparchus.analysis.solvers.UnivariateSolver;
  24. import org.hipparchus.exception.MathRuntimeException;
  25. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  26. import org.hipparchus.geometry.euclidean.threed.Rotation;
  27. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  28. import org.hipparchus.util.FastMath;
  29. import org.hipparchus.util.MathUtils;
  30. import org.hipparchus.util.SinCos;
  31. import org.orekit.bodies.BodyShape;
  32. import org.orekit.bodies.FieldGeodeticPoint;
  33. import org.orekit.bodies.GeodeticPoint;
  34. import org.orekit.errors.OrekitException;
  35. import org.orekit.time.AbsoluteDate;
  36. import org.orekit.time.FieldAbsoluteDate;
  37. import org.orekit.utils.Constants;
  38. import org.orekit.utils.FieldPVCoordinates;
  39. import org.orekit.utils.PVCoordinates;
  40. import org.orekit.utils.PVCoordinatesProvider;
  41. import org.orekit.utils.TimeStampedPVCoordinates;


  44. /** Topocentric frame.
  45.  * <p>Frame associated to a position near the surface of a body shape.</p>
  46.  * <p>
  47.  * The origin of the frame is at the defining {@link GeodeticPoint geodetic point}
  48.  * location, and the right-handed canonical trihedra is:
  49.  * </p>
  50.  * <ul>
  51.  *   <li>X axis in the local horizontal plane (normal to zenith direction) and
  52.  *   following the local parallel towards East</li>
  53.  *   <li>Y axis in the horizontal plane (normal to zenith direction) and
  54.  *   following the local meridian towards North</li>
  55.  *   <li>Z axis towards Zenith direction</li>
  56.  * </ul>
  57.  * @author V&eacute;ronique Pommier-Maurussane
  58.  */
  59. public class TopocentricFrame extends Frame implements PVCoordinatesProvider {

  61.     /** Serializable UID. */
  62.     private static final long serialVersionUID = -5997915708080966466L;

  64.     /** Body shape on which the local point is defined. */
  65.     private final BodyShape parentShape;

  67.     /** Point where the topocentric frame is defined. */
  68.     private final GeodeticPoint point;

  70.     /** Simple constructor.
  71.      * @param parentShape body shape on which the local point is defined
  72.      * @param point local surface point where topocentric frame is defined
  73.      * @param name the string representation
  74.      */
  75.     public TopocentricFrame(final BodyShape parentShape, final GeodeticPoint point,
  76.                             final String name) {

  78.         super(parentShape.getBodyFrame(),
  79.               new Transform(AbsoluteDate.ARBITRARY_EPOCH,
  80.                             new Transform(AbsoluteDate.ARBITRARY_EPOCH,
  81.                                           parentShape.transform(point).negate()),
  82.                             new Transform(AbsoluteDate.ARBITRARY_EPOCH,
  83.                                           new Rotation(point.getEast(), point.getZenith(),
  84.                                                        Vector3D.PLUS_I, Vector3D.PLUS_K),
  85.                                           Vector3D.ZERO)),
  86.               name, false);
  87.         this.parentShape = parentShape;
  88.         this.point = point;
  89.     }

  91.     /** Get the body shape on which the local point is defined.
  92.      * @return body shape on which the local point is defined
  93.      */
  94.     public BodyShape getParentShape() {
  95.         return parentShape;
  96.     }

  98.     /** Get the surface point defining the origin of the frame.
  99.      * @return surface point defining the origin of the frame
  100.      */
  101.     public GeodeticPoint getPoint() {
  102.         return point;
  103.     }

  105.     /** Get the surface point defining the origin of the frame.
  106.      * @param <T> tyoe of the elements
  107.      * @param field of the elements
  108.      * @return surface point defining the origin of the frame
  109.      * @since 9.3
  110.      */
  111.     public <T extends RealFieldElement<T>> FieldGeodeticPoint<T> getPoint(final Field<T> field) {
  112.         final T zero = field.getZero();
  113.         return new FieldGeodeticPoint<>(zero.add(point.getLatitude()),
  114.                                         zero.add(point.getLongitude()),
  115.                                         zero.add(point.getAltitude()));
  116.     }

  118.     /** Get the zenith direction of topocentric frame, expressed in parent shape frame.
  119.      * <p>The zenith direction is defined as the normal to local horizontal plane.</p>
  120.      * @return unit vector in the zenith direction
  121.      * @see #getNadir()
  122.      */
  123.     public Vector3D getZenith() {
  124.         return point.getZenith();
  125.     }

  127.     /** Get the nadir direction of topocentric frame, expressed in parent shape frame.
  128.      * <p>The nadir direction is the opposite of zenith direction.</p>
  129.      * @return unit vector in the nadir direction
  130.      * @see #getZenith()
  131.      */
  132.     public Vector3D getNadir() {
  133.         return point.getNadir();
  134.     }

  136.    /** Get the north direction of topocentric frame, expressed in parent shape frame.
  137.      * <p>The north direction is defined in the horizontal plane
  138.      * (normal to zenith direction) and following the local meridian.</p>
  139.      * @return unit vector in the north direction
  140.      * @see #getSouth()
  141.      */
  142.     public Vector3D getNorth() {
  143.         return point.getNorth();
  144.     }

  146.     /** Get the south direction of topocentric frame, expressed in parent shape frame.
  147.      * <p>The south direction is the opposite of north direction.</p>
  148.      * @return unit vector in the south direction
  149.      * @see #getNorth()
  150.      */
  151.     public Vector3D getSouth() {
  152.         return point.getSouth();
  153.     }

  155.     /** Get the east direction of topocentric frame, expressed in parent shape frame.
  156.      * <p>The east direction is defined in the horizontal plane
  157.      * in order to complete direct triangle (east, north, zenith).</p>
  158.      * @return unit vector in the east direction
  159.      * @see #getWest()
  160.      */
  161.     public Vector3D getEast() {
  162.         return point.getEast();
  163.     }

  165.     /** Get the west direction of topocentric frame, expressed in parent shape frame.
  166.      * <p>The west direction is the opposite of east direction.</p>
  167.      * @return unit vector in the west direction
  168.      * @see #getEast()
  169.      */
  170.     public Vector3D getWest() {
  171.         return point.getWest();
  172.     }

  174.     /** Get the elevation of a point with regards to the local point.
  175.      * <p>The elevation is the angle between the local horizontal and
  176.      * the direction from local point to given point.</p>
  177.      * @param extPoint point for which elevation shall be computed
  178.      * @param frame frame in which the point is defined
  179.      * @param date computation date
  180.      * @return elevation of the point
  181.      */
  182.     public double getElevation(final Vector3D extPoint, final Frame frame,
  183.                                final AbsoluteDate date) {

  185.         // Transform given point from given frame to topocentric frame
  186.         final Transform t = frame.getTransformTo(this, date);
  187.         final Vector3D extPointTopo = t.transformPosition(extPoint);

  189.         // Elevation angle is PI/2 - angle between zenith and given point direction
  190.         return extPointTopo.getDelta();
  191.     }

  193.     /** Get the elevation of a point with regards to the local point.
  194.      * <p>The elevation is the angle between the local horizontal and
  195.      * the direction from local point to given point.</p>
  196.      * @param <T> type of the elements
  197.      * @param extPoint point for which elevation shall be computed
  198.      * @param frame frame in which the point is defined
  199.      * @param date computation date
  200.      * @return elevation of the point
  201.      * @since 9.3
  202.      */
  203.     public <T extends RealFieldElement<T>> T getElevation(final FieldVector3D<T> extPoint, final Frame frame,
  204.                                                           final FieldAbsoluteDate<T> date) {

  206.         // Transform given point from given frame to topocentric frame
  207.         final FieldTransform<T> t = frame.getTransformTo(this, date);
  208.         final FieldVector3D<T> extPointTopo = t.transformPosition(extPoint);

  210.         // Elevation angle is PI/2 - angle between zenith and given point direction
  211.         return extPointTopo.getDelta();
  212.     }

  214.     /** Get the azimuth of a point with regards to the topocentric frame center point.
  215.      * <p>The azimuth is the angle between the North direction at local point and
  216.      * the projection in local horizontal plane of the direction from local point
  217.      * to given point. Azimuth angles are counted clockwise, i.e positive towards the East.</p>
  218.      * @param extPoint point for which elevation shall be computed
  219.      * @param frame frame in which the point is defined
  220.      * @param date computation date
  221.      * @return azimuth of the point
  222.      */
  223.     public double getAzimuth(final Vector3D extPoint, final Frame frame,
  224.                              final AbsoluteDate date) {

  226.         // Transform given point from given frame to topocentric frame
  227.         final Transform t = getTransformTo(frame, date).getInverse();
  228.         final Vector3D extPointTopo = t.transformPosition(extPoint);

  230.         // Compute azimuth
  231.         double azimuth = FastMath.atan2(extPointTopo.getX(), extPointTopo.getY());
  232.         if (azimuth < 0.) {
  233.             azimuth += MathUtils.TWO_PI;
  234.         }
  235.         return azimuth;

  237.     }

  239.     /** Get the azimuth of a point with regards to the topocentric frame center point.
  240.      * <p>The azimuth is the angle between the North direction at local point and
  241.      * the projection in local horizontal plane of the direction from local point
  242.      * to given point. Azimuth angles are counted clockwise, i.e positive towards the East.</p>
  243.      * @param <T> type of the elements
  244.      * @param extPoint point for which elevation shall be computed
  245.      * @param frame frame in which the point is defined
  246.      * @param date computation date
  247.      * @return azimuth of the point
  248.      * @since 9.3
  249.      */
  250.     public <T extends RealFieldElement<T>> T getAzimuth(final FieldVector3D<T> extPoint, final Frame frame,
  251.                                                         final FieldAbsoluteDate<T> date) {

  253.         // Transform given point from given frame to topocentric frame
  254.         final FieldTransform<T> t = getTransformTo(frame, date).getInverse();
  255.         final FieldVector3D<T> extPointTopo = t.transformPosition(extPoint);

  257.         // Compute azimuth
  258.         T azimuth = FastMath.atan2(extPointTopo.getX(), extPointTopo.getY());
  259.         if (azimuth.getReal() < 0.) {
  260.             azimuth = azimuth.add(MathUtils.TWO_PI);
  261.         }
  262.         return azimuth;

  264.     }

  266.     /** Get the range of a point with regards to the topocentric frame center point.
  267.      * @param extPoint point for which range shall be computed
  268.      * @param frame frame in which the point is defined
  269.      * @param date computation date
  270.      * @return range (distance) of the point
  271.      */
  272.     public double getRange(final Vector3D extPoint, final Frame frame,
  273.                            final AbsoluteDate date) {

  275.         // Transform given point from given frame to topocentric frame
  276.         final Transform t = frame.getTransformTo(this, date);
  277.         final Vector3D extPointTopo = t.transformPosition(extPoint);

  279.         // Compute range
  280.         return extPointTopo.getNorm();

  282.     }

  284.     /** Get the range of a point with regards to the topocentric frame center point.
  285.      * @param <T> type of the elements
  286.      * @param extPoint point for which range shall be computed
  287.      * @param frame frame in which the point is defined
  288.      * @param date computation date
  289.      * @return range (distance) of the point
  290.      * @since 9.3
  291.      */
  292.     public <T extends RealFieldElement<T>> T getRange(final FieldVector3D<T> extPoint, final Frame frame,
  293.                                                       final FieldAbsoluteDate<T> date) {

  295.         // Transform given point from given frame to topocentric frame
  296.         final FieldTransform<T> t = frame.getTransformTo(this, date);
  297.         final FieldVector3D<T> extPointTopo = t.transformPosition(extPoint);

  299.         // Compute range
  300.         return extPointTopo.getNorm();

  302.     }

  304.     /** Get the range rate of a point with regards to the topocentric frame center point.
  305.      * @param extPV point/velocity for which range rate shall be computed
  306.      * @param frame frame in which the point is defined
  307.      * @param date computation date
  308.      * @return range rate of the point (positive if point departs from frame)
  309.      */
  310.     public double getRangeRate(final PVCoordinates extPV, final Frame frame,
  311.                                final AbsoluteDate date) {

  313.         // Transform given point from given frame to topocentric frame
  314.         final Transform t = frame.getTransformTo(this, date);
  315.         final PVCoordinates extPVTopo = t.transformPVCoordinates(extPV);

  317.         // Compute range rate (doppler) : relative rate along the line of sight
  318.         return Vector3D.dotProduct(extPVTopo.getPosition(), extPVTopo.getVelocity()) /
  319.                extPVTopo.getPosition().getNorm();

  321.     }

  323.     /** Get the range rate of a point with regards to the topocentric frame center point.
  324.      * @param <T> type of the elements
  325.      * @param extPV point/velocity for which range rate shall be computed
  326.      * @param frame frame in which the point is defined
  327.      * @param date computation date
  328.      * @return range rate of the point (positive if point departs from frame)
  329.      * @since 9.3
  330.      */
  331.     public <T extends RealFieldElement<T>> T getRangeRate(final FieldPVCoordinates<T> extPV, final Frame frame,
  332.                                                           final FieldAbsoluteDate<T> date) {

  334.         // Transform given point from given frame to topocentric frame
  335.         final FieldTransform<T> t = frame.getTransformTo(this, date);
  336.         final FieldPVCoordinates<T> extPVTopo = t.transformPVCoordinates(extPV);

  338.         // Compute range rate (doppler) : relative rate along the line of sight
  339.         return FieldVector3D.dotProduct(extPVTopo.getPosition(), extPVTopo.getVelocity()).divide(
  340.                extPVTopo.getPosition().getNorm());

  342.     }

  344.     /**
  345.      * Compute the limit visibility point for a satellite in a given direction.
  346.      * <p>
  347.      * This method can be used to compute visibility circles around ground stations
  348.      * for example, using a simple loop on azimuth, with either a fixed elevation
  349.      * or an elevation that depends on azimuth to take ground masks into account.
  350.      * </p>
  351.      * @param radius satellite distance to Earth center
  352.      * @param azimuth pointing azimuth from station
  353.      * @param elevation pointing elevation from station
  354.      * @return limit visibility point for the satellite
  355.      */
  356.     public GeodeticPoint computeLimitVisibilityPoint(final double radius,
  357.                                                      final double azimuth, final double elevation) {
  358.         try {
  359.             // convergence threshold on point position: 1mm
  360.             final double deltaP = 0.001;
  361.             final UnivariateSolver solver =
  362.                     new BracketingNthOrderBrentSolver(deltaP / Constants.WGS84_EARTH_EQUATORIAL_RADIUS,
  363.                                                       deltaP, deltaP, 5);

  365.             // find the distance such that a point in the specified direction and at the solved-for
  366.             // distance is exactly at the specified radius
  367.             final double distance = solver.solve(1000, new UnivariateFunction() {
  368.                 /** {@inheritDoc} */
  369.                 public double value(final double x) {
  370.                     final GeodeticPoint gp = pointAtDistance(azimuth, elevation, x);
  371.                     return parentShape.transform(gp).getNorm() - radius;
  372.                 }
  373.             }, 0, 2 * radius);

  375.             // return the limit point
  376.             return pointAtDistance(azimuth, elevation, distance);

  378.         } catch (MathRuntimeException mrte) {
  379.             throw new OrekitException(mrte);
  380.         }
  381.     }

  383.     /** Compute the point observed from the station at some specified distance.
  384.      * @param azimuth pointing azimuth from station
  385.      * @param elevation pointing elevation from station
  386.      * @param distance distance to station
  387.      * @return observed point
  388.      */
  389.     public GeodeticPoint pointAtDistance(final double azimuth, final double elevation,
  390.                                          final double distance) {
  391.         final SinCos scAz  = FastMath.sinCos(azimuth);
  392.         final SinCos scEl  = FastMath.sinCos(elevation);
  393.         final Vector3D  observed = new Vector3D(distance * scEl.cos() * scAz.sin(),
  394.                                                 distance * scEl.cos() * scAz.cos(),
  395.                                                 distance * scEl.sin());
  396.         return parentShape.transform(observed, this, AbsoluteDate.ARBITRARY_EPOCH);
  397.     }

  399.     /** Get the {@link PVCoordinates} of the topocentric frame origin in the selected frame.
  400.      * @param date current date
  401.      * @param frame the frame where to define the position
  402.      * @return position/velocity of the topocentric frame origin (m and m/s)
  403.      */
  404.     public TimeStampedPVCoordinates getPVCoordinates(final AbsoluteDate date, final Frame frame) {
  405.         return getTransformTo(frame, date).transformPVCoordinates(new TimeStampedPVCoordinates(date,
  406.                                                                                                Vector3D.ZERO,
  407.                                                                                                Vector3D.ZERO,
  408.                                                                                                Vector3D.ZERO));
  409.     }

  411. }
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