Package org.orekit.bodies

Class OneAxisEllipsoid

java.lang.Object
org.orekit.bodies.Ellipsoid
org.orekit.bodies.OneAxisEllipsoid
All Implemented Interfaces:
BodyShape
Direct Known Subclasses:
ReferenceEllipsoid
public class OneAxisEllipsoid extends Ellipsoid implements BodyShape
Modeling of a one-axis ellipsoid.

One-axis ellipsoids is a good approximate model for most planet-size and larger natural bodies. It is the equilibrium shape reached by a fluid body under its own gravity field when it rotates. The symmetry axis is the rotation or polar axis.

Author:
Luc Maisonobe, Guylaine Prat

  • Constructor Details

  • Method Details

    • setAngularThreshold

      public void setAngularThreshold(double angularThreshold)
      Set the angular convergence threshold.

      The angular threshold is used both to identify points close to the ellipse axes and as the convergence threshold used to stop the iterations in the transform(Vector3D, Frame, AbsoluteDate) method.

      If this method is not called, the default value is set to 10-12.

      Parameters:
      angularThreshold - angular convergence threshold (rad)

    • getEquatorialRadius

      public double getEquatorialRadius()
      Get the equatorial radius of the body.
      Returns:
      equatorial radius of the body (m)

    • getFlattening

      public double getFlattening()
      Get the flattening of the body: f = (a-b)/a.
      Returns:
      the flattening

    • getEccentricitySquared

      public double getEccentricitySquared()
      Get the first eccentricity squared of the ellipsoid: e^2 = f * (2.0 - f).
      Returns:
      the eccentricity squared

    • getEccentricity

      public double getEccentricity()
      Get the first eccentricity of the ellipsoid: e = sqrt(f * (2.0 - f)).
      Returns:
      the eccentricity

    • getBodyFrame

      public Frame getBodyFrame()
      Get body frame related to body shape.

      Be mindful that the OneAxisEllipsoid.getBodyFrame() and the OneAxisEllipsoid.getFrame() methods return the same object.

      Specified by:
      getBodyFrame in interface BodyShape
      Returns:
      body frame related to body shape

    • getCartesianIntersectionPoint

      public Vector3D getCartesianIntersectionPoint(Line line, Vector3D close, Frame frame, AbsoluteDate date)
      Get the intersection point of a line with the surface of the body.

      A line may have several intersection points with a closed surface (we consider the one point case as a degenerated two points case). The close parameter is used to select which of these points should be returned. The selected point is the one that is closest to the close point.

      This method is similar to pointAtAltitude(Line, double, Vector3D, Frame, AbsoluteDate) pointAtAltitude} except it returns a point in the body frame (the other method returns a point in the sameframe as the input line)

      Parameters:
      line - test line (may intersect the body or not)
      close - point used for intersections selection
      frame - frame in which line is expressed
      date - date of the line in given frame
      Returns:
      intersection point in body frame at altitude zero or null if the line does not intersect the surface
      Since:
      9.3

    • getIntersectionPoint

      public GeodeticPoint getIntersectionPoint(Line line, Vector3D close, Frame frame, AbsoluteDate date)
      Get the intersection point of a line with the surface of the body.

      A line may have several intersection points with a closed surface (we consider the one point case as a degenerated two points case). The close parameter is used to select which of these points should be returned. The selected point is the one that is closest to the close point.

      Specified by:
      getIntersectionPoint in interface BodyShape
      Parameters:
      line - test line (may intersect the body or not)
      close - point used for intersections selection
      frame - frame in which line is expressed
      date - date of the line in given frame
      Returns:
      intersection point at altitude zero or null if the line does not intersect the surface

    • getCartesianIntersectionPoint

      public <T extends CalculusFieldElement<T>> FieldVector3D<T> getCartesianIntersectionPoint(FieldLine<T> line, FieldVector3D<T> close, Frame frame, FieldAbsoluteDate<T> date)
      Get the intersection point of a line with the surface of the body.

      A line may have several intersection points with a closed surface (we consider the one point case as a degenerated two points case). The close parameter is used to select which of these points should be returned. The selected point is the one that is closest to the close point.

      This method is similar to pointAtAltitude except it returns a point in the body frame (the other method returns a point in the same frame as the input line)

      Type Parameters:
      T - type of the field elements
      Parameters:
      line - test line (may intersect the body or not)
      close - point used for intersections selection
      frame - frame in which line is expressed
      date - date of the line in given frame
      Returns:
      intersection point in body frame at altitude zero or null if the line does not intersect the surface
      Since:
      9.3

    • getIntersectionPoint

      public <T extends CalculusFieldElement<T>> FieldGeodeticPoint<T> getIntersectionPoint(FieldLine<T> line, FieldVector3D<T> close, Frame frame, FieldAbsoluteDate<T> date)
      Get the intersection point of a line with the surface of the body.

      A line may have several intersection points with a closed surface (we consider the one point case as a degenerated two points case). The close parameter is used to select which of these points should be returned. The selected point is the one that is closest to the close point.

      Specified by:
      getIntersectionPoint in interface BodyShape
      Type Parameters:
      T - type of the field elements
      Parameters:
      line - test line (may intersect the body or not)
      close - point used for intersections selection
      frame - frame in which line is expressed
      date - date of the line in given frame
      Returns:
      intersection point at altitude zero or null if the line does not intersect the surface

    • transform

      public Vector3D transform(GeodeticPoint point)
      Transform a surface-relative point to a Cartesian point.
      Specified by:
      transform in interface BodyShape
      Parameters:
      point - surface-relative point
      Returns:
      point at the same location but as a Cartesian point

    • transform

      public <T extends CalculusFieldElement<T>> FieldVector3D<T> transform(FieldGeodeticPoint<T> point)
      Transform a surface-relative point to a Cartesian point.
      Specified by:
      transform in interface BodyShape
      Type Parameters:
      T - type of the filed elements
      Parameters:
      point - surface-relative point
      Returns:
      point at the same location but as a Cartesian point

    • projectToGround

      public Vector3D projectToGround(Vector3D point, AbsoluteDate date, Frame frame)
      Project a point to the ground.
      Specified by:
      projectToGround in interface BodyShape
      Parameters:
      point - point to project
      date - current date
      frame - frame in which moving point is expressed
      Returns:
      ground point exactly at the local vertical of specified point, in the same frame as specified point
      See Also:

    • projectToGround

      public TimeStampedPVCoordinates projectToGround(TimeStampedPVCoordinates pv, Frame frame)
      Project a moving point to the ground.
      Specified by:
      projectToGround in interface BodyShape
      Parameters:
      pv - moving point
      frame - frame in which moving point is expressed
      Returns:
      ground point exactly at the local vertical of specified point, in the same frame as specified point
      See Also:

    • transform

      public GeodeticPoint transform(Vector3D point, Frame frame, AbsoluteDate date)
      Transform a Cartesian point to a surface-relative point.

      This method is based on Toshio Fukushima's algorithm which uses Halley's method. transformation from Cartesian to Geodetic Coordinates Accelerated by Halley's Method, Toshio Fukushima, Journal of Geodesy 9(12):689-693, February 2006

      Some changes have been added to the original method:

      • in order to handle more accurately corner cases near the pole
      • in order to handle properly corner cases near the equatorial plane, even far inside the ellipsoid
      • in order to handle very flat ellipsoids

      In some rare cases (for example very flat ellipsoid, or points close to ellipsoid center), the loop may fail to converge. As this seems to happen only in degenerate cases, a design choice was to return an approximate point corresponding to last iteration. This point may be incorrect and fail to give the initial point back if doing roundtrip by calling transform(GeodeticPoint). This design choice was made to avoid NaNs appearing for example in inter-satellites visibility checks when two satellites are almost on opposite sides of Earth. The intermediate points far within the Earth should not prevent the detection algorithm to find visibility start/end.

      Specified by:
      transform in interface BodyShape
      Parameters:
      point - Cartesian point
      frame - frame in which Cartesian point is expressed
      date - date of the computation (used for frames conversions)
      Returns:
      point at the same location but as a surface-relative point

    • transform

      public <T extends CalculusFieldElement<T>> FieldGeodeticPoint<T> transform(FieldVector3D<T> point, Frame frame, FieldAbsoluteDate<T> date)
      Transform a Cartesian point to a surface-relative point.

      This method is based on Toshio Fukushima's algorithm which uses Halley's method. transformation from Cartesian to Geodetic Coordinates Accelerated by Halley's Method, Toshio Fukushima, Journal of Geodesy 9(12):689-693, February 2006

      Some changes have been added to the original method:

      • in order to handle more accurately corner cases near the pole
      • in order to handle properly corner cases near the equatorial plane, even far inside the ellipsoid
      • in order to handle very flat ellipsoids

      In some rare cases (for example very flat ellipsoid, or points close to ellipsoid center), the loop may fail to converge. As this seems to happen only in degenerate cases, a design choice was to return an approximate point corresponding to last iteration. This point may be incorrect and fail to give the initial point back if doing roundtrip by calling transform(GeodeticPoint). This design choice was made to avoid NaNs appearing for example in inter-satellites visibility checks when two satellites are almost on opposite sides of Earth. The intermediate points far within the Earth should not prevent the detection algorithm to find visibility start/end.

      Specified by:
      transform in interface BodyShape
      Type Parameters:
      T - type of the filed elements
      Parameters:
      point - Cartesian point
      frame - frame in which Cartesian point is expressed
      date - date of the computation (used for frames conversions)
      Returns:
      point at the same location but as a surface-relative point

    • transform

      public FieldGeodeticPoint<UnivariateDerivative2> transform(PVCoordinates point, Frame frame, AbsoluteDate date)
      Transform a Cartesian point to a surface-relative point.
      Parameters:
      point - Cartesian point
      frame - frame in which Cartesian point is expressed
      date - date of the computation (used for frames conversions)
      Returns:
      point at the same location but as a surface-relative point, using time as the single derivation parameter

    • azimuthBetweenPoints

      public double azimuthBetweenPoints(GeodeticPoint origin, GeodeticPoint destination)
      Compute the azimuth angle from local north between the two points. The angle is calculated clockwise from local north at the origin point and follows the rhumb line to the destination point.
      Parameters:
      origin - the origin point, at which the azimuth angle will be computed (non-null)
      destination - the destination point, to which the angle is defined (non-null)
      Returns:
      the resulting azimuth angle (radians, [0-2pi))
      Since:
      11.3

    • azimuthBetweenPoints

      public <T extends CalculusFieldElement<T>> T azimuthBetweenPoints(FieldGeodeticPoint<T> origin, FieldGeodeticPoint<T> destination)
      Compute the azimuth angle from local north between the two points.

      The angle is calculated clockwise from local north at the origin point and follows the rhumb line to the destination point.

      Type Parameters:
      T - the type of field elements
      Parameters:
      origin - the origin point, at which the azimuth angle will be computed (non-null)
      destination - the destination point, to which the angle is defined (non-null)
      Returns:
      the resulting azimuth angle (radians, [0-2pi))
      Since:
      11.3

    • geodeticToIsometricLatitude

      public double geodeticToIsometricLatitude(double geodeticLatitude)
      Compute the isometric latitude corresponding to the provided latitude.
      Parameters:
      geodeticLatitude - the latitude (radians, within interval [-pi/2, +pi/2])
      Returns:
      the isometric latitude (radians)
      Since:
      11.3

    • geodeticToIsometricLatitude

      public <T extends CalculusFieldElement<T>> T geodeticToIsometricLatitude(T geodeticLatitude)
      Compute the isometric latitude corresponding to the provided latitude.
      Type Parameters:
      T - the type of field elements
      Parameters:
      geodeticLatitude - the latitude (radians, within interval [-pi/2, +pi/2])
      Returns:
      the isometric latitude (radians)
      Since:
      11.3

    • lowestAltitudeIntermediate

      public GeodeticPoint lowestAltitudeIntermediate(Vector3D endpoint1, Vector3D endpoint2)
      Find intermediate point of lowest altitude along a line between two endpoints.
      Parameters:
      endpoint1 - first endpoint, in body frame
      endpoint2 - second endpoint, in body frame
      Returns:
      point with lowest altitude between endpoint1 and endpoint2.
      Since:
      12.0

    • lowestAltitudeIntermediate

      public <T extends CalculusFieldElement<T>> FieldGeodeticPoint<T> lowestAltitudeIntermediate(FieldVector3D<T> endpoint1, FieldVector3D<T> endpoint2)
      Find intermediate point of lowest altitude along a line between two endpoints.
      Type Parameters:
      T - type of the field elements
      Parameters:
      endpoint1 - first endpoint, in body frame
      endpoint2 - second endpoint, in body frame
      Returns:
      point with lowest altitude between endpoint1 and endpoint2.
      Since:
      12.0

    • pointAtAltitude

      public Vector3D pointAtAltitude(Line line, double altitude, Vector3D close, Frame frame, AbsoluteDate date)
      Get point at some altitude along a line.

      A line may have several intersection points with a closed surface at some altitude (we consider the one point case as a degenerated two points case). The close parameter is used to select which of these points should be returned. The selected point is the one that is closest to the close point.

      This is a generalized version of getCartesianIntersectionPoint(Line, Vector3D, Frame, AbsoluteDate), with a non-zero altitude, except that it returns a point in the same frame as input line (the other method returns a point in the body frame).

      This method was adapted from the sister Rugged library.

      Parameters:
      line - test line (may intersect the body or not)
      altitude - altitude with respect to ellipsoid (m)
      close - point used for intersections selection
      frame - frame in which line is expressed
      date - date of the line in given frame
      Returns:
      intersection point at specified altitude zero or null if the line does not intersect the iso-altitude surface
      Since:
      13.1.1

    • pointAtAltitude

      public <T extends CalculusFieldElement<T>> FieldVector3D<T> pointAtAltitude(FieldLine<T> line, T altitude, FieldVector3D<T> close, Frame frame, FieldAbsoluteDate<T> date)
      Get point at some altitude along a line.

      A line may have several intersection points with a closed surface at some altitude (we consider the one point case as a degenerated two points case). The close parameter is used to select which of these points should be returned. The selected point is the one that is closest to the close point.

      This is a generalized version of getCartesianIntersectionPoint(Line, Vector3D, Frame, AbsoluteDate), with a non-zero altitude, except that it returns a point in the same frame as input line (the other method returns a point in the body frame).

      This method was adapted from the sister Rugged library.

      Type Parameters:
      T - type of the field elements
      Parameters:
      line - test line (may intersect the body or not)
      altitude - altitude with respect to ellipsoid (m)
      close - point used for intersections selection
      frame - frame in which line is expressed
      date - date of the line in given frame
      Returns:
      intersection point at specified altitude zero or null if the line does not intersect the iso-altitude surface
      Since:
      13.1.1

    • getLongitude

      public double getLongitude(Vector3D point, Frame frame, AbsoluteDate date)
      Computes the longitude of a surface-relative point. This has its own method for performance with symmetrical bodies around the Z axis.
      Specified by:
      getLongitude in interface BodyShape
      Parameters:
      point - Cartesian point
      frame - frame in which Cartesian point is expressed
      date - date of the computation (used for frames conversions)
      Returns:
      longitude of surface-relative point

    • getLongitude

      public <T extends CalculusFieldElement<T>> T getLongitude(FieldVector3D<T> point, Frame frame, FieldAbsoluteDate<T> date)
      Computes the longitude of a surface-relative point. This has its own method for performance with symmetrical bodies around the Z axis.
      Specified by:
      getLongitude in interface BodyShape
      Type Parameters:
      T - field type
      Parameters:
      point - Cartesian point
      frame - frame in which Cartesian point is expressed
      date - date of the computation (used for frames conversions)
      Returns:
      longitude of surface-relative point