## Class OneAxisEllipsoid

• All Implemented Interfaces:
Serializable, 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
Serialized Form
• ### Constructor Summary

Constructors
Constructor Description
OneAxisEllipsoid​(double ae, double f, Frame bodyFrame)
Simple constructor.
• ### Method Summary

All Methods
Modifier and Type Method Description
<T extends CalculusFieldElement<T>>T azimuthBetweenPoints​(FieldGeodeticPoint<T> origin, FieldGeodeticPoint<T> destination)
Compute the azimuth angle from local north between the two points.
double azimuthBetweenPoints​(GeodeticPoint origin, GeodeticPoint destination)
Compute the azimuth angle from local north between the two points.
double geodeticToIsometricLatitude​(double geodeticLatitude)
Compute the isometric latitude corresponding to the provided latitude.
<T extends CalculusFieldElement<T>>T geodeticToIsometricLatitude​(T geodeticLatitude)
Compute the isometric latitude corresponding to the provided latitude.
Frame getBodyFrame()
Get body frame related to body shape.
<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.
Vector3D getCartesianIntersectionPoint​(Line line, Vector3D close, Frame frame, AbsoluteDate date)
Get the intersection point of a line with the surface of the body.
double getEccentricity()
Get the first eccentricity of the ellipsoid: e = sqrt(f * (2.0 - f)).
double getEccentricitySquared()
Get the first eccentricity squared of the ellipsoid: e^2 = f * (2.0 - f).
double getEquatorialRadius()
Get the equatorial radius of the body.
double getFlattening()
Get the flattening of the body: f = (a-b)/a.
<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.
GeodeticPoint getIntersectionPoint​(Line line, Vector3D close, Frame frame, AbsoluteDate date)
Get the intersection point of a line with the surface of the body.
<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.
GeodeticPoint lowestAltitudeIntermediate​(Vector3D endpoint1, Vector3D endpoint2)
Find intermediate point of lowest altitude along a line between two endpoints.
Vector3D projectToGround​(Vector3D point, AbsoluteDate date, Frame frame)
Project a point to the ground.
TimeStampedPVCoordinates projectToGround​(TimeStampedPVCoordinates pv, Frame frame)
Project a moving point to the ground.
void setAngularThreshold​(double angularThreshold)
Set the angular convergence threshold.
<T extends CalculusFieldElement<T>>FieldGeodeticPoint<T> transform​(FieldVector3D<T> point, Frame frame, FieldAbsoluteDate<T> date)
Transform a Cartesian point to a surface-relative point.
GeodeticPoint transform​(Vector3D point, Frame frame, AbsoluteDate date)
Transform a Cartesian point to a surface-relative point.
<T extends CalculusFieldElement<T>>FieldVector3D<T> transform​(FieldGeodeticPoint<T> point)
Transform a surface-relative point to a Cartesian point.
Vector3D transform​(GeodeticPoint point)
Transform a surface-relative point to a Cartesian point.
FieldGeodeticPoint<DerivativeStructure> transform​(PVCoordinates point, Frame frame, AbsoluteDate date)
Transform a Cartesian point to a surface-relative point.
• ### Methods inherited from class org.orekit.bodies.Ellipsoid

getA, getB, getC, getFrame, getPlaneSection, getPlaneSection, isInside, isInside, pointOnLimb, pointOnLimb
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Method Detail

• #### 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)

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.
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.

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
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.

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
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
BodyShape.projectToGround(TimeStampedPVCoordinates, Frame)
• #### 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
BodyShape.projectToGround(Vector3D, AbsoluteDate, Frame)
• #### 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<DerivativeStructure> 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:
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:
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