org.orekit.bodies

Class OneAxisEllipsoid

java.lang.Object

org.orekit.bodies.Ellipsoid

org.orekit.bodies.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

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
OneAxisEllipsoid(double ae, double f, Frame bodyFrame) Simple constructor.

Method Summary

Modifier and Type	Method and Description
<T extends org.hipparchus.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 org.hipparchus.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 org.hipparchus.CalculusFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T>	getCartesianIntersectionPoint(org.hipparchus.geometry.euclidean.threed.FieldLine<T> line, org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> close, Frame frame, FieldAbsoluteDate<T> date) Get the intersection point of a line with the surface of the body.
org.hipparchus.geometry.euclidean.threed.Vector3D	getCartesianIntersectionPoint(org.hipparchus.geometry.euclidean.threed.Line line, org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.CalculusFieldElement<T>> FieldGeodeticPoint<T>	getIntersectionPoint(org.hipparchus.geometry.euclidean.threed.FieldLine<T> line, org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> close, Frame frame, FieldAbsoluteDate<T> date) Get the intersection point of a line with the surface of the body.
GeodeticPoint	getIntersectionPoint(org.hipparchus.geometry.euclidean.threed.Line line, org.hipparchus.geometry.euclidean.threed.Vector3D close, Frame frame, AbsoluteDate date) Get the intersection point of a line with the surface of the body.
<T extends org.hipparchus.CalculusFieldElement<T>> FieldGeodeticPoint<T>	lowestAltitudeIntermediate(org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> endpoint1, org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> endpoint2) Find intermediate point of lowest altitude along a line between two endpoints.
GeodeticPoint	lowestAltitudeIntermediate(org.hipparchus.geometry.euclidean.threed.Vector3D endpoint1, org.hipparchus.geometry.euclidean.threed.Vector3D endpoint2) Find intermediate point of lowest altitude along a line between two endpoints.
TimeStampedPVCoordinates	projectToGround(TimeStampedPVCoordinates pv, Frame frame) Project a moving point to the ground.
org.hipparchus.geometry.euclidean.threed.Vector3D	projectToGround(org.hipparchus.geometry.euclidean.threed.Vector3D point, AbsoluteDate date, Frame frame) Project a point to the ground.
void	setAngularThreshold(double angularThreshold) Set the angular convergence threshold.
<T extends org.hipparchus.CalculusFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T>	transform(FieldGeodeticPoint<T> point) Transform a surface-relative point to a Cartesian point.
<T extends org.hipparchus.CalculusFieldElement<T>> FieldGeodeticPoint<T>	transform(org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> point, Frame frame, FieldAbsoluteDate<T> date) Transform a Cartesian point to a surface-relative point.
org.hipparchus.geometry.euclidean.threed.Vector3D	transform(GeodeticPoint point) Transform a surface-relative point to a Cartesian point.
FieldGeodeticPoint<org.hipparchus.analysis.differentiation.DerivativeStructure>	transform(PVCoordinates point, Frame frame, AbsoluteDate date) Transform a Cartesian point to a surface-relative point.
GeodeticPoint	transform(org.hipparchus.geometry.euclidean.threed.Vector3D 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

Constructor Detail

OneAxisEllipsoid

public OneAxisEllipsoid(double ae,
                        double f,
                        Frame bodyFrame)

Simple constructor.

Standard values for Earth models can be found in the Constants class:

Ellipsoid Models

model	ae (m)	f
GRS 80	Constants.GRS80_EARTH_EQUATORIAL_RADIUS	Constants.GRS80_EARTH_FLATTENING
WGS84	Constants.WGS84_EARTH_EQUATORIAL_RADIUS	Constants.WGS84_EARTH_FLATTENING
IERS96	Constants.IERS96_EARTH_EQUATORIAL_RADIUS	Constants.IERS96_EARTH_FLATTENING
IERS2003	Constants.IERS2003_EARTH_EQUATORIAL_RADIUS	Constants.IERS2003_EARTH_FLATTENING
IERS2010	Constants.IERS2010_EARTH_EQUATORIAL_RADIUS	Constants.IERS2010_EARTH_FLATTENING

Parameters:

ae - equatorial radius

f - the flattening (f = (a-b)/a)

bodyFrame - body frame related to body shape

See Also:

FramesFactory.getITRF(org.orekit.utils.IERSConventions, boolean)

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)

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.

Specified by:

getBodyFrame in interface BodyShape

Returns:

body frame related to body shape

getCartesianIntersectionPoint

public org.hipparchus.geometry.euclidean.threed.Vector3D getCartesianIntersectionPoint(org.hipparchus.geometry.euclidean.threed.Line line,
                                                                                       org.hipparchus.geometry.euclidean.threed.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(org.hipparchus.geometry.euclidean.threed.Line line,
                                          org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.CalculusFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> getCartesianIntersectionPoint(org.hipparchus.geometry.euclidean.threed.FieldLine<T> line,
                                                                                                                                                  org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.CalculusFieldElement<T>> FieldGeodeticPoint<T> getIntersectionPoint(org.hipparchus.geometry.euclidean.threed.FieldLine<T> line,
                                                                                                     org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.CalculusFieldElement<T>> org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.geometry.euclidean.threed.Vector3D projectToGround(org.hipparchus.geometry.euclidean.threed.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:

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

See Also:

BodyShape.projectToGround(Vector3D, AbsoluteDate, Frame)

transform

public GeodeticPoint transform(org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.CalculusFieldElement<T>> FieldGeodeticPoint<T> transform(org.hipparchus.geometry.euclidean.threed.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<org.hipparchus.analysis.differentiation.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 org.hipparchus.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 org.hipparchus.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(org.hipparchus.geometry.euclidean.threed.Vector3D endpoint1,
                                                org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.CalculusFieldElement<T>> FieldGeodeticPoint<T> lowestAltitudeIntermediate(org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> endpoint1,
                                                                                                           org.hipparchus.geometry.euclidean.threed.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