Class Transform
 java.lang.Object

 org.orekit.frames.Transform

 All Implemented Interfaces:
Serializable
,StaticTransform
,TimeShiftable<Transform>
,TimeStamped
public class Transform extends Object implements TimeShiftable<Transform>, Serializable, StaticTransform
Transformation class in three dimensional space.This class represents the transformation engine between
frames
. It is used both to define the relationship between each frame and its parent frame and to gather all individual transforms into one operation when converting between frames far away from each other.The convention used in OREKIT is vectorial transformation. It means that a transformation is defined as a transform to apply to the coordinates of a vector expressed in the old frame to obtain the same vector expressed in the new frame.
Instances of this class are guaranteed to be immutable.
Examples
Example of translation from R_{A} to R_{B}
We want to transform the
PVCoordinates
PV_{A} to PV_{B} with :PV_{A} = ({1, 0, 0}, {2, 0, 0}, {3, 0, 0});
PV_{B} = ({0, 0, 0}, {0, 0, 0}, {0, 0, 0});The transform to apply then is defined as follows :
Vector3D translation = new Vector3D(1, 0, 0); Vector3D velocity = new Vector3D(2, 0, 0); Vector3D acceleration = new Vector3D(3, 0, 0); Transform R1toR2 = new Transform(date, translation, velocity, acceleration); PVB = R1toR2.transformPVCoordinates(PVA);
Example of rotation from R_{A} to R_{B}
We want to transform the
PVCoordinates
PV_{A} to PV_{B} withPV_{A} = ({1, 0, 0}, { 1, 0, 0});
PV_{B} = ({0, 1, 0}, {2, 1, 0});The transform to apply then is defined as follows :
Rotation rotation = new Rotation(Vector3D.PLUS_K, FastMath.PI / 2); Vector3D rotationRate = new Vector3D(0, 0, 2); Transform R1toR2 = new Transform(rotation, rotationRate); PVB = R1toR2.transformPVCoordinates(PVA);
 Author:
 Luc Maisonobe, Fabien Maussion
 See Also:
 Serialized Form


Constructor Summary
Constructors Constructor Description Transform(AbsoluteDate date, Rotation rotation)
Build a rotation transform.Transform(AbsoluteDate date, Rotation rotation, Vector3D rotationRate)
Build a rotation transform.Transform(AbsoluteDate date, Rotation rotation, Vector3D rotationRate, Vector3D rotationAcceleration)
Build a rotation transform.Transform(AbsoluteDate date, Vector3D translation)
Build a translation transform.Transform(AbsoluteDate date, Vector3D translation, Vector3D velocity)
Build a translation transform, with its first time derivative.Transform(AbsoluteDate date, Vector3D translation, Vector3D velocity, Vector3D acceleration)
Build a translation transform, with its first and second time derivatives.Transform(AbsoluteDate date, Transform first, Transform second)
Build a transform by combining two existing ones.Transform(AbsoluteDate date, AngularCoordinates angular)
Build a rotation transform.Transform(AbsoluteDate date, PVCoordinates cartesian)
Build a translation transform, with its first time derivative.Transform(AbsoluteDate date, PVCoordinates cartesian, AngularCoordinates angular)
Build a transform from its primitive operations.

Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description Transform
freeze()
Get a frozen transform.Vector3D
getAcceleration()
Get the second time derivative of the translation.AngularCoordinates
getAngular()
Get the underlying elementary angular part.PVCoordinates
getCartesian()
Get the underlying elementary Cartesian part.AbsoluteDate
getDate()
Get the date.Transform
getInverse()
Get the inverse transform of the instance.void
getJacobian(CartesianDerivativesFilter selector, double[][] jacobian)
Compute the Jacobian of thetransformPVCoordinates(PVCoordinates)
method of the transform.Rotation
getRotation()
Get the underlying elementary rotation.Vector3D
getRotationAcceleration()
Get the second time derivative of the rotation.Vector3D
getRotationRate()
Get the first time derivative of the rotation.Vector3D
getTranslation()
Get the underlying elementary translation.Vector3D
getVelocity()
Get the first time derivative of the translation.Transform
interpolate(AbsoluteDate interpolationDate, Stream<Transform> sample)
Interpolate a transform from a sample set of existing transforms.static Transform
interpolate(AbsoluteDate date, CartesianDerivativesFilter cFilter, AngularDerivativesFilter aFilter, Collection<Transform> sample)
Interpolate a transform from a sample set of existing transforms.Transform
shiftedBy(double dt)
Get a timeshifted instance.StaticTransform
staticShiftedBy(double dt)
Shift the transform in time considering all rates, then return only the translation and rotation portion of the transform.StaticTransform
toStaticTransform()
Create a socalled static transform from the instance.<T extends CalculusFieldElement<T>>
FieldPVCoordinates<T>transformPVCoordinates(FieldPVCoordinates<T> pv)
TransformFieldPVCoordinates
including kinematic effects.PVCoordinates
transformPVCoordinates(PVCoordinates pva)
TransformPVCoordinates
including kinematic effects.<T extends CalculusFieldElement<T>>
TimeStampedFieldPVCoordinates<T>transformPVCoordinates(TimeStampedFieldPVCoordinates<T> pv)
TransformTimeStampedFieldPVCoordinates
including kinematic effects.TimeStampedPVCoordinates
transformPVCoordinates(TimeStampedPVCoordinates pv)
TransformTimeStampedPVCoordinates
including kinematic effects.
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.orekit.frames.StaticTransform
transformLine, transformPosition, transformPosition, transformVector, transformVector

Methods inherited from interface org.orekit.time.TimeStamped
durationFrom




Field Detail

IDENTITY
public static final Transform IDENTITY
Identity transform.


Constructor Detail

Transform
public Transform(AbsoluteDate date, PVCoordinates cartesian, AngularCoordinates angular)
Build a transform from its primitive operations. Parameters:
date
 date of the transformcartesian
 Cartesian coordinates of the target frame with respect to the original frameangular
 angular coordinates of the target frame with respect to the original frame

Transform
public Transform(AbsoluteDate date, Vector3D translation)
Build a translation transform. Parameters:
date
 date of the transformtranslation
 translation to apply (i.e. coordinates of the transformed origin, or coordinates of the origin of the old frame in the new frame)

Transform
public Transform(AbsoluteDate date, Rotation rotation)
Build a rotation transform. Parameters:
date
 date of the transformrotation
 rotation to apply ( i.e. rotation to apply to the coordinates of a vector expressed in the old frame to obtain the same vector expressed in the new frame )

Transform
public Transform(AbsoluteDate date, Vector3D translation, Vector3D velocity)
Build a translation transform, with its first time derivative. Parameters:
date
 date of the transformtranslation
 translation to apply (i.e. coordinates of the transformed origin, or coordinates of the origin of the old frame in the new frame)velocity
 the velocity of the translation (i.e. origin of the old frame velocity in the new frame)

Transform
public Transform(AbsoluteDate date, Vector3D translation, Vector3D velocity, Vector3D acceleration)
Build a translation transform, with its first and second time derivatives. Parameters:
date
 date of the transformtranslation
 translation to apply (i.e. coordinates of the transformed origin, or coordinates of the origin of the old frame in the new frame)velocity
 the velocity of the translation (i.e. origin of the old frame velocity in the new frame)acceleration
 the acceleration of the translation (i.e. origin of the old frame acceleration in the new frame)

Transform
public Transform(AbsoluteDate date, PVCoordinates cartesian)
Build a translation transform, with its first time derivative. Parameters:
date
 date of the transformcartesian
 Cartesian part of the transformation to apply (i.e. coordinates of the transformed origin, or coordinates of the origin of the old frame in the new frame, with their derivatives)

Transform
public Transform(AbsoluteDate date, Rotation rotation, Vector3D rotationRate)
Build a rotation transform. Parameters:
date
 date of the transformrotation
 rotation to apply ( i.e. rotation to apply to the coordinates of a vector expressed in the old frame to obtain the same vector expressed in the new frame )rotationRate
 the axis of the instant rotation expressed in the new frame. (norm representing angular rate)

Transform
public Transform(AbsoluteDate date, Rotation rotation, Vector3D rotationRate, Vector3D rotationAcceleration)
Build a rotation transform. Parameters:
date
 date of the transformrotation
 rotation to apply ( i.e. rotation to apply to the coordinates of a vector expressed in the old frame to obtain the same vector expressed in the new frame )rotationRate
 the axis of the instant rotationrotationAcceleration
 the axis of the instant rotation expressed in the new frame. (norm representing angular rate)

Transform
public Transform(AbsoluteDate date, AngularCoordinates angular)
Build a rotation transform. Parameters:
date
 date of the transformangular
 angular part of the transformation to apply (i.e. rotation to apply to the coordinates of a vector expressed in the old frame to obtain the same vector expressed in the new frame, with its rotation rate)

Transform
public Transform(AbsoluteDate date, Transform first, Transform second)
Build a transform by combining two existing ones.Note that the dates of the two existing transformed are ignored, and the combined transform date is set to the date supplied in this constructor without any attempt to shift the raw transforms. This is a design choice allowing user full control of the combination.
 Parameters:
date
 date of the transformfirst
 first transform appliedsecond
 second transform applied


Method Detail

getDate
public AbsoluteDate getDate()
Get the date. Specified by:
getDate
in interfaceTimeStamped
 Returns:
 date attached to the object

shiftedBy
public Transform shiftedBy(double dt)
Get a timeshifted instance. Specified by:
shiftedBy
in interfaceTimeShiftable<Transform>
 Parameters:
dt
 time shift in seconds Returns:
 a new instance, shifted with respect to instance (which is not changed)

staticShiftedBy
public StaticTransform staticShiftedBy(double dt)
Shift the transform in time considering all rates, then return only the translation and rotation portion of the transform. Parameters:
dt
 time shift in seconds. Returns:
 shifted transform as a static transform. It is static in the sense that it can only be used to transform directions and positions, but not velocities or accelerations.
 See Also:
shiftedBy(double)

toStaticTransform
public StaticTransform toStaticTransform()
Create a socalled static transform from the instance. Returns:
 static part of the transform. It is static in the sense that it can only be used to transform directions and positions, but not velocities or accelerations.
 See Also:
StaticTransform

interpolate
public Transform interpolate(AbsoluteDate interpolationDate, Stream<Transform> sample)
Interpolate a transform from a sample set of existing transforms.Calling this method is equivalent to call
interpolate(AbsoluteDate, CartesianDerivativesFilter, AngularDerivativesFilter, Collection)
withcFilter
set toCartesianDerivativesFilter.USE_PVA
andaFilter
set toAngularDerivativesFilter.USE_RRA
set to true. Parameters:
interpolationDate
 interpolation datesample
 sample points on which interpolation should be done Returns:
 a new instance, interpolated at specified date

interpolate
public static Transform interpolate(AbsoluteDate date, CartesianDerivativesFilter cFilter, AngularDerivativesFilter aFilter, Collection<Transform> sample)
Interpolate a transform from a sample set of existing transforms.Note that even if first time derivatives (velocities and rotation rates) from sample can be ignored, the interpolated instance always includes interpolated derivatives. This feature can be used explicitly to compute these derivatives when it would be too complex to compute them from an analytical formula: just compute a few sample points from the explicit formula and set the derivatives to zero in these sample points, then use interpolation to add derivatives consistent with the positions and rotations.
As this implementation of interpolation is polynomial, it should be used only with small samples (about 1020 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).
 Parameters:
date
 interpolation datecFilter
 filter for derivatives from the sample to use in interpolationaFilter
 filter for derivatives from the sample to use in interpolationsample
 sample points on which interpolation should be done Returns:
 a new instance, interpolated at specified date
 Since:
 7.0

getInverse
public Transform getInverse()
Get the inverse transform of the instance. Specified by:
getInverse
in interfaceStaticTransform
 Returns:
 inverse transform of the instance

freeze
public Transform freeze()
Get a frozen transform.This method creates a copy of the instance but frozen in time, i.e. with velocity, acceleration and rotation rate forced to zero.
 Returns:
 a new transform, without any timedependent parts

transformPVCoordinates
public PVCoordinates transformPVCoordinates(PVCoordinates pva)
TransformPVCoordinates
including kinematic effects. Parameters:
pva
 the positionvelocityacceleration triplet to transform. Returns:
 transformed positionvelocityacceleration

transformPVCoordinates
public TimeStampedPVCoordinates transformPVCoordinates(TimeStampedPVCoordinates pv)
TransformTimeStampedPVCoordinates
including kinematic effects.In order to allow the user more flexibility, this method does not check for consistency between the transform
date
and the timestamped positionvelocitydate
. The returned value will always have the samedate
as the input argument, regardless of the instancedate
. Parameters:
pv
 timestamped positionvelocity to transform. Returns:
 transformed timestamped positionvelocity
 Since:
 7.0

transformPVCoordinates
public <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> transformPVCoordinates(FieldPVCoordinates<T> pv)
TransformFieldPVCoordinates
including kinematic effects. Type Parameters:
T
 type of the field elements Parameters:
pv
 positionvelocity to transform. Returns:
 transformed positionvelocity

transformPVCoordinates
public <T extends CalculusFieldElement<T>> TimeStampedFieldPVCoordinates<T> transformPVCoordinates(TimeStampedFieldPVCoordinates<T> pv)
TransformTimeStampedFieldPVCoordinates
including kinematic effects.In order to allow the user more flexibility, this method does not check for consistency between the transform
date
and the timestamped positionvelocitydate
. The returned value will always have the samedate
as the input argument, regardless of the instancedate
. Type Parameters:
T
 type of the field elements Parameters:
pv
 timestamped positionvelocity to transform. Returns:
 transformed timestamped positionvelocity
 Since:
 7.0

getJacobian
public void getJacobian(CartesianDerivativesFilter selector, double[][] jacobian)
Compute the Jacobian of thetransformPVCoordinates(PVCoordinates)
method of the transform.Element
jacobian[i][j]
is the derivative of Cartesian coordinate i of the transformedPVCoordinates
with respect to Cartesian coordinate j of the inputPVCoordinates
in methodtransformPVCoordinates(PVCoordinates)
.This definition implies that if we define positionvelocity coordinates
PV₁ = transform.transformPVCoordinates(PV₀), then
their differentials dPV₁ and dPV₀ will obey the following relation where J is the matrix computed by this method:
dPV₁ = J × dPV₀
 Parameters:
selector
 selector specifying the size of the upper left corner that must be filled (either 3x3 for positions only, 6x6 for positions and velocities, 9x9 for positions, velocities and accelerations)jacobian
 placeholder matrix whose upperleft corner is to be filled with the Jacobian, the rest of the matrix remaining untouched

getCartesian
public PVCoordinates getCartesian()
Get the underlying elementary Cartesian part.A transform can be uniquely represented as an elementary translation followed by an elementary rotation. This method returns this unique elementary translation with its derivative.
 Returns:
 underlying elementary Cartesian part
 See Also:
getTranslation()
,getVelocity()

getTranslation
public Vector3D getTranslation()
Get the underlying elementary translation.A transform can be uniquely represented as an elementary translation followed by an elementary rotation. This method returns this unique elementary translation.
 Specified by:
getTranslation
in interfaceStaticTransform
 Returns:
 underlying elementary translation
 See Also:
getCartesian()
,getVelocity()
,getAcceleration()

getVelocity
public Vector3D getVelocity()
Get the first time derivative of the translation. Returns:
 first time derivative of the translation
 See Also:
getCartesian()
,getTranslation()
,getAcceleration()

getAcceleration
public Vector3D getAcceleration()
Get the second time derivative of the translation. Returns:
 second time derivative of the translation
 See Also:
getCartesian()
,getTranslation()
,getVelocity()

getAngular
public AngularCoordinates getAngular()
Get the underlying elementary angular part.A transform can be uniquely represented as an elementary translation followed by an elementary rotation. This method returns this unique elementary rotation with its derivative.
 Returns:
 underlying elementary angular part
 See Also:
getRotation()
,getRotationRate()
,getRotationAcceleration()

getRotation
public Rotation getRotation()
Get the underlying elementary rotation.A transform can be uniquely represented as an elementary translation followed by an elementary rotation. This method returns this unique elementary rotation.
 Specified by:
getRotation
in interfaceStaticTransform
 Returns:
 underlying elementary rotation
 See Also:
getAngular()
,getRotationRate()
,getRotationAcceleration()

getRotationRate
public Vector3D getRotationRate()
Get the first time derivative of the rotation.The norm represents the angular rate.
 Returns:
 First time derivative of the rotation
 See Also:
getAngular()
,getRotation()
,getRotationAcceleration()

getRotationAcceleration
public Vector3D getRotationAcceleration()
Get the second time derivative of the rotation. Returns:
 Second time derivative of the rotation
 See Also:
getAngular()
,getRotation()
,getRotationRate()

