## Class FieldTransform<T extends CalculusFieldElement<T>>

• Type Parameters:
T - the type of the field elements
All Implemented Interfaces:
FieldStaticTransform<T>, FieldTimeShiftable<FieldTransform<T>,​T>, TimeShiftable<FieldTransform<T>>, TimeStamped

public class FieldTransform<T extends CalculusFieldElement<T>>
extends Object
implements FieldTimeShiftable<FieldTransform<T>,​T>, FieldStaticTransform<T>
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 RA to RB

We want to transform the FieldPVCoordinates PVA to PVB with :

PVA = ({1, 0, 0}, {2, 0, 0}, {3, 0, 0});
PVB = ({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.transformPVCoordinate(PVA);


### Example of rotation from RA to RB

We want to transform the FieldPVCoordinates PVA to PVB with

PVA = ({1, 0, 0}, { 1, 0, 0});
PVB = ({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);

Since:
9.0
Author:
Luc Maisonobe, Fabien Maussion
• ### Constructor Summary

Constructors
Constructor Description
FieldTransform​(Field<T> field, Transform transform)
Build a transform from a regular transform.
FieldTransform​(FieldAbsoluteDate<T> date, FieldRotation<T> rotation)
Build a rotation transform.
FieldTransform​(FieldAbsoluteDate<T> date, FieldRotation<T> rotation, FieldVector3D<T> rotationRate)
Build a rotation transform.
FieldTransform​(FieldAbsoluteDate<T> date, FieldRotation<T> rotation, FieldVector3D<T> rotationRate, FieldVector3D<T> rotationAcceleration)
Build a rotation transform.
FieldTransform​(FieldAbsoluteDate<T> date, FieldVector3D<T> translation)
Build a translation transform.
FieldTransform​(FieldAbsoluteDate<T> date, FieldVector3D<T> translation, FieldVector3D<T> velocity)
Build a translation transform, with its first time derivative.
FieldTransform​(FieldAbsoluteDate<T> date, FieldVector3D<T> translation, FieldVector3D<T> velocity, FieldVector3D<T> acceleration)
Build a translation transform, with its first and second time derivatives.
FieldTransform​(FieldAbsoluteDate<T> date, FieldTransform<T> first, FieldTransform<T> second)
Build a transform by combining two existing ones.
FieldTransform​(FieldAbsoluteDate<T> date, FieldAngularCoordinates<T> angular)
Build a rotation transform.
FieldTransform​(FieldAbsoluteDate<T> date, FieldPVCoordinates<T> cartesian)
Build a translation transform, with its first time derivative.
• ### Method Summary

All Methods
Modifier and Type Method Description
FieldTransform<T> freeze()
Get a frozen transform.
FieldVector3D<T> getAcceleration()
Get the second time derivative of the translation.
FieldAngularCoordinates<T> getAngular()
Get the underlying elementary angular part.
FieldPVCoordinates<T> getCartesian()
Get the underlying elementary Cartesian part.
AbsoluteDate getDate()
Get the date.
FieldAbsoluteDate<T> getFieldDate()
Get the date.
static <T extends CalculusFieldElement<T>>FieldTransform<T> getIdentity​(Field<T> field)
Get the identity transform.
FieldTransform<T> getInverse()
Get the inverse transform of the instance.
void getJacobian​(CartesianDerivativesFilter selector, T[][] jacobian)
Compute the Jacobian of the transformPVCoordinates(FieldPVCoordinates) method of the transform.
FieldRotation<T> getRotation()
Get the underlying elementary rotation.
FieldVector3D<T> getRotationAcceleration()
Get the second time derivative of the rotation.
FieldVector3D<T> getRotationRate()
Get the first time derivative of the rotation.
FieldVector3D<T> getTranslation()
Get the underlying elementary translation.
FieldVector3D<T> getVelocity()
Get the first time derivative of the translation.
static <T extends CalculusFieldElement<T>>FieldTransform<T> interpolate​(FieldAbsoluteDate<T> interpolationDate, Collection<FieldTransform<T>> sample)
Interpolate a transform from a sample set of existing transforms.
static <T extends CalculusFieldElement<T>>FieldTransform<T> interpolate​(FieldAbsoluteDate<T> date, CartesianDerivativesFilter cFilter, AngularDerivativesFilter aFilter, Collection<FieldTransform<T>> sample)
Interpolate a transform from a sample set of existing transforms.
static <T extends CalculusFieldElement<T>>FieldTransform<T> interpolate​(FieldAbsoluteDate<T> date, CartesianDerivativesFilter cFilter, AngularDerivativesFilter aFilter, Stream<FieldTransform<T>> sample)
Interpolate a transform from a sample set of existing transforms.
FieldTransform<T> shiftedBy​(double dt)
Get a time-shifted instance.
FieldTransform<T> shiftedBy​(T dt)
Get a time-shifted instance.
FieldStaticTransform<T> staticShiftedBy​(T dt)
Shift the transform in time considering all rates, then return only the translation and rotation portion of the transform.
FieldStaticTransform<T> toStaticTransform()
Create a so-called static transform from the instance.
FieldPVCoordinates<T> transformPVCoordinates​(FieldPVCoordinates<T> pv)
Transform TimeStampedFieldPVCoordinates including kinematic effects.
FieldPVCoordinates<T> transformPVCoordinates​(PVCoordinates pv)
Transform TimeStampedPVCoordinates including kinematic effects.
TimeStampedFieldPVCoordinates<T> transformPVCoordinates​(TimeStampedFieldPVCoordinates<T> pv)
Transform TimeStampedFieldPVCoordinates including kinematic effects.
TimeStampedFieldPVCoordinates<T> transformPVCoordinates​(TimeStampedPVCoordinates pv)
Transform TimeStampedPVCoordinates 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.FieldStaticTransform

transformLine, transformLine, transformPosition, transformPosition, transformVector, transformVector
• ### Methods inherited from interface org.orekit.time.TimeStamped

durationFrom
• ### Constructor Detail

• #### FieldTransform

public FieldTransform​(Field<T> field,
Transform transform)
Build a transform from a regular transform.
Parameters:
field - field of the elements
transform - regular transform to convert
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldVector3D<T> translation)
Build a translation transform.
Parameters:
date - date of the transform
translation - translation to apply (i.e. coordinates of the transformed origin, or coordinates of the origin of the old frame in the new frame)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldRotation<T> rotation)
Build a rotation transform.
Parameters:
date - date of the transform
rotation - 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 )
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldVector3D<T> translation,
FieldVector3D<T> velocity)
Build a translation transform, with its first time derivative.
Parameters:
date - date of the transform
translation - 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)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldVector3D<T> translation,
FieldVector3D<T> velocity,
FieldVector3D<T> acceleration)
Build a translation transform, with its first and second time derivatives.
Parameters:
date - date of the transform
translation - 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)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldPVCoordinates<T> cartesian)
Build a translation transform, with its first time derivative.
Parameters:
date - date of the transform
cartesian - 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)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldRotation<T> rotation,
FieldVector3D<T> rotationRate)
Build a rotation transform.
Parameters:
date - date of the transform
rotation - 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)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldRotation<T> rotation,
FieldVector3D<T> rotationRate,
FieldVector3D<T> rotationAcceleration)
Build a rotation transform.
Parameters:
date - date of the transform
rotation - 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
rotationAcceleration - the axis of the instant rotation expressed in the new frame. (norm representing angular rate)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldAngularCoordinates<T> angular)
Build a rotation transform.
Parameters:
date - date of the transform
angular - 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)
• #### FieldTransform

public FieldTransform​(FieldAbsoluteDate<T> date,
FieldTransform<T> first,
FieldTransform<T> 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 transform
first - first transform applied
second - second transform applied
• ### Method Detail

• #### getIdentity

public static <T extends CalculusFieldElement<T>> FieldTransform<T> getIdentity​(Field<T> field)
Get the identity transform.
Type Parameters:
T - the type of the field elements
Parameters:
field - field for the components
Returns:
identity transform
• #### getDate

public AbsoluteDate getDate()
Get the date.
Specified by:
getDate in interface TimeStamped
Returns:
date attached to the object
• #### getFieldDate

public FieldAbsoluteDate<T> getFieldDate()
Get the date.
Returns:
date attached to the object
• #### shiftedBy

public FieldTransform<T> shiftedBy​(double dt)
Get a time-shifted instance.
Specified by:
shiftedBy in interface TimeShiftable<T extends CalculusFieldElement<T>>
Parameters:
dt - time shift in seconds
Returns:
a new instance, shifted with respect to instance (which is not changed)
• #### shiftedBy

public FieldTransform<T> shiftedBy​(T dt)
Get a time-shifted instance.
Specified by:
shiftedBy in interface FieldTimeShiftable<FieldTransform<T extends CalculusFieldElement<T>>,​T extends CalculusFieldElement<T>>
Parameters:
dt - time shift in seconds
Returns:
a new instance, shifted with respect to instance (which is not changed)
• #### staticShiftedBy

public FieldStaticTransform<T> staticShiftedBy​(T 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.
shiftedBy(double)
• #### toStaticTransform

public FieldStaticTransform<T> toStaticTransform()
Create a so-called 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.
FieldStaticTransform
• #### interpolate

public static <T extends CalculusFieldElement<T>> FieldTransform<T> interpolate​(FieldAbsoluteDate<T> date,
CartesianDerivativesFilter cFilter,
AngularDerivativesFilter aFilter,
Collection<FieldTransform<T>> 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 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Type Parameters:
T - the type of the field elements
Parameters:
date - interpolation date
cFilter - filter for derivatives from the sample to use in interpolation
aFilter - filter for derivatives from the sample to use in interpolation
sample - sample points on which interpolation should be done
Returns:
a new instance, interpolated at specified date
• #### interpolate

public static <T extends CalculusFieldElement<T>> FieldTransform<T> interpolate​(FieldAbsoluteDate<T> date,
CartesianDerivativesFilter cFilter,
AngularDerivativesFilter aFilter,
Stream<FieldTransform<T>> 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 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Type Parameters:
T - the type of the field elements
Parameters:
date - interpolation date
cFilter - filter for derivatives from the sample to use in interpolation
aFilter - filter for derivatives from the sample to use in interpolation
sample - sample points on which interpolation should be done
Returns:
a new instance, interpolated at specified date
• #### getInverse

public FieldTransform<T> getInverse()
Get the inverse transform of the instance.
Specified by:
getInverse in interface FieldStaticTransform<T extends CalculusFieldElement<T>>
Returns:
inverse transform of the instance
• #### freeze

public FieldTransform<T> 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 time-dependent parts
• #### transformPVCoordinates

public FieldPVCoordinates<T> transformPVCoordinates​(PVCoordinates pv)
Transform TimeStampedPVCoordinates including kinematic effects.

In order to allow the user more flexibility, this method does not check for consistency between the transform date and the time-stamped position-velocity date. The returned value will always have the same date as the input argument, regardless of the instance date.

Parameters:
pv - time-stamped position-velocity to transform.
Returns:
transformed time-stamped position-velocity
• #### transformPVCoordinates

public TimeStampedFieldPVCoordinates<T> transformPVCoordinates​(TimeStampedPVCoordinates pv)
Transform TimeStampedPVCoordinates including kinematic effects.

In order to allow the user more flexibility, this method does not check for consistency between the transform date and the time-stamped position-velocity date. The returned value will always have the same date as the input argument, regardless of the instance date.

Parameters:
pv - time-stamped position-velocity to transform.
Returns:
transformed time-stamped position-velocity
• #### transformPVCoordinates

public FieldPVCoordinates<T> transformPVCoordinates​(FieldPVCoordinates<T> pv)
Transform TimeStampedFieldPVCoordinates including kinematic effects.

BEWARE! This method does explicit computation of velocity and acceleration by combining the transform velocity, acceleration, rotation rate and rotation acceleration with the velocity and acceleration from the argument. This implies that this method should not be used when derivatives are contained in the field elements (typically when using DerivativeStructure elements where time is one of the differentiation parameter), otherwise the time derivatives would be computed twice, once explicitly in this method and once implicitly in the field operations. If time derivatives are contained in the field elements themselves, then rather than this method the transformPosition method should be used, so the derivatives are computed once, as part of the field. This method is rather expected to be used when the field elements are DerivativeStructure instances where the differentiation parameters are not time (they can typically be initial state for computing state transition matrices or force models parameters, or ground stations positions, ...).

In order to allow the user more flexibility, this method does not check for consistency between the transform date and the time-stamped position-velocity date. The returned value will always have the same date as the input argument, regardless of the instance date.

Parameters:
pv - time-stamped position-velocity to transform.
Returns:
transformed time-stamped position-velocity
• #### transformPVCoordinates

public TimeStampedFieldPVCoordinates<T> transformPVCoordinates​(TimeStampedFieldPVCoordinates<T> pv)
Transform TimeStampedFieldPVCoordinates including kinematic effects.

BEWARE! This method does explicit computation of velocity and acceleration by combining the transform velocity, acceleration, rotation rate and rotation acceleration with the velocity and acceleration from the argument. This implies that this method should not be used when derivatives are contained in the field elements (typically when using DerivativeStructure elements where time is one of the differentiation parameter), otherwise the time derivatives would be computed twice, once explicitly in this method and once implicitly in the field operations. If time derivatives are contained in the field elements themselves, then rather than this method the transformPosition method should be used, so the derivatives are computed once, as part of the field. This method is rather expected to be used when the field elements are DerivativeStructure instances where the differentiation parameters are not time (they can typically be initial state for computing state transition matrices or force models parameters, or ground stations positions, ...).

In order to allow the user more flexibility, this method does not check for consistency between the transform date and the time-stamped position-velocity date. The returned value will always have the same date as the input argument, regardless of the instance date.

Parameters:
pv - time-stamped position-velocity to transform.
Returns:
transformed time-stamped position-velocity
• #### getJacobian

public void getJacobian​(CartesianDerivativesFilter selector,
T[][] jacobian)
Compute the Jacobian of the transformPVCoordinates(FieldPVCoordinates) method of the transform.

Element jacobian[i][j] is the derivative of Cartesian coordinate i of the transformed FieldPVCoordinates with respect to Cartesian coordinate j of the input FieldPVCoordinates in method transformPVCoordinates(FieldPVCoordinates).

This definition implies that if we define position-velocity 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 upper-left corner is to be filled with the Jacobian, the rest of the matrix remaining untouched
• #### getCartesian

public FieldPVCoordinates<T> 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
getTranslation(), getVelocity()
• #### getTranslation

public FieldVector3D<T> 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 interface FieldStaticTransform<T extends CalculusFieldElement<T>>
Returns:
underlying elementary translation
getCartesian(), getVelocity(), getAcceleration()
• #### getRotation

public FieldRotation<T> 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 interface FieldStaticTransform<T extends CalculusFieldElement<T>>
Returns:
underlying elementary rotation
getAngular(), getRotationRate(), getRotationAcceleration()