## Class 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 RA to RB

We want to transform the PVCoordinates 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.transformPVCoordinates(PVA);


### Example of rotation from RA to RB

We want to transform the PVCoordinates 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);

Author:
Luc Maisonobe, Fabien Maussion
Serialized Form
• ### Field Summary

Fields
Modifier and Type Field Description
static Transform IDENTITY
Identity transform.
• ### 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
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 the transformPVCoordinates(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 time-shifted 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 so-called static transform from the instance.
<T extends CalculusFieldElement<T>>FieldPVCoordinates<T> transformPVCoordinates​(FieldPVCoordinates<T> pv)
Transform FieldPVCoordinates including kinematic effects.
PVCoordinates transformPVCoordinates​(PVCoordinates pva)
Transform PVCoordinates including kinematic effects.
<T extends CalculusFieldElement<T>>TimeStampedFieldPVCoordinates<T> transformPVCoordinates​(TimeStampedFieldPVCoordinates<T> pv)
Transform TimeStampedFieldPVCoordinates including kinematic effects.
TimeStampedPVCoordinates 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.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 transform
cartesian - Cartesian coordinates of the target frame with respect to the original frame
angular - 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 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)
• #### Transform

public Transform​(AbsoluteDate date,
Rotation 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 )
• #### Transform

public Transform​(AbsoluteDate date,
Vector3D translation,
Vector3D 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)
• #### 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 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)
• #### Transform

public Transform​(AbsoluteDate date,
PVCoordinates 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)
• #### Transform

public Transform​(AbsoluteDate date,
Rotation rotation,
Vector3D 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)
• #### Transform

public Transform​(AbsoluteDate date,
Rotation rotation,
Vector3D rotationRate,
Vector3D 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)
• #### Transform

public Transform​(AbsoluteDate date,
AngularCoordinates 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)
• #### 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 transform
first - first transform applied
second - second transform applied
• ### Method Detail

• #### getDate

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

public Transform shiftedBy​(double dt)
Get a time-shifted instance.
Specified by:
shiftedBy in interface TimeShiftable<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.
shiftedBy(double)
• #### toStaticTransform

public StaticTransform 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.
StaticTransform
• #### 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 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

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
Since:
7.0
• #### getInverse

public Transform getInverse()
Get the inverse transform of the instance.
Specified by:
getInverse in interface StaticTransform
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 time-dependent parts
• #### transformPVCoordinates

public PVCoordinates transformPVCoordinates​(PVCoordinates pva)
Transform PVCoordinates including kinematic effects.
Parameters:
pva - the position-velocity-acceleration triplet to transform.
Returns:
transformed position-velocity-acceleration
• #### transformPVCoordinates

public TimeStampedPVCoordinates 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
Since:
7.0
• #### transformPVCoordinates

public <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> transformPVCoordinates​(FieldPVCoordinates<T> pv)
Transform FieldPVCoordinates including kinematic effects.
Type Parameters:
T - type of the field elements
Parameters:
pv - position-velocity to transform.
Returns:
transformed position-velocity
• #### transformPVCoordinates

public <T extends CalculusFieldElement<T>> TimeStampedFieldPVCoordinates<T> transformPVCoordinates​(TimeStampedFieldPVCoordinates<T> pv)
Transform TimeStampedFieldPVCoordinates 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.

Type Parameters:
T - type of the field elements
Parameters:
pv - time-stamped position-velocity to transform.
Returns:
transformed time-stamped position-velocity
Since:
7.0
• #### getJacobian

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

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

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 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
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 interface StaticTransform
Returns:
underlying elementary translation
getCartesian(), getVelocity(), getAcceleration()
• #### 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 interface StaticTransform
Returns:
underlying elementary rotation
getAngular(), getRotationRate(), getRotationAcceleration()