Transform (ORbit Extrapolation KIT 10.1 API)

java.lang.Object
- org.orekit.frames.Transform

All Implemented Interfaces:

Serializable, TimeInterpolable<Transform>, TimeShiftable<Transform>, TimeStamped
```
public class Transform
extends Object
implements TimeStamped, TimeShiftable<Transform>, TimeInterpolable<Transform>, Serializable
```
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 with
PV_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

Field Summary

Fields
Modifier and Type Field and Description

static Transform IDENTITY
Identity transform.

Fields
Modifier and Type	Field and Description
`static Transform`	`IDENTITY` Identity transform.

Constructor Summary

Constructors
Constructor and Description
`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, 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, Transform first, Transform second)` Build a transform by combining two existing ones.
`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.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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.
`static Transform`	`interpolate(AbsoluteDate date, CartesianDerivativesFilter cFilter, AngularDerivativesFilter aFilter, Collection<Transform> sample)` Interpolate a transform from a sample set of existing transforms.
`Transform`	`interpolate(AbsoluteDate interpolationDate, Stream<Transform> sample)` Get an interpolated instance.
`Transform`	`shiftedBy(double dt)` Get a time-shifted instance.
`Line`	`transformLine(Line line)` Transform a line.
`<T extends RealFieldElement<T>> FieldVector3D<T>`	`transformPosition(FieldVector3D<T> position)` Transform a position vector (including translation effects).
`Vector3D`	`transformPosition(Vector3D position)` Transform a position vector (including translation effects).
`<T extends RealFieldElement<T>> FieldPVCoordinates<T>`	`transformPVCoordinates(FieldPVCoordinates<T> pv)` Transform `FieldPVCoordinates` including kinematic effects.
`PVCoordinates`	`transformPVCoordinates(PVCoordinates pva)` Transform `PVCoordinates` including kinematic effects.
`<T extends RealFieldElement<T>> TimeStampedFieldPVCoordinates<T>`	`transformPVCoordinates(TimeStampedFieldPVCoordinates<T> pv)` Transform `TimeStampedFieldPVCoordinates` including kinematic effects.
`TimeStampedPVCoordinates`	`transformPVCoordinates(TimeStampedPVCoordinates pv)` Transform `TimeStampedPVCoordinates` including kinematic effects.
`<T extends RealFieldElement<T>> FieldVector3D<T>`	`transformVector(FieldVector3D<T> vector)` Transform a vector (ignoring translation effects).
`Vector3D`	`transformVector(Vector3D vector)` Transform a vector (ignoring translation 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.time.TimeInterpolable
interpolate

- Field Detail
  - IDENTITY
```
public static final Transform IDENTITY
```
    Identity transform.
- Constructor Detail
  - 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)
  - interpolate
```
public Transform interpolate(AbsoluteDate interpolationDate,
                             Stream<Transform> sample)
```
    Get an interpolated instance.
    Note that the state of the current instance may not be used in the interpolation process, only its type and non interpolable fields are used (for example central attraction coefficient or frame when interpolating orbits). The interpolable fields taken into account are taken only from the states of the sample points. So if the state of the instance must be used, the instance should be included in the sample points.
    
    Note that this method is designed for small samples only (say up to about 10-20 points) so it can be implemented using polynomial interpolation (typically Hermite interpolation). Using too much points may induce Runge's phenomenon and numerical problems (including NaN appearing).
    
    Calling this method is equivalent to call interpolate(AbsoluteDate, CartesianDerivativesFilter, AngularDerivativesFilter, Collection) with cFilter set to CartesianDerivativesFilter.USE_PVA and aFilter set to AngularDerivativesFilter.USE_RRA set to true.
    
    Specified by:
    
    interpolate in interface TimeInterpolable<Transform>
    
    Parameters:
    
    interpolationDate - interpolation date
    
    sample - 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 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.
    
    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
  - transformPosition
```
public Vector3D transformPosition(Vector3D position)
```
    Transform a position vector (including translation effects).
    
    Parameters:
    
    position - vector to transform
    
    Returns:
    
    transformed position
  - transformPosition
```
public <T extends RealFieldElement<T>> FieldVector3D<T> transformPosition(FieldVector3D<T> position)
```
    Transform a position vector (including translation effects).
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    position - vector to transform
    
    Returns:
    
    transformed position
  - transformVector
```
public Vector3D transformVector(Vector3D vector)
```
    Transform a vector (ignoring translation effects).
    
    Parameters:
    
    vector - vector to transform
    
    Returns:
    
    transformed vector
  - transformVector
```
public <T extends RealFieldElement<T>> FieldVector3D<T> transformVector(FieldVector3D<T> vector)
```
    Transform a vector (ignoring translation effects).
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    vector - vector to transform
    
    Returns:
    
    transformed vector
  - transformLine
```
public Line transformLine(Line line)
```
    Transform a line.
    
    Parameters:
    
    line - to transform
    
    Returns:
    
    transformed line
  - 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 RealFieldElement<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 RealFieldElement<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
    
    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.
    
    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.
    
    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()

Class Transform

Examples

Example of translation from RA to RB

Example of rotation from RA to RB

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.orekit.time.TimeInterpolable

Field Detail

IDENTITY

Constructor Detail

Transform

Transform

Transform

Transform

Transform

Transform

Transform

Transform

Transform

Method Detail

getDate

shiftedBy

interpolate

interpolate

getInverse

freeze

transformPosition

transformPosition

transformVector

transformVector

transformLine

transformPVCoordinates

transformPVCoordinates

transformPVCoordinates

transformPVCoordinates

getJacobian

getCartesian

getTranslation

getVelocity

getAcceleration

getAngular

getRotation

getRotationRate

getRotationAcceleration

Example of translation from R_A to R_B

Example of rotation from R_A to R_B