Package org.orekit.frames

Class 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 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
    See Also:
    Serialized Form

    • Field Detail

      • IDENTITY

        public static final Transform IDENTITY
        Identity transform.

    • Constructor Detail

      • Transform

        public Transform​(AbsoluteDate date,
                 org.hipparchus.geometry.euclidean.threed.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,
                 org.hipparchus.geometry.euclidean.threed.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,
                 org.hipparchus.geometry.euclidean.threed.Vector3D translation,
                 org.hipparchus.geometry.euclidean.threed.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,
                 org.hipparchus.geometry.euclidean.threed.Vector3D translation,
                 org.hipparchus.geometry.euclidean.threed.Vector3D velocity,
                 org.hipparchus.geometry.euclidean.threed.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,
                 org.hipparchus.geometry.euclidean.threed.Rotation rotation,
                 org.hipparchus.geometry.euclidean.threed.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,
                 org.hipparchus.geometry.euclidean.threed.Rotation rotation,
                 org.hipparchus.geometry.euclidean.threed.Vector3D rotationRate,
                 org.hipparchus.geometry.euclidean.threed.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

      • 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 org.hipparchus.geometry.euclidean.threed.Vector3D transformPosition​(org.hipparchus.geometry.euclidean.threed.Vector3D position)
        Transform a position vector (including translation effects).
        Parameters:
        position - vector to transform
        Returns:
        transformed position

      • transformPosition

        public <T extends org.hipparchus.RealFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> transformPosition​(org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.geometry.euclidean.threed.Vector3D transformVector​(org.hipparchus.geometry.euclidean.threed.Vector3D vector)
        Transform a vector (ignoring translation effects).
        Parameters:
        vector - vector to transform
        Returns:
        transformed vector

      • transformVector

        public <T extends org.hipparchus.RealFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> transformVector​(org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.geometry.euclidean.threed.Line transformLine​(org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.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 org.hipparchus.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 org.hipparchus.geometry.euclidean.threed.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 org.hipparchus.geometry.euclidean.threed.Vector3D getVelocity()
        Get the first time derivative of the translation.
        Returns:
        first time derivative of the translation
        See Also:
        getCartesian(), getTranslation(), getAcceleration()

      • getAcceleration

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