FieldTransform.java
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package org.orekit.frames;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.List;
import java.util.stream.Stream;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.geometry.euclidean.threed.FieldLine;
import org.hipparchus.geometry.euclidean.threed.FieldRotation;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.time.FieldTimeInterpolator;
import org.orekit.time.FieldTimeShiftable;
import org.orekit.utils.AngularDerivativesFilter;
import org.orekit.utils.CartesianDerivativesFilter;
import org.orekit.utils.FieldAngularCoordinates;
import org.orekit.utils.FieldPVCoordinates;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.TimeStampedFieldAngularCoordinates;
import org.orekit.utils.TimeStampedFieldAngularCoordinatesHermiteInterpolator;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
import org.orekit.utils.TimeStampedFieldPVCoordinatesHermiteInterpolator;
import org.orekit.utils.TimeStampedPVCoordinates;
/** Transformation class in three-dimensional space.
*
* <p>This class represents the transformation engine between {@link Frame 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.</p>
* <p>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.
*
* <p>Instances of this class are guaranteed to be immutable.</p>
*
* <h2> Examples </h2>
*
* <h3> Example of translation from R<sub>A</sub> to R<sub>B</sub> </h3>
*
* <p> We want to transform the {@link FieldPVCoordinates} PV<sub>A</sub> to
* PV<sub>B</sub> with :
* <p> PV<sub>A</sub> = ({1, 0, 0}, {2, 0, 0}, {3, 0, 0}); <br>
* PV<sub>B</sub> = ({0, 0, 0}, {0, 0, 0}, {0, 0, 0});
*
* <p> The transform to apply then is defined as follows :
*
* <pre>
* 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);
* </pre>
*
* <h3> Example of rotation from R<sub>A</sub> to R<sub>B</sub> </h3>
* <p> We want to transform the {@link FieldPVCoordinates} PV<sub>A</sub> to
* PV<sub>B</sub> with
*
* <p> PV<sub>A</sub> = ({1, 0, 0}, { 1, 0, 0}); <br>
* PV<sub>B</sub> = ({0, 1, 0}, {-2, 1, 0});
*
* <p> The transform to apply then is defined as follows :
*
* <pre>
* 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);
* </pre>
*
* @author Luc Maisonobe
* @author Fabien Maussion
* @param <T> the type of the field elements
* @since 9.0
*/
public class FieldTransform<T extends CalculusFieldElement<T>>
implements FieldTimeShiftable<FieldTransform<T>, T>, FieldKinematicTransform<T> {
/** Date of the transform. */
private final FieldAbsoluteDate<T> date;
/** Date of the transform. */
private final AbsoluteDate aDate;
/** Cartesian coordinates of the target frame with respect to the original frame. */
private final FieldPVCoordinates<T> cartesian;
/** Angular coordinates of the target frame with respect to the original frame. */
private final FieldAngularCoordinates<T> angular;
/** Build a transform from its primitive operations.
* @param date date of the transform
* @param aDate date of the transform
* @param cartesian Cartesian coordinates of the target frame with respect to the original frame
* @param angular angular coordinates of the target frame with respect to the original frame
*/
private FieldTransform(final FieldAbsoluteDate<T> date, final AbsoluteDate aDate,
final FieldPVCoordinates<T> cartesian,
final FieldAngularCoordinates<T> angular) {
this.date = date;
this.aDate = aDate;
this.cartesian = cartesian;
this.angular = angular;
}
/** Build a transform from a regular transform.
* @param field field of the elements
* @param transform regular transform to convert
*/
public FieldTransform(final Field<T> field, final Transform transform) {
this(new FieldAbsoluteDate<>(field, transform.getDate()), transform.getDate(),
new FieldPVCoordinates<>(field, transform.getCartesian()),
new FieldAngularCoordinates<>(field, transform.getAngular()));
}
/** Build a translation transform.
* @param date date of the transform
* @param translation translation to apply (i.e. coordinates of
* the transformed origin, or coordinates of the origin of the
* old frame in the new frame)
*/
public FieldTransform(final FieldAbsoluteDate<T> date, final FieldVector3D<T> translation) {
this(date, date.toAbsoluteDate(),
new FieldPVCoordinates<>(translation,
FieldVector3D.getZero(date.getField()),
FieldVector3D.getZero(date.getField())),
FieldAngularCoordinates.getIdentity(date.getField()));
}
/** Build a rotation transform.
* @param date date of the transform
* @param 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 )
*/
public FieldTransform(final FieldAbsoluteDate<T> date, final FieldRotation<T> rotation) {
this(date, date.toAbsoluteDate(),
FieldPVCoordinates.getZero(date.getField()),
new FieldAngularCoordinates<>(rotation,
FieldVector3D.getZero(date.getField()),
FieldVector3D.getZero(date.getField())));
}
/** Build a translation transform, with its first time derivative.
* @param date date of the transform
* @param translation translation to apply (i.e. coordinates of
* the transformed origin, or coordinates of the origin of the
* old frame in the new frame)
* @param velocity the velocity of the translation (i.e. origin
* of the old frame velocity in the new frame)
*/
public FieldTransform(final FieldAbsoluteDate<T> date,
final FieldVector3D<T> translation,
final FieldVector3D<T> velocity) {
this(date,
new FieldPVCoordinates<>(translation,
velocity,
FieldVector3D.getZero(date.getField())));
}
/** Build a translation transform, with its first and second time derivatives.
* @param date date of the transform
* @param translation translation to apply (i.e. coordinates of
* the transformed origin, or coordinates of the origin of the
* old frame in the new frame)
* @param velocity the velocity of the translation (i.e. origin
* of the old frame velocity in the new frame)
* @param acceleration the acceleration of the translation (i.e. origin
* of the old frame acceleration in the new frame)
*/
public FieldTransform(final FieldAbsoluteDate<T> date, final FieldVector3D<T> translation,
final FieldVector3D<T> velocity, final FieldVector3D<T> acceleration) {
this(date,
new FieldPVCoordinates<>(translation, velocity, acceleration));
}
/** Build a translation transform, with its first time derivative.
* @param date date of the transform
* @param 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)
*/
public FieldTransform(final FieldAbsoluteDate<T> date, final FieldPVCoordinates<T> cartesian) {
this(date, date.toAbsoluteDate(),
cartesian,
FieldAngularCoordinates.getIdentity(date.getField()));
}
/** Build a rotation transform.
* @param date date of the transform
* @param 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 )
* @param rotationRate the axis of the instant rotation
* expressed in the new frame. (norm representing angular rate)
*/
public FieldTransform(final FieldAbsoluteDate<T> date,
final FieldRotation<T> rotation,
final FieldVector3D<T> rotationRate) {
this(date,
new FieldAngularCoordinates<>(rotation,
rotationRate,
FieldVector3D.getZero(date.getField())));
}
/** Build a rotation transform.
* @param date date of the transform
* @param 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 )
* @param rotationRate the axis of the instant rotation
* @param rotationAcceleration the axis of the instant rotation
* expressed in the new frame. (norm representing angular rate)
*/
public FieldTransform(final FieldAbsoluteDate<T> date,
final FieldRotation<T> rotation,
final FieldVector3D<T> rotationRate,
final FieldVector3D<T> rotationAcceleration) {
this(date, new FieldAngularCoordinates<>(rotation, rotationRate, rotationAcceleration));
}
/** Build a rotation transform.
* @param date date of the transform
* @param 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)
*/
public FieldTransform(final FieldAbsoluteDate<T> date, final FieldAngularCoordinates<T> angular) {
this(date, date.toAbsoluteDate(),
FieldPVCoordinates.getZero(date.getField()),
angular);
}
/** Build a transform by combining two existing ones.
* <p>
* Note that the dates of the two existing transformed are <em>ignored</em>,
* 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.
* </p>
* @param date date of the transform
* @param first first transform applied
* @param second second transform applied
*/
public FieldTransform(final FieldAbsoluteDate<T> date,
final FieldTransform<T> first,
final FieldTransform<T> second) {
this(date, date.toAbsoluteDate(),
new FieldPVCoordinates<>(FieldStaticTransform.compositeTranslation(first, second),
compositeVelocity(first, second),
compositeAcceleration(first, second)),
new FieldAngularCoordinates<>(FieldStaticTransform.compositeRotation(first, second),
compositeRotationRate(first, second),
compositeRotationAcceleration(first, second)));
}
/** Get the identity transform.
* @param field field for the components
* @param <T> the type of the field elements
* @return identity transform
*/
public static <T extends CalculusFieldElement<T>> FieldTransform<T> getIdentity(final Field<T> field) {
return new FieldIdentityTransform<>(field);
}
/** Compute a composite velocity.
* @param first first applied transform
* @param second second applied transform
* @param <T> the type of the field elements
* @return velocity part of the composite transform
*/
private static <T extends CalculusFieldElement<T>> FieldVector3D<T> compositeVelocity(final FieldTransform<T> first, final FieldTransform<T> second) {
final FieldVector3D<T> v1 = first.cartesian.getVelocity();
final FieldRotation<T> r1 = first.angular.getRotation();
final FieldVector3D<T> o1 = first.angular.getRotationRate();
final FieldVector3D<T> p2 = second.cartesian.getPosition();
final FieldVector3D<T> v2 = second.cartesian.getVelocity();
final FieldVector3D<T> crossP = FieldVector3D.crossProduct(o1, p2);
return v1.add(r1.applyInverseTo(v2.add(crossP)));
}
/** Compute a composite acceleration.
* @param first first applied transform
* @param second second applied transform
* @param <T> the type of the field elements
* @return acceleration part of the composite transform
*/
private static <T extends CalculusFieldElement<T>> FieldVector3D<T> compositeAcceleration(final FieldTransform<T> first, final FieldTransform<T> second) {
final FieldVector3D<T> a1 = first.cartesian.getAcceleration();
final FieldRotation<T> r1 = first.angular.getRotation();
final FieldVector3D<T> o1 = first.angular.getRotationRate();
final FieldVector3D<T> oDot1 = first.angular.getRotationAcceleration();
final FieldVector3D<T> p2 = second.cartesian.getPosition();
final FieldVector3D<T> v2 = second.cartesian.getVelocity();
final FieldVector3D<T> a2 = second.cartesian.getAcceleration();
final FieldVector3D<T> crossCrossP = FieldVector3D.crossProduct(o1, FieldVector3D.crossProduct(o1, p2));
final FieldVector3D<T> crossV = FieldVector3D.crossProduct(o1, v2);
final FieldVector3D<T> crossDotP = FieldVector3D.crossProduct(oDot1, p2);
return a1.add(r1.applyInverseTo(new FieldVector3D<>(1, a2, 2, crossV, 1, crossCrossP, 1, crossDotP)));
}
/** Compute a composite rotation rate.
* @param first first applied transform
* @param second second applied transform
* @param <T> the type of the field elements
* @return rotation rate part of the composite transform
*/
private static <T extends CalculusFieldElement<T>> FieldVector3D<T> compositeRotationRate(final FieldTransform<T> first, final FieldTransform<T> second) {
final FieldVector3D<T> o1 = first.angular.getRotationRate();
final FieldRotation<T> r2 = second.angular.getRotation();
final FieldVector3D<T> o2 = second.angular.getRotationRate();
return o2.add(r2.applyTo(o1));
}
/** Compute a composite rotation acceleration.
* @param first first applied transform
* @param second second applied transform
* @param <T> the type of the field elements
* @return rotation acceleration part of the composite transform
*/
private static <T extends CalculusFieldElement<T>> FieldVector3D<T> compositeRotationAcceleration(final FieldTransform<T> first, final FieldTransform<T> second) {
final FieldVector3D<T> o1 = first.angular.getRotationRate();
final FieldVector3D<T> oDot1 = first.angular.getRotationAcceleration();
final FieldRotation<T> r2 = second.angular.getRotation();
final FieldVector3D<T> o2 = second.angular.getRotationRate();
final FieldVector3D<T> oDot2 = second.angular.getRotationAcceleration();
return new FieldVector3D<>( 1, oDot2,
1, r2.applyTo(oDot1),
-1, FieldVector3D.crossProduct(o2, r2.applyTo(o1)));
}
/** {@inheritDoc} */
@Override
public AbsoluteDate getDate() {
return aDate;
}
/** Get the date.
* @return date attached to the object
*/
@Override
public FieldAbsoluteDate<T> getFieldDate() {
return date;
}
/** {@inheritDoc} */
@Override
public FieldTransform<T> shiftedBy(final double dt) {
return new FieldTransform<>(date.shiftedBy(dt), aDate.shiftedBy(dt),
cartesian.shiftedBy(dt), angular.shiftedBy(dt));
}
/** Get a time-shifted instance.
* @param dt time shift in seconds
* @return a new instance, shifted with respect to instance (which is not changed)
*/
public FieldTransform<T> shiftedBy(final T dt) {
return new FieldTransform<>(date.shiftedBy(dt), aDate.shiftedBy(dt.getReal()),
cartesian.shiftedBy(dt), angular.shiftedBy(dt));
}
/**
* Shift the transform in time considering all rates, then return only the
* translation and rotation portion of the transform.
*
* @param dt time shift in seconds.
* @return 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 #shiftedBy(double)
*/
public FieldStaticTransform<T> staticShiftedBy(final T dt) {
return FieldStaticTransform.of(date.shiftedBy(dt),
cartesian.positionShiftedBy(dt),
angular.rotationShiftedBy(dt));
}
/**
* Create a so-called static transform from the instance.
*
* @return 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 FieldStaticTransform
*/
public FieldStaticTransform<T> toStaticTransform() {
return FieldStaticTransform.of(date, cartesian.getPosition(), angular.getRotation());
}
/** Interpolate a transform from a sample set of existing transforms.
* <p>
* Calling this method is equivalent to call {@link #interpolate(FieldAbsoluteDate,
* CartesianDerivativesFilter, AngularDerivativesFilter, Collection)} with {@code cFilter}
* set to {@link CartesianDerivativesFilter#USE_PVA} and {@code aFilter} set to
* {@link AngularDerivativesFilter#USE_RRA}
* set to true.
* </p>
* @param interpolationDate interpolation date
* @param sample sample points on which interpolation should be done
* @param <T> the type of the field elements
* @return a new instance, interpolated at specified date
*/
public static <T extends CalculusFieldElement<T>> FieldTransform<T> interpolate(final FieldAbsoluteDate<T> interpolationDate,
final Collection<FieldTransform<T>> sample) {
return interpolate(interpolationDate,
CartesianDerivativesFilter.USE_PVA, AngularDerivativesFilter.USE_RRA,
sample);
}
/** Interpolate a transform from a sample set of existing transforms.
* <p>
* 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.
* </p>
* <p>
* As this implementation of interpolation is polynomial, it should be used only
* with small samples (about 10-20 points) in order to avoid <a
* href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
* and numerical problems (including NaN appearing).
* </p>
* @param date interpolation date
* @param cFilter filter for derivatives from the sample to use in interpolation
* @param aFilter filter for derivatives from the sample to use in interpolation
* @param sample sample points on which interpolation should be done
* @return a new instance, interpolated at specified date
* @param <T> the type of the field elements
*/
public static <T extends CalculusFieldElement<T>> FieldTransform<T> interpolate(final FieldAbsoluteDate<T> date,
final CartesianDerivativesFilter cFilter,
final AngularDerivativesFilter aFilter,
final Collection<FieldTransform<T>> sample) {
return interpolate(date, cFilter, aFilter, sample.stream());
}
/** Interpolate a transform from a sample set of existing transforms.
* <p>
* 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.
* </p>
* <p>
* As this implementation of interpolation is polynomial, it should be used only
* with small samples (about 10-20 points) in order to avoid <a
* href="http://en.wikipedia.org/wiki/Runge%27s_phenomenon">Runge's phenomenon</a>
* and numerical problems (including NaN appearing).
* </p>
* @param date interpolation date
* @param cFilter filter for derivatives from the sample to use in interpolation
* @param aFilter filter for derivatives from the sample to use in interpolation
* @param sample sample points on which interpolation should be done
* @return a new instance, interpolated at specified date
* @param <T> the type of the field elements
*/
public static <T extends CalculusFieldElement<T>> FieldTransform<T> interpolate(final FieldAbsoluteDate<T> date,
final CartesianDerivativesFilter cFilter,
final AngularDerivativesFilter aFilter,
final Stream<FieldTransform<T>> sample) {
// Create samples
final List<TimeStampedFieldPVCoordinates<T>> datedPV = new ArrayList<>();
final List<TimeStampedFieldAngularCoordinates<T>> datedAC = new ArrayList<>();
sample.forEach(t -> {
datedPV.add(new TimeStampedFieldPVCoordinates<>(t.getDate(), t.getTranslation(), t.getVelocity(), t.getAcceleration()));
datedAC.add(new TimeStampedFieldAngularCoordinates<>(t.getDate(), t.getRotation(), t.getRotationRate(), t.getRotationAcceleration()));
});
// Create interpolators
final FieldTimeInterpolator<TimeStampedFieldPVCoordinates<T>, T> pvInterpolator =
new TimeStampedFieldPVCoordinatesHermiteInterpolator<>(datedPV.size(), cFilter);
final FieldTimeInterpolator<TimeStampedFieldAngularCoordinates<T>, T> angularInterpolator =
new TimeStampedFieldAngularCoordinatesHermiteInterpolator<>(datedPV.size(), aFilter);
// Interpolate
final TimeStampedFieldPVCoordinates<T> interpolatedPV = pvInterpolator.interpolate(date, datedPV);
final TimeStampedFieldAngularCoordinates<T> interpolatedAC = angularInterpolator.interpolate(date, datedAC);
return new FieldTransform<>(date, date.toAbsoluteDate(), interpolatedPV, interpolatedAC);
}
/** Get the inverse transform of the instance.
* @return inverse transform of the instance
*/
@Override
public FieldTransform<T> getInverse() {
final FieldRotation<T> r = angular.getRotation();
final FieldVector3D<T> o = angular.getRotationRate();
final FieldVector3D<T> oDot = angular.getRotationAcceleration();
final FieldVector3D<T> rp = r.applyTo(cartesian.getPosition());
final FieldVector3D<T> rv = r.applyTo(cartesian.getVelocity());
final FieldVector3D<T> ra = r.applyTo(cartesian.getAcceleration());
final FieldVector3D<T> pInv = rp.negate();
final FieldVector3D<T> crossP = FieldVector3D.crossProduct(o, rp);
final FieldVector3D<T> vInv = crossP.subtract(rv);
final FieldVector3D<T> crossV = FieldVector3D.crossProduct(o, rv);
final FieldVector3D<T> crossDotP = FieldVector3D.crossProduct(oDot, rp);
final FieldVector3D<T> crossCrossP = FieldVector3D.crossProduct(o, crossP);
final FieldVector3D<T> aInv = new FieldVector3D<>(-1, ra,
2, crossV,
1, crossDotP,
-1, crossCrossP);
return new FieldTransform<>(date, aDate, new FieldPVCoordinates<>(pInv, vInv, aInv), angular.revert());
}
/** Get a frozen transform.
* <p>
* This method creates a copy of the instance but frozen in time,
* i.e. with velocity, acceleration and rotation rate forced to zero.
* </p>
* @return a new transform, without any time-dependent parts
*/
public FieldTransform<T> freeze() {
return new FieldTransform<>(date, aDate,
new FieldPVCoordinates<>(cartesian.getPosition(),
FieldVector3D.getZero(date.getField()),
FieldVector3D.getZero(date.getField())),
new FieldAngularCoordinates<>(angular.getRotation(),
FieldVector3D.getZero(date.getField()),
FieldVector3D.getZero(date.getField())));
}
/** Transform {@link TimeStampedPVCoordinates} including kinematic effects.
* <p>
* In order to allow the user more flexibility, this method does <em>not</em> check for
* consistency between the transform {@link #getDate() date} and the time-stamped
* position-velocity {@link TimeStampedPVCoordinates#getDate() date}. The returned
* value will always have the same {@link TimeStampedPVCoordinates#getDate() date} as
* the input argument, regardless of the instance {@link #getDate() date}.
* </p>
* @param pv time-stamped position-velocity to transform.
* @return transformed time-stamped position-velocity
*/
public FieldPVCoordinates<T> transformPVCoordinates(final PVCoordinates pv) {
return angular.applyTo(new FieldPVCoordinates<>(cartesian.getPosition().add(pv.getPosition()),
cartesian.getVelocity().add(pv.getVelocity()),
cartesian.getAcceleration().add(pv.getAcceleration())));
}
/** Transform {@link TimeStampedPVCoordinates} including kinematic effects.
* <p>
* In order to allow the user more flexibility, this method does <em>not</em> check for
* consistency between the transform {@link #getDate() date} and the time-stamped
* position-velocity {@link TimeStampedPVCoordinates#getDate() date}. The returned
* value will always have the same {@link TimeStampedPVCoordinates#getDate() date} as
* the input argument, regardless of the instance {@link #getDate() date}.
* </p>
* @param pv time-stamped position-velocity to transform.
* @return transformed time-stamped position-velocity
*/
public TimeStampedFieldPVCoordinates<T> transformPVCoordinates(final TimeStampedPVCoordinates pv) {
return angular.applyTo(new TimeStampedFieldPVCoordinates<>(pv.getDate(),
cartesian.getPosition().add(pv.getPosition()),
cartesian.getVelocity().add(pv.getVelocity()),
cartesian.getAcceleration().add(pv.getAcceleration())));
}
/** Transform {@link TimeStampedFieldPVCoordinates} including kinematic effects.
* <p>
* 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
* <em>not</em> be used when derivatives are contained in the {@link CalculusFieldElement field
* elements} (typically when using {@link org.hipparchus.analysis.differentiation.DerivativeStructure
* 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 {@link #transformPosition(FieldVector3D) 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 {@link
* org.hipparchus.analysis.differentiation.DerivativeStructure 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, ...).
* </p>
* <p>
* In order to allow the user more flexibility, this method does <em>not</em> check for
* consistency between the transform {@link #getDate() date} and the time-stamped
* position-velocity {@link TimeStampedFieldPVCoordinates#getDate() date}. The returned
* value will always have the same {@link TimeStampedFieldPVCoordinates#getDate() date} as
* the input argument, regardless of the instance {@link #getDate() date}.
* </p>
* @param pv time-stamped position-velocity to transform.
* @return transformed time-stamped position-velocity
*/
public FieldPVCoordinates<T> transformPVCoordinates(final FieldPVCoordinates<T> pv) {
return angular.applyTo(new FieldPVCoordinates<>(pv.getPosition().add(cartesian.getPosition()),
pv.getVelocity().add(cartesian.getVelocity()),
pv.getAcceleration().add(cartesian.getAcceleration())));
}
/** Transform {@link TimeStampedFieldPVCoordinates} including kinematic effects.
* <p>
* 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
* <em>not</em> be used when derivatives are contained in the {@link CalculusFieldElement field
* elements} (typically when using {@link org.hipparchus.analysis.differentiation.DerivativeStructure
* 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 {@link #transformPosition(FieldVector3D) 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 {@link
* org.hipparchus.analysis.differentiation.DerivativeStructure 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, ...).
* </p>
* <p>
* In order to allow the user more flexibility, this method does <em>not</em> check for
* consistency between the transform {@link #getDate() date} and the time-stamped
* position-velocity {@link TimeStampedFieldPVCoordinates#getDate() date}. The returned
* value will always have the same {@link TimeStampedFieldPVCoordinates#getDate() date} as
* the input argument, regardless of the instance {@link #getDate() date}.
* </p>
* @param pv time-stamped position-velocity to transform.
* @return transformed time-stamped position-velocity
*/
public TimeStampedFieldPVCoordinates<T> transformPVCoordinates(final TimeStampedFieldPVCoordinates<T> pv) {
return angular.applyTo(new TimeStampedFieldPVCoordinates<>(pv.getDate(),
pv.getPosition().add(cartesian.getPosition()),
pv.getVelocity().add(cartesian.getVelocity()),
pv.getAcceleration().add(cartesian.getAcceleration())));
}
/** Compute the Jacobian of the {@link #transformPVCoordinates(FieldPVCoordinates)}
* method of the transform.
* <p>
* Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i
* of the transformed {@link FieldPVCoordinates} with respect to Cartesian coordinate j
* of the input {@link FieldPVCoordinates} in method {@link #transformPVCoordinates(FieldPVCoordinates)}.
* </p>
* <p>
* This definition implies that if we define position-velocity coordinates
* <pre>PV₁ = transform.transformPVCoordinates(PV₀)</pre>
* then their differentials dPV₁ and dPV₀ will obey the following relation
* where J is the matrix computed by this method:
* <pre>dPV₁ = J × dPV₀</pre>
*
* @param 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)
* @param jacobian placeholder matrix whose upper-left corner is to be filled with
* the Jacobian, the rest of the matrix remaining untouched
*/
public void getJacobian(final CartesianDerivativesFilter selector, final T[][] jacobian) {
final T zero = date.getField().getZero();
// elementary matrix for rotation
final T[][] mData = angular.getRotation().getMatrix();
// dP1/dP0
System.arraycopy(mData[0], 0, jacobian[0], 0, 3);
System.arraycopy(mData[1], 0, jacobian[1], 0, 3);
System.arraycopy(mData[2], 0, jacobian[2], 0, 3);
if (selector.getMaxOrder() >= 1) {
// dP1/dV0
Arrays.fill(jacobian[0], 3, 6, zero);
Arrays.fill(jacobian[1], 3, 6, zero);
Arrays.fill(jacobian[2], 3, 6, zero);
// dV1/dP0
final FieldVector3D<T> o = angular.getRotationRate();
final T ox = o.getX();
final T oy = o.getY();
final T oz = o.getZ();
for (int i = 0; i < 3; ++i) {
jacobian[3][i] = oz.multiply(mData[1][i]).subtract(oy.multiply(mData[2][i]));
jacobian[4][i] = ox.multiply(mData[2][i]).subtract(oz.multiply(mData[0][i]));
jacobian[5][i] = oy.multiply(mData[0][i]).subtract(ox.multiply(mData[1][i]));
}
// dV1/dV0
System.arraycopy(mData[0], 0, jacobian[3], 3, 3);
System.arraycopy(mData[1], 0, jacobian[4], 3, 3);
System.arraycopy(mData[2], 0, jacobian[5], 3, 3);
if (selector.getMaxOrder() >= 2) {
// dP1/dA0
Arrays.fill(jacobian[0], 6, 9, zero);
Arrays.fill(jacobian[1], 6, 9, zero);
Arrays.fill(jacobian[2], 6, 9, zero);
// dV1/dA0
Arrays.fill(jacobian[3], 6, 9, zero);
Arrays.fill(jacobian[4], 6, 9, zero);
Arrays.fill(jacobian[5], 6, 9, zero);
// dA1/dP0
final FieldVector3D<T> oDot = angular.getRotationAcceleration();
final T oDotx = oDot.getX();
final T oDoty = oDot.getY();
final T oDotz = oDot.getZ();
for (int i = 0; i < 3; ++i) {
jacobian[6][i] = oDotz.multiply(mData[1][i]).subtract(oDoty.multiply(mData[2][i])).add(oz.multiply(jacobian[4][i]).subtract(oy.multiply(jacobian[5][i])));
jacobian[7][i] = oDotx.multiply(mData[2][i]).subtract(oDotz.multiply(mData[0][i])).add(ox.multiply(jacobian[5][i]).subtract(oz.multiply(jacobian[3][i])));
jacobian[8][i] = oDoty.multiply(mData[0][i]).subtract(oDotx.multiply(mData[1][i])).add(oy.multiply(jacobian[3][i]).subtract(ox.multiply(jacobian[4][i])));
}
// dA1/dV0
for (int i = 0; i < 3; ++i) {
jacobian[6][i + 3] = oz.multiply(mData[1][i]).subtract(oy.multiply(mData[2][i])).multiply(2);
jacobian[7][i + 3] = ox.multiply(mData[2][i]).subtract(oz.multiply(mData[0][i])).multiply(2);
jacobian[8][i + 3] = oy.multiply(mData[0][i]).subtract(ox.multiply(mData[1][i])).multiply(2);
}
// dA1/dA0
System.arraycopy(mData[0], 0, jacobian[6], 6, 3);
System.arraycopy(mData[1], 0, jacobian[7], 6, 3);
System.arraycopy(mData[2], 0, jacobian[8], 6, 3);
}
}
}
/** Get the underlying elementary Cartesian part.
* <p>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.</p>
* @return underlying elementary Cartesian part
* @see #getTranslation()
* @see #getVelocity()
*/
public FieldPVCoordinates<T> getCartesian() {
return cartesian;
}
/** Get the underlying elementary translation.
* <p>A transform can be uniquely represented as an elementary
* translation followed by an elementary rotation. This method
* returns this unique elementary translation.</p>
* @return underlying elementary translation
* @see #getCartesian()
* @see #getVelocity()
* @see #getAcceleration()
*/
public FieldVector3D<T> getTranslation() {
return cartesian.getPosition();
}
/** Get the first time derivative of the translation.
* @return first time derivative of the translation
* @see #getCartesian()
* @see #getTranslation()
* @see #getAcceleration()
*/
public FieldVector3D<T> getVelocity() {
return cartesian.getVelocity();
}
/** Get the second time derivative of the translation.
* @return second time derivative of the translation
* @see #getCartesian()
* @see #getTranslation()
* @see #getVelocity()
*/
public FieldVector3D<T> getAcceleration() {
return cartesian.getAcceleration();
}
/** Get the underlying elementary angular part.
* <p>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.</p>
* @return underlying elementary angular part
* @see #getRotation()
* @see #getRotationRate()
* @see #getRotationAcceleration()
*/
public FieldAngularCoordinates<T> getAngular() {
return angular;
}
/** Get the underlying elementary rotation.
* <p>A transform can be uniquely represented as an elementary
* translation followed by an elementary rotation. This method
* returns this unique elementary rotation.</p>
* @return underlying elementary rotation
* @see #getAngular()
* @see #getRotationRate()
* @see #getRotationAcceleration()
*/
public FieldRotation<T> getRotation() {
return angular.getRotation();
}
/** Get the first time derivative of the rotation.
* <p>The norm represents the angular rate.</p>
* @return First time derivative of the rotation
* @see #getAngular()
* @see #getRotation()
* @see #getRotationAcceleration()
*/
public FieldVector3D<T> getRotationRate() {
return angular.getRotationRate();
}
/** Get the second time derivative of the rotation.
* @return Second time derivative of the rotation
* @see #getAngular()
* @see #getRotation()
* @see #getRotationRate()
*/
public FieldVector3D<T> getRotationAcceleration() {
return angular.getRotationAcceleration();
}
/** Specialized class for identity transform. */
private static class FieldIdentityTransform<T extends CalculusFieldElement<T>> extends FieldTransform<T> {
/** Simple constructor.
* @param field field for the components
*/
FieldIdentityTransform(final Field<T> field) {
super(FieldAbsoluteDate.getArbitraryEpoch(field),
FieldAbsoluteDate.getArbitraryEpoch(field).toAbsoluteDate(),
FieldPVCoordinates.getZero(field),
FieldAngularCoordinates.getIdentity(field));
}
/** {@inheritDoc} */
@Override
public FieldTransform<T> shiftedBy(final double dt) {
return this;
}
/** {@inheritDoc} */
@Override
public FieldTransform<T> getInverse() {
return this;
}
/** {@inheritDoc} */
@Override
public FieldVector3D<T> transformPosition(final FieldVector3D<T> position) {
return position;
}
/** {@inheritDoc} */
@Override
public FieldVector3D<T> transformVector(final FieldVector3D<T> vector) {
return vector;
}
/** {@inheritDoc} */
@Override
public FieldLine<T> transformLine(final FieldLine<T> line) {
return line;
}
/** {@inheritDoc} */
@Override
public FieldPVCoordinates<T> transformPVCoordinates(final FieldPVCoordinates<T> pv) {
return pv;
}
/** {@inheritDoc} */
@Override
public FieldTransform<T> freeze() {
return this;
}
/** {@inheritDoc} */
@Override
public void getJacobian(final CartesianDerivativesFilter selector, final T[][] jacobian) {
final int n = 3 * (selector.getMaxOrder() + 1);
for (int i = 0; i < n; ++i) {
Arrays.fill(jacobian[i], 0, n, getFieldDate().getField().getZero());
jacobian[i][i] = getFieldDate().getField().getOne();
}
}
}
}