TimeStampedAngularCoordinates.java

/* Copyright 2002-2019 CS Systèmes d'Information
 * Licensed to CS Systèmes d'Information (CS) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * CS licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
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package org.orekit.utils;

import java.util.Collection;

import org.hipparchus.analysis.differentiation.DerivativeStructure;
import org.hipparchus.analysis.interpolation.HermiteInterpolator;
import org.hipparchus.geometry.euclidean.threed.FieldRotation;
import org.hipparchus.geometry.euclidean.threed.Rotation;
import org.hipparchus.geometry.euclidean.threed.RotationConvention;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitInternalError;
import org.orekit.errors.OrekitMessages;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.TimeStamped;

/** {@link TimeStamped time-stamped} version of {@link AngularCoordinates}.
 * <p>Instances of this class are guaranteed to be immutable.</p>
 * @author Luc Maisonobe
 * @since 7.0
 */
public class TimeStampedAngularCoordinates extends AngularCoordinates implements TimeStamped {

    /** Serializable UID. */
    private static final long serialVersionUID = 20140723L;

    /** The date. */
    private final AbsoluteDate date;

    /** Builds a rotation/rotation rate pair.
     * @param date coordinates date
     * @param rotation rotation
     * @param rotationRate rotation rate Ω (rad/s)
     * @param rotationAcceleration rotation acceleration dΩ/dt (rad²/s²)
     */
    public TimeStampedAngularCoordinates(final AbsoluteDate date,
                                         final Rotation rotation,
                                         final Vector3D rotationRate,
                                         final Vector3D rotationAcceleration) {
        super(rotation, rotationRate, rotationAcceleration);
        this.date = date;
    }

    /** Build the rotation that transforms a pair of pv coordinates into another pair.

     * <p><em>WARNING</em>! This method requires much more stringent assumptions on
     * its parameters than the similar {@link Rotation#Rotation(Vector3D, Vector3D,
     * Vector3D, Vector3D) constructor} from the {@link Rotation Rotation} class.
     * As far as the Rotation constructor is concerned, the {@code v₂} vector from
     * the second pair can be slightly misaligned. The Rotation constructor will
     * compensate for this misalignment and create a rotation that ensure {@code
     * v₁ = r(u₁)} and {@code v₂ ∈ plane (r(u₁), r(u₂))}. <em>THIS IS NOT
     * TRUE ANYMORE IN THIS CLASS</em>! As derivatives are involved and must be
     * preserved, this constructor works <em>only</em> if the two pairs are fully
     * consistent, i.e. if a rotation exists that fulfill all the requirements: {@code
     * v₁ = r(u₁)}, {@code v₂ = r(u₂)}, {@code dv₁/dt = dr(u₁)/dt}, {@code dv₂/dt
     * = dr(u₂)/dt}, {@code d²v₁/dt² = d²r(u₁)/dt²}, {@code d²v₂/dt² = d²r(u₂)/dt²}.</p>

     * @param date coordinates date
     * @param u1 first vector of the origin pair
     * @param u2 second vector of the origin pair
     * @param v1 desired image of u1 by the rotation
     * @param v2 desired image of u2 by the rotation
     * @param tolerance relative tolerance factor used to check singularities
     */
    public TimeStampedAngularCoordinates(final AbsoluteDate date,
                                         final PVCoordinates u1, final PVCoordinates u2,
                                         final PVCoordinates v1, final PVCoordinates v2,
                                         final double tolerance) {
        super(u1, u2, v1, v2, tolerance);
        this.date = date;
    }

    /** Build one of the rotations that transform one pv coordinates into another one.

     * <p>Except for a possible scale factor, if the instance were
     * applied to the vector u it will produce the vector v. There is an
     * infinite number of such rotations, this constructor choose the
     * one with the smallest associated angle (i.e. the one whose axis
     * is orthogonal to the (u, v) plane). If u and v are collinear, an
     * arbitrary rotation axis is chosen.</p>

     * @param date coordinates date
     * @param u origin vector
     * @param v desired image of u by the rotation
     */
    public TimeStampedAngularCoordinates(final AbsoluteDate date,
                                         final PVCoordinates u, final PVCoordinates v) {
        super(u, v);
        this.date = date;
    }

    /** Builds a TimeStampedAngularCoordinates from  a {@link FieldRotation}&lt;{@link DerivativeStructure}&gt;.
     * <p>
     * The rotation components must have time as their only derivation parameter and
     * have consistent derivation orders.
     * </p>
     * @param date coordinates date
     * @param r rotation with time-derivatives embedded within the coordinates
     */
    public TimeStampedAngularCoordinates(final AbsoluteDate date,
                                         final FieldRotation<DerivativeStructure> r) {
        super(r);
        this.date = date;
    }

    /** {@inheritDoc} */
    public AbsoluteDate getDate() {
        return date;
    }

    /** Revert a rotation/rotation rate pair.
     * Build a pair which reverse the effect of another pair.
     * @return a new pair whose effect is the reverse of the effect
     * of the instance
     */
    public TimeStampedAngularCoordinates revert() {
        return new TimeStampedAngularCoordinates(date,
                                                 getRotation().revert(),
                                                 getRotation().applyInverseTo(getRotationRate().negate()),
                                                 getRotation().applyInverseTo(getRotationAcceleration().negate()));
    }

    /** Get a time-shifted state.
     * <p>
     * The state can be slightly shifted to close dates. This shift is based on
     * a simple linear model. It is <em>not</em> intended as a replacement for
     * proper attitude propagation but should be sufficient for either small
     * time shifts or coarse accuracy.
     * </p>
     * @param dt time shift in seconds
     * @return a new state, shifted with respect to the instance (which is immutable)
     */
    public TimeStampedAngularCoordinates shiftedBy(final double dt) {
        final AngularCoordinates sac = super.shiftedBy(dt);
        return new TimeStampedAngularCoordinates(date.shiftedBy(dt),
                                                 sac.getRotation(), sac.getRotationRate(), sac.getRotationAcceleration());

    }

    /** Add an offset from the instance.
     * <p>
     * We consider here that the offset rotation is applied first and the
     * instance is applied afterward. Note that angular coordinates do <em>not</em>
     * commute under this operation, i.e. {@code a.addOffset(b)} and {@code
     * b.addOffset(a)} lead to <em>different</em> results in most cases.
     * </p>
     * <p>
     * The two methods {@link #addOffset(AngularCoordinates) addOffset} and
     * {@link #subtractOffset(AngularCoordinates) subtractOffset} are designed
     * so that round trip applications are possible. This means that both {@code
     * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
     * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
     * </p>
     * @param offset offset to subtract
     * @return new instance, with offset subtracted
     * @see #subtractOffset(AngularCoordinates)
     */
    @Override
    public TimeStampedAngularCoordinates addOffset(final AngularCoordinates offset) {
        final Vector3D rOmega    = getRotation().applyTo(offset.getRotationRate());
        final Vector3D rOmegaDot = getRotation().applyTo(offset.getRotationAcceleration());
        return new TimeStampedAngularCoordinates(date,
                                                 getRotation().compose(offset.getRotation(), RotationConvention.VECTOR_OPERATOR),
                                                 getRotationRate().add(rOmega),
                                                 new Vector3D( 1.0, getRotationAcceleration(),
                                                               1.0, rOmegaDot,
                                                              -1.0, Vector3D.crossProduct(getRotationRate(), rOmega)));
    }

    /** Subtract an offset from the instance.
     * <p>
     * We consider here that the offset rotation is applied first and the
     * instance is applied afterward. Note that angular coordinates do <em>not</em>
     * commute under this operation, i.e. {@code a.subtractOffset(b)} and {@code
     * b.subtractOffset(a)} lead to <em>different</em> results in most cases.
     * </p>
     * <p>
     * The two methods {@link #addOffset(AngularCoordinates) addOffset} and
     * {@link #subtractOffset(AngularCoordinates) subtractOffset} are designed
     * so that round trip applications are possible. This means that both {@code
     * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
     * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
     * </p>
     * @param offset offset to subtract
     * @return new instance, with offset subtracted
     * @see #addOffset(AngularCoordinates)
     */
    @Override
    public TimeStampedAngularCoordinates subtractOffset(final AngularCoordinates offset) {
        return addOffset(offset.revert());
    }

    /** Interpolate angular coordinates.
     * <p>
     * The interpolated instance is created by polynomial Hermite interpolation
     * on Rodrigues vector ensuring rotation rate remains the exact derivative of rotation.
     * </p>
     * <p>
     * This method is based on Sergei Tanygin's paper <a
     * href="http://www.agi.com/downloads/resources/white-papers/Attitude-interpolation.pdf">Attitude
     * Interpolation</a>, changing the norm of the vector to match the modified Rodrigues
     * vector as described in Malcolm D. Shuster's paper <a
     * href="http://www.ladispe.polito.it/corsi/Meccatronica/02JHCOR/2011-12/Slides/Shuster_Pub_1993h_J_Repsurv_scan.pdf">A
     * Survey of Attitude Representations</a>. This change avoids the singularity at π.
     * There is still a singularity at 2π, which is handled by slightly offsetting all rotations
     * when this singularity is detected. Another change is that the mean linear motion
     * is first removed before interpolation and added back after interpolation. This allows
     * to use interpolation even when the sample covers much more than one turn and even
     * when sample points are separated by more than one turn.
     * </p>
     * <p>
     * Note that even if first and second time derivatives (rotation rates and acceleration)
     * 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 rotations.
     * </p>
     * @param date interpolation date
     * @param filter filter for derivatives from the sample to use in interpolation
     * @param sample sample points on which interpolation should be done
     * @return a new position-velocity, interpolated at specified date
     */
    public static TimeStampedAngularCoordinates interpolate(final AbsoluteDate date,
                                                            final AngularDerivativesFilter filter,
                                                            final Collection<TimeStampedAngularCoordinates> sample) {

        // set up safety elements for 2π singularity avoidance
        final double epsilon   = 2 * FastMath.PI / sample.size();
        final double threshold = FastMath.min(-(1.0 - 1.0e-4), -FastMath.cos(epsilon / 4));

        // set up a linear model canceling mean rotation rate
        final Vector3D meanRate;
        if (filter != AngularDerivativesFilter.USE_R) {
            Vector3D sum = Vector3D.ZERO;
            for (final TimeStampedAngularCoordinates datedAC : sample) {
                sum = sum.add(datedAC.getRotationRate());
            }
            meanRate = new Vector3D(1.0 / sample.size(), sum);
        } else {
            if (sample.size() < 2) {
                throw new OrekitException(OrekitMessages.NOT_ENOUGH_DATA_FOR_INTERPOLATION,
                                          sample.size());
            }
            Vector3D sum = Vector3D.ZERO;
            TimeStampedAngularCoordinates previous = null;
            for (final TimeStampedAngularCoordinates datedAC : sample) {
                if (previous != null) {
                    sum = sum.add(estimateRate(previous.getRotation(), datedAC.getRotation(),
                                               datedAC.date.durationFrom(previous.date)));
                }
                previous = datedAC;
            }
            meanRate = new Vector3D(1.0 / (sample.size() - 1), sum);
        }
        TimeStampedAngularCoordinates offset =
            new TimeStampedAngularCoordinates(date, Rotation.IDENTITY, meanRate, Vector3D.ZERO);

        boolean restart = true;
        for (int i = 0; restart && i < sample.size() + 2; ++i) {

            // offset adaptation parameters
            restart = false;

            // set up an interpolator taking derivatives into account
            final HermiteInterpolator interpolator = new HermiteInterpolator();

            // add sample points
            double sign = +1.0;
            Rotation previous = Rotation.IDENTITY;

            for (final TimeStampedAngularCoordinates ac : sample) {

                // remove linear offset from the current coordinates
                final double dt = ac.date.durationFrom(date);
                final TimeStampedAngularCoordinates fixed = ac.subtractOffset(offset.shiftedBy(dt));

                // make sure all interpolated points will be on the same branch
                final double dot = MathArrays.linearCombination(fixed.getRotation().getQ0(), previous.getQ0(),
                                                                fixed.getRotation().getQ1(), previous.getQ1(),
                                                                fixed.getRotation().getQ2(), previous.getQ2(),
                                                                fixed.getRotation().getQ3(), previous.getQ3());
                sign = FastMath.copySign(1.0, dot * sign);
                previous = fixed.getRotation();

                // check modified Rodrigues vector singularity
                if (fixed.getRotation().getQ0() * sign < threshold) {
                    // the sample point is close to a modified Rodrigues vector singularity
                    // we need to change the linear offset model to avoid this
                    restart = true;
                    break;
                }

                final double[][] rodrigues = fixed.getModifiedRodrigues(sign);
                switch (filter) {
                    case USE_RRA:
                        // populate sample with rotation, rotation rate and acceleration data
                        interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1], rodrigues[2]);
                        break;
                    case USE_RR:
                        // populate sample with rotation and rotation rate data
                        interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1]);
                        break;
                    case USE_R:
                        // populate sample with rotation data only
                        interpolator.addSamplePoint(dt, rodrigues[0]);
                        break;
                    default :
                        // this should never happen
                        throw new OrekitInternalError(null);
                }
            }

            if (restart) {
                // interpolation failed, some intermediate rotation was too close to 2π
                // we need to offset all rotations to avoid the singularity
                offset = offset.addOffset(new AngularCoordinates(new Rotation(Vector3D.PLUS_I,
                                                                              epsilon,
                                                                              RotationConvention.VECTOR_OPERATOR),
                                                                 Vector3D.ZERO, Vector3D.ZERO));
            } else {
                // interpolation succeeded with the current offset
                final double[][] p = interpolator.derivatives(0.0, 2);
                final AngularCoordinates ac = createFromModifiedRodrigues(p);
                return new TimeStampedAngularCoordinates(offset.getDate(),
                                                         ac.getRotation(),
                                                         ac.getRotationRate(),
                                                         ac.getRotationAcceleration()).addOffset(offset);
            }

        }

        // this should never happen
        throw new OrekitInternalError(null);

    }

}