OneAxisEllipsoid.java
/* Copyright 2002-2016 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,
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* See the License for the specific language governing permissions and
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package org.orekit.bodies;
import java.io.Serializable;
import org.hipparchus.analysis.differentiation.DerivativeStructure;
import org.hipparchus.geometry.euclidean.oned.Vector1D;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.geometry.euclidean.threed.Line;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.geometry.euclidean.twod.Vector2D;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.orekit.errors.OrekitException;
import org.orekit.frames.Frame;
import org.orekit.frames.Transform;
import org.orekit.time.AbsoluteDate;
import org.orekit.utils.PVCoordinates;
import org.orekit.utils.TimeStampedPVCoordinates;
/** Modeling of a one-axis ellipsoid.
* <p>One-axis ellipsoids is a good approximate model for most planet-size
* and larger natural bodies. It is the equilibrium shape reached by
* a fluid body under its own gravity field when it rotates. The symmetry
* axis is the rotation or polar axis.</p>
* @author Luc Maisonobe
*/
public class OneAxisEllipsoid extends Ellipsoid implements BodyShape {
/** Serializable UID. */
private static final long serialVersionUID = 20130518L;
/** Body frame related to body shape. */
private final Frame bodyFrame;
/** Equatorial radius power 2. */
private final double ae2;
/** Flattening. */
private final double f;
/** Eccentricity power 2. */
private final double e2;
/** 1 minus flatness. */
private final double g;
/** g * g. */
private final double g2;
/** Convergence limit. */
private double angularThreshold;
/** Simple constructor.
* <p>Standard values for Earth models can be found in the {@link org.orekit.utils.Constants Constants} class:</p>
* <table border="1" cellpadding="5">
* <caption>Ellipsoid Models</caption>
* <tr bgcolor="#ccccff"><th>model</th><th>a<sub>e</sub> (m)</th> <th>f</th></tr>
* <tr><td bgcolor="#eeeeff">GRS 80</td>
* <td>{@link org.orekit.utils.Constants#GRS80_EARTH_EQUATORIAL_RADIUS Constants.GRS80_EARTH_EQUATORIAL_RADIUS}</td>
* <td>{@link org.orekit.utils.Constants#GRS80_EARTH_FLATTENING Constants.GRS80_EARTH_FLATTENING}</td></tr>
* <tr><td bgcolor="#eeeeff">WGS84</td>
* <td>{@link org.orekit.utils.Constants#WGS84_EARTH_EQUATORIAL_RADIUS Constants.WGS84_EARTH_EQUATORIAL_RADIUS}</td>
* <td>{@link org.orekit.utils.Constants#WGS84_EARTH_FLATTENING Constants.WGS84_EARTH_FLATTENING}</td></tr>
* </table>
* @param ae equatorial radius
* @param f the flattening (f = (a-b)/a)
* @param bodyFrame body frame related to body shape
* @see org.orekit.frames.FramesFactory#getITRF(org.orekit.utils.IERSConventions, boolean)
*/
public OneAxisEllipsoid(final double ae, final double f,
final Frame bodyFrame) {
super(bodyFrame, ae, ae, ae * (1.0 - f));
this.f = f;
this.ae2 = ae * ae;
this.e2 = f * (2.0 - f);
this.g = 1.0 - f;
this.g2 = g * g;
setAngularThreshold(1.0e-12);
this.bodyFrame = bodyFrame;
}
/** Set the angular convergence threshold.
* <p>The angular threshold is used both to identify points close to
* the ellipse axes and as the convergence threshold used to
* stop the iterations in the {@link #transform(Vector3D, Frame,
* AbsoluteDate)} method.</p>
* <p>If this method is not called, the default value is set to
* 10<sup>-12</sup>.</p>
* @param angularThreshold angular convergence threshold (rad)
*/
public void setAngularThreshold(final double angularThreshold) {
this.angularThreshold = angularThreshold;
}
/** Get the equatorial radius of the body.
* @return equatorial radius of the body (m)
*/
public double getEquatorialRadius() {
return getA();
}
/** Get the flattening of the body: f = (a-b)/a.
* @return the flattening
*/
public double getFlattening() {
return f;
}
/** {@inheritDoc} */
public Frame getBodyFrame() {
return bodyFrame;
}
/** {@inheritDoc} */
public GeodeticPoint getIntersectionPoint(final Line line, final Vector3D close,
final Frame frame, final AbsoluteDate date)
throws OrekitException {
// transform line and close to body frame
final Transform frameToBodyFrame = frame.getTransformTo(bodyFrame, date);
final Line lineInBodyFrame = frameToBodyFrame.transformLine(line);
final Vector3D closeInBodyFrame = frameToBodyFrame.transformPosition(close);
final double closeAbscissa = lineInBodyFrame.toSubSpace(closeInBodyFrame).getX();
// compute some miscellaneous variables outside of the loop
final Vector3D point = lineInBodyFrame.getOrigin();
final double x = point.getX();
final double y = point.getY();
final double z = point.getZ();
final double z2 = z * z;
final double r2 = x * x + y * y;
final Vector3D direction = lineInBodyFrame.getDirection();
final double dx = direction.getX();
final double dy = direction.getY();
final double dz = direction.getZ();
final double cz2 = dx * dx + dy * dy;
// abscissa of the intersection as a root of a 2nd degree polynomial :
// a k^2 - 2 b k + c = 0
final double a = 1.0 - e2 * cz2;
final double b = -(g2 * (x * dx + y * dy) + z * dz);
final double c = g2 * (r2 - ae2) + z2;
final double b2 = b * b;
final double ac = a * c;
if (b2 < ac) {
return null;
}
final double s = FastMath.sqrt(b2 - ac);
final double k1 = (b < 0) ? (b - s) / a : c / (b + s);
final double k2 = c / (a * k1);
// select the right point
final double k =
(FastMath.abs(k1 - closeAbscissa) < FastMath.abs(k2 - closeAbscissa)) ? k1 : k2;
final Vector3D intersection = lineInBodyFrame.toSpace(new Vector1D(k));
final double ix = intersection.getX();
final double iy = intersection.getY();
final double iz = intersection.getZ();
final double lambda = FastMath.atan2(iy, ix);
final double phi = FastMath.atan2(iz, g2 * FastMath.sqrt(ix * ix + iy * iy));
return new GeodeticPoint(phi, lambda, 0.0);
}
/** {@inheritDoc} */
public Vector3D transform(final GeodeticPoint point) {
final double longitude = point.getLongitude();
final double cLambda = FastMath.cos(longitude);
final double sLambda = FastMath.sin(longitude);
final double latitude = point.getLatitude();
final double cPhi = FastMath.cos(latitude);
final double sPhi = FastMath.sin(latitude);
final double h = point.getAltitude();
final double n = getA() / FastMath.sqrt(1.0 - e2 * sPhi * sPhi);
final double r = (n + h) * cPhi;
return new Vector3D(r * cLambda, r * sLambda, (g2 * n + h) * sPhi);
}
/** Transform a surface-relative point to a Cartesian point.
* @param point surface-relative point, using time as the single derivation parameter
* @return point at the same location but as a Cartesian point including derivatives
*/
public PVCoordinates transform(final FieldGeodeticPoint<DerivativeStructure> point) {
final DerivativeStructure latitude = point.getLatitude();
final DerivativeStructure longitude = point.getLongitude();
final DerivativeStructure altitude = point.getAltitude();
final DerivativeStructure cLambda = longitude.cos();
final DerivativeStructure sLambda = longitude.sin();
final DerivativeStructure cPhi = latitude.cos();
final DerivativeStructure sPhi = latitude.sin();
final DerivativeStructure n = sPhi.multiply(sPhi).multiply(e2).subtract(1.0).negate().sqrt().reciprocal().multiply(getA());
final DerivativeStructure r = n.add(altitude).multiply(cPhi);
return new PVCoordinates(new FieldVector3D<DerivativeStructure>(r.multiply(cLambda),
r.multiply(sLambda),
sPhi.multiply(altitude.add(n.multiply(g2)))));
}
/** {@inheritDoc} */
public Vector3D projectToGround(final Vector3D point, final AbsoluteDate date, final Frame frame)
throws OrekitException {
// transform point to body frame
final Transform toBody = frame.getTransformTo(bodyFrame, date);
final Vector3D p = toBody.transformPosition(point);
final double z = p.getZ();
final double r = FastMath.hypot(p.getX(), p.getY());
// set up the 2D meridian ellipse
final Ellipse meridian = new Ellipse(Vector3D.ZERO,
new Vector3D(p.getX() / r, p.getY() / r, 0),
Vector3D.PLUS_K,
getA(), getC(), bodyFrame);
// find the closest point in the meridian plane
final Vector3D groundPoint = meridian.toSpace(meridian.projectToEllipse(new Vector2D(r, z)));
// transform point back to initial frame
return toBody.getInverse().transformPosition(groundPoint);
}
/** {@inheritDoc} */
public TimeStampedPVCoordinates projectToGround(final TimeStampedPVCoordinates pv, final Frame frame)
throws OrekitException {
// transform point to body frame
final Transform toBody = frame.getTransformTo(bodyFrame, pv.getDate());
final TimeStampedPVCoordinates pvInBodyFrame = toBody.transformPVCoordinates(pv);
final Vector3D p = pvInBodyFrame.getPosition();
final double r = FastMath.hypot(p.getX(), p.getY());
// set up the 2D ellipse corresponding to first principal curvature along meridian
final Vector3D meridian = new Vector3D(p.getX() / r, p.getY() / r, 0);
final Ellipse firstPrincipalCurvature =
new Ellipse(Vector3D.ZERO, meridian, Vector3D.PLUS_K, getA(), getC(), bodyFrame);
// project coordinates in the meridian plane
final TimeStampedPVCoordinates gpFirst = firstPrincipalCurvature.projectToEllipse(pvInBodyFrame);
final Vector3D gpP = gpFirst.getPosition();
final double gr = MathArrays.linearCombination(gpP.getX(), meridian.getX(),
gpP.getY(), meridian.getY());
final double gz = gpP.getZ();
// topocentric frame
final Vector3D east = new Vector3D(-meridian.getY(), meridian.getX(), 0);
final Vector3D zenith = new Vector3D(gr * getC() / getA(), meridian, gz * getA() / getC(), Vector3D.PLUS_K).normalize();
final Vector3D north = Vector3D.crossProduct(zenith, east);
// set up the ellipse corresponding to second principal curvature in the zenith/east plane
final Ellipse secondPrincipalCurvature = getPlaneSection(gpP, north);
final TimeStampedPVCoordinates gpSecond = secondPrincipalCurvature.projectToEllipse(pvInBodyFrame);
final Vector3D gpV = gpFirst.getVelocity().add(gpSecond.getVelocity());
final Vector3D gpA = gpFirst.getAcceleration().add(gpSecond.getAcceleration());
// moving projected point
final TimeStampedPVCoordinates groundPV =
new TimeStampedPVCoordinates(pv.getDate(), gpP, gpV, gpA);
// transform moving projected point back to initial frame
return toBody.getInverse().transformPVCoordinates(groundPV);
}
/** {@inheritDoc} */
public GeodeticPoint transform(final Vector3D point, final Frame frame, final AbsoluteDate date)
throws OrekitException {
// transform point to body frame
final Vector3D pointInBodyFrame = frame.getTransformTo(bodyFrame, date).transformPosition(point);
final double r2 = pointInBodyFrame.getX() * pointInBodyFrame.getX() +
pointInBodyFrame.getY() * pointInBodyFrame.getY();
final double r = FastMath.sqrt(r2);
final double z = pointInBodyFrame.getZ();
// set up the 2D meridian ellipse
final Ellipse meridian = new Ellipse(Vector3D.ZERO,
new Vector3D(pointInBodyFrame.getX() / r, pointInBodyFrame.getY() / r, 0),
Vector3D.PLUS_K,
getA(), getC(), bodyFrame);
// project point on the 2D meridian ellipse
final Vector2D ellipsePoint = meridian.projectToEllipse(new Vector2D(r, z));
// relative position of test point with respect to its ellipse sub-point
final double dr = r - ellipsePoint.getX();
final double dz = z - ellipsePoint.getY();
final double insideIfNegative = g2 * (r2 - ae2) + z * z;
return new GeodeticPoint(FastMath.atan2(ellipsePoint.getY(), g2 * ellipsePoint.getX()),
FastMath.atan2(pointInBodyFrame.getY(), pointInBodyFrame.getX()),
FastMath.copySign(FastMath.hypot(dr, dz), insideIfNegative));
}
/** Transform a Cartesian point to a surface-relative point.
* @param point Cartesian point
* @param frame frame in which Cartesian point is expressed
* @param date date of the computation (used for frames conversions)
* @return point at the same location but as a surface-relative point,
* using time as the single derivation parameter
* @exception OrekitException if point cannot be converted to body frame
*/
public FieldGeodeticPoint<DerivativeStructure> transform(final PVCoordinates point,
final Frame frame, final AbsoluteDate date)
throws OrekitException {
// transform point to body frame
final Transform toBody = frame.getTransformTo(bodyFrame, date);
final PVCoordinates pointInBodyFrame = toBody.transformPVCoordinates(point);
final FieldVector3D<DerivativeStructure> p = pointInBodyFrame.toDerivativeStructureVector(2);
final DerivativeStructure pr2 = p.getX().multiply(p.getX()).add(p.getY().multiply(p.getY()));
final DerivativeStructure pr = pr2.sqrt();
final DerivativeStructure pz = p.getZ();
// project point on the ellipsoid surface
final TimeStampedPVCoordinates groundPoint = projectToGround(new TimeStampedPVCoordinates(date, pointInBodyFrame),
bodyFrame);
final FieldVector3D<DerivativeStructure> gp = groundPoint.toDerivativeStructureVector(2);
final DerivativeStructure gpr2 = gp.getX().multiply(gp.getX()).add(gp.getY().multiply(gp.getY()));
final DerivativeStructure gpr = gpr2.sqrt();
final DerivativeStructure gpz = gp.getZ();
// relative position of test point with respect to its ellipse sub-point
final DerivativeStructure dr = pr.subtract(gpr);
final DerivativeStructure dz = pz.subtract(gpz);
final double insideIfNegative = g2 * (pr2.getReal() - ae2) + pz.getReal() * pz.getReal();
return new FieldGeodeticPoint<DerivativeStructure>(DerivativeStructure.atan2(gpz, gpr.multiply(g2)),
DerivativeStructure.atan2(p.getY(), p.getX()),
DerivativeStructure.hypot(dr, dz).copySign(insideIfNegative));
}
/** Replace the instance with a data transfer object for serialization.
* <p>
* This intermediate class serializes the files supported names, the
* ephemeris type and the body name.
* </p>
* @return data transfer object that will be serialized
*/
private Object writeReplace() {
return new DataTransferObject(getA(), f, bodyFrame, angularThreshold);
}
/** Internal class used only for serialization. */
private static class DataTransferObject implements Serializable {
/** Serializable UID. */
private static final long serialVersionUID = 20130518L;
/** Equatorial radius. */
private final double ae;
/** Flattening. */
private final double f;
/** Body frame related to body shape. */
private final Frame bodyFrame;
/** Convergence limit. */
private final double angularThreshold;
/** Simple constructor.
* @param ae equatorial radius
* @param f the flattening (f = (a-b)/a)
* @param bodyFrame body frame related to body shape
* @param angularThreshold convergence limit
*/
DataTransferObject(final double ae, final double f,
final Frame bodyFrame, final double angularThreshold) {
this.ae = ae;
this.f = f;
this.bodyFrame = bodyFrame;
this.angularThreshold = angularThreshold;
}
/** Replace the deserialized data transfer object with a
* {@link JPLCelestialBody}.
* @return replacement {@link JPLCelestialBody}
*/
private Object readResolve() {
final OneAxisEllipsoid ellipsoid = new OneAxisEllipsoid(ae, f, bodyFrame);
ellipsoid.setAngularThreshold(angularThreshold);
return ellipsoid;
}
}
}