/*
* GeoTools - The Open Source Java GIS Toolkit
* http://geotools.org
*
* (C) 2002-2008, Open Source Geospatial Foundation (OSGeo)
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation;
* version 2.1 of the License.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*/
package org.geotools.referencing.operation.transform;
import javax.vecmath.Point3d;
import org.opengis.referencing.FactoryException;
import org.opengis.referencing.crs.CoordinateReferenceSystem;
import org.opengis.referencing.operation.CoordinateOperation;
import org.opengis.referencing.operation.MathTransform;
import org.opengis.referencing.operation.TransformException;
import org.geotools.referencing.crs.DefaultGeocentricCRS;
import org.geotools.referencing.crs.DefaultGeographicCRS;
import org.geotools.referencing.datum.DefaultEllipsoid;
import org.geotools.referencing.operation.TransformTestBase;
import org.junit.*;
import static org.junit.Assert.*;
/**
* Test the following transformation classes with the geocentric transform:
*
* <ul>
* <li>{@link CoordinateOperation}</li>
* <li>{@link GeocentricTransform}</li>
* <li>{@link DefaultEllipsoid}</li>
* </ul>
*
*
* @source $URL$
* @version $Id$
* @author Martin Desruisseaux (IRD)
*/
public final class GeocentricTransformTest extends TransformTestBase {
/**
* Tests the orthodromic distance computed by {@link DefaultEllipsoid}. There is actually two
* algorithms used: one for the ellipsoidal model, and a simpler one for spherical model.
* We test the ellipsoidal model using know values of nautical mile at different latitude.
* Then, we test the spherical model with random values. If JDK 1.4 assertion is enabled,
* the spherical model will compare its result with the ellipsoidal one.
*
* Note about nautical mile:
*
* "Le mille marin était, en principe, la longueur de la minute sexagésimale du méridien
* à la latitude de 45°. Cette longueur dépendait donc des valeurs adoptées pour le rayon
* équatorial de la terre et son aplatissement. En France, le décret du 3 mai 1961 sur les
* unités de mesure, fixe à 1852 mètres la longueur du mille marin qui est également la
* valeur adoptée pour le mille marin international."
*
* Source: Office de la langue française, 1996
* http://www.granddictionnaire.com
*/
@Test
public void testEllipsoid() throws FactoryException {
final DefaultEllipsoid e = DefaultEllipsoid.WGS84;
final double hm = 0.5/60; // Half of a minute of angle, in degrees.
/*
* Test the ellipsoidal model.
*/
assertEquals("Nautical mile at equator", 1842.78, e.orthodromicDistance(0, 00-hm, 0, 00+hm), 0.2);
assertEquals("Nautical mile at North pole", 1861.67, e.orthodromicDistance(0, 90-2*hm, 0, 90), 0.2);
assertEquals("Nautical mile at South pole", 1861.67, e.orthodromicDistance(0, 2*hm-90, 0, -90), 0.2);
assertEquals("International nautical mile", 1852.00, e.orthodromicDistance(0, 45-hm, 0, 45+hm), 0.2);
for (double i=0.01; i<180; i+=1) {
final double base = 180*random.nextDouble()-90;
assertEquals(i+"° rotation", e.getSemiMajorAxis()*Math.toRadians(i),
e.orthodromicDistance(base, 0, base+i, 0), 0.2);
}
/*
* Test the spherical model. The factory method should create
* a specialized class, which is not the usual Ellipsoid class.
*/
final double radius = e.getSemiMajorAxis();
final double circumference = (radius*1.00000001) * (2*Math.PI);
final DefaultEllipsoid s = DefaultEllipsoid.createEllipsoid("Sphere", radius, radius, e.getAxisUnit());
assertTrue("Spheroid class", !DefaultEllipsoid.class.equals(s.getClass()));
for (double i=0; i<=180; i+=1) {
final double base = 360*random.nextDouble()-180;
assertEquals(i+"° rotation", s.getSemiMajorAxis()*Math.toRadians(i),
s.orthodromicDistance(base, 0, base+i, 0), 0.001);
}
for (double i=-90; i<=+90; i+=1) {
final double meridian = 360*random.nextDouble()-180;
assertEquals(i+"° rotation", s.getSemiMajorAxis()*Math.toRadians(Math.abs(i)),
s.orthodromicDistance(meridian, 0, meridian, i), 0.001);
}
for (int i=0; i<100; i++) {
final double y1 = -90 + 180*random.nextDouble();
final double y2 = -90 + 180*random.nextDouble();
final double x1 = -180 + 360*random.nextDouble();
final double x2 = -180 + 360*random.nextDouble();
final double distance = s.orthodromicDistance(x1, y1, x2, y2);
assertTrue("Range of legal values", distance>=0 && distance<=circumference);
}
}
/**
* Tests the {@link GeocentricTransform} class.
*/
@Test
public void testGeocentricTransform() throws FactoryException, TransformException {
/*
* Gets the math transform from WGS84 to a geocentric transform.
*/
final DefaultEllipsoid ellipsoid = DefaultEllipsoid.WGS84;
final CoordinateReferenceSystem sourceCRS = DefaultGeographicCRS.WGS84_3D;
final CoordinateReferenceSystem targetCRS = DefaultGeocentricCRS.CARTESIAN;
final CoordinateOperation operation = opFactory.createOperation(sourceCRS, targetCRS);
final MathTransform transform = operation.getMathTransform();
final int dimension = transform.getSourceDimensions();
assertEquals("Source dimension", 3, dimension);
assertEquals("Target dimension", 3, transform.getTargetDimensions());
assertSame("Inverse transform", transform, transform.inverse().inverse());
assertInterfaced(transform);
/*
* Construct an array of 850 random points. The first 8 points
* are initialized to know values. Other points are left random.
*/
final double cartesianDistance[] = new double[4];
final double orthodromicDistance[] = new double[4];
final double[] array0 = new double[900]; // Must be divisible by 3.
for (int i=0; i<array0.length; i++) {
final int range;
switch (i % 3) {
case 0: range = 360; break; // Longitude
case 1: range = 180; break; // Latitidue
case 2: range = 10000; break; // Altitude
default: range = 0; break; // Should not happen
}
array0[i] = range*random.nextDouble()-(range/2);
}
array0[0]=35.0; array0[1]=24.0; array0[2]=8000; // 24°N 35°E 8km
array0[3]=34.8; array0[4]=24.7; array0[5]=5000; // ... about 80 km away
cartesianDistance [0] = 80284.00;
orthodromicDistance[0] = 80302.99; // Not really exact.
array0[6]= 0; array0[ 7]=0.0; array0[ 8]=0;
array0[9]=180; array0[10]=0.0; array0[11]=0; // Antipodes; distance should be 2*6378.137 km
cartesianDistance [1] = ellipsoid.getSemiMajorAxis() * 2;
orthodromicDistance[1] = ellipsoid.getSemiMajorAxis() * Math.PI;
array0[12]= 0; array0[13]=-90; array0[14]=0;
array0[15]=180; array0[16]=+90; array0[17]=0; // Antipodes; distance should be 2*6356.752 km
cartesianDistance [2] = ellipsoid.getSemiMinorAxis() * 2;
orthodromicDistance[2] = 20003931.46;
array0[18]= 95; array0[19]=-38; array0[20]=0;
array0[21]=-85; array0[22]=+38; array0[23]=0; // Antipodes
cartesianDistance [3] = 12740147.19;
orthodromicDistance[3] = 20003867.86;
/*
* Transform all points, and then inverse transform then. The resulting
* <code>array2</code> array should be equals to <code>array0</code>
* except for rounding errors. We tolerate maximal error of 0.1 second
* in longitude or latitude and 1 cm in height.
*/
final double[] array1 = new double[array0.length];
final double[] array2 = new double[array0.length];
transform .transform(array0, 0, array1, 0, array0.length/dimension);
transform.inverse().transform(array1, 0, array2, 0, array1.length/dimension);
assertPointsEqual("transform(Geographic --> Geocentric --> Geographic)", array0, array2,
new double[] {0.1/3600, 0.1/3600, 0.01});
/*
* Compare the distances between "special" points with expected distances.
* This test the ellipsoid orthodromic distance computation as well.
* We require a precision of 10 centimeters.
*/
for (int i=0; i<array0.length/6; i++) {
final int base = i*6;
final Point3d pt1 = new Point3d(array1[base+0], array1[base+1], array1[base+2]);
final Point3d pt2 = new Point3d(array1[base+3], array1[base+4], array1[base+5]);
final double cartesian = pt1.distance(pt2);
if (i < cartesianDistance.length) {
assertEquals("Cartesian distance["+i+']', cartesianDistance[i], cartesian, 0.1);
}
/*
* Compare with orthodromic distance. Distance is computed using an ellipsoid
* at the maximal altitude (i.e. the length of semi-major axis is increased to
* fit the maximal altitude).
*/
try {
final double altitude = Math.max(array0[base+2], array0[base+5]);
final DefaultEllipsoid ellip = DefaultEllipsoid.createFlattenedSphere("Temporary",
ellipsoid.getSemiMajorAxis()+altitude,
ellipsoid.getInverseFlattening(),
ellipsoid.getAxisUnit());
double orthodromic = ellip.orthodromicDistance(array0[base+0], array0[base+1],
array0[base+3], array0[base+4]);
orthodromic = Math.hypot(orthodromic, array0[base+2] - array0[base+5]);
if (i < orthodromicDistance.length) {
assertEquals("Orthodromic distance["+i+']', orthodromicDistance[i], orthodromic, 0.1);
}
assertTrue("Distance consistency["+i+']', cartesian <= orthodromic);
} catch (ArithmeticException exception) {
// Orthodromic distance computation didn't converge. Ignore...
}
}
}
}