Source Code Cross Referenced for StereographicUSGS.java in  » GIS » GeoTools-2.4.1 » org » geotools » referencing » operation » projection » Java Source Code / Java DocumentationJava Source Code and Java Documentation

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Java Source Code / Java Documentation » GIS » GeoTools 2.4.1 » org.geotools.referencing.operation.projection 
Source Cross Referenced  Class Diagram Java Document (Java Doc) 


001:        /*
002:         *    GeoTools - OpenSource mapping toolkit
003:         *    http://geotools.org
004:         *
005:         *   (C) 2003-2006, Geotools Project Managment Committee (PMC)
006:         *   (C) 2003, Gerald I. Evenden
007:         *   (C) 2001, Institut de Recherche pour le Développement
008:         *   (C) 2000, Frank Warmerdam
009:         *   (C) 1999, Fisheries and Oceans Canada
010:         *
011:         *    This library is free software; you can redistribute it and/or
012:         *    modify it under the terms of the GNU Lesser General Public
013:         *    License as published by the Free Software Foundation; either
014:         *    version 2.1 of the License, or (at your option) any later version.
015:         *
016:         *    This library is distributed in the hope that it will be useful,
017:         *    but WITHOUT ANY WARRANTY; without even the implied warranty of
018:         *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
019:         *    Lesser General Public License for more details.
020:         *
021:         *    This package contains formulas from the PROJ package of USGS.
022:         *    USGS's work is fully acknowledged here. This derived work has
023:         *    been relicensed under LGPL with Frank Warmerdam's permission.
024:         */
025:        package org.geotools.referencing.operation.projection;
026:
027:        // J2SE dependencies and extensions
028:        import java.awt.geom.Point2D;
029:
030:        // OpenGIS dependencies
031:        import org.opengis.parameter.ParameterValueGroup;
032:        import org.opengis.parameter.ParameterDescriptorGroup;
033:        import org.opengis.parameter.ParameterNotFoundException;
034:
035:        // Geotools dependencies
036:        import org.geotools.resources.XMath;
037:        import org.geotools.resources.i18n.Errors;
038:        import org.geotools.resources.i18n.ErrorKeys;
039:
040:        /**
041:         * The USGS oblique/equatorial case of the Stereographic projection. This is similar but
042:         * <strong>NOT</strong> equal to EPSG code 9809 ({@code "Oblique_Stereographic"} EPSG name).
043:         * The later is rather implemented by {@link ObliqueStereographic}.
044:         * <p>
045:         * This class is not public in order to keep names that closely match the ones in common usage
046:         * (i.e. this projection is called just "Stereographic" in ESRI). Furthermore, the "USGS" name
047:         * is not really accurate for a class to be extended by {@link ObliqueStereographic}.
048:         *
049:         * @since 2.4
050:         * @source $URL: http://svn.geotools.org/geotools/tags/2.4.1/modules/library/referencing/src/main/java/org/geotools/referencing/operation/projection/StereographicUSGS.java $
051:         * @version $Id: StereographicUSGS.java 24576 2007-02-24 00:07:40Z desruisseaux $
052:         * @author André Gosselin
053:         * @author Martin Desruisseaux
054:         * @author Rueben Schulz
055:         */
056:        class StereographicUSGS extends Stereographic {
057:            /**
058:             * Maximum number of iterations for iterative computations.
059:             */
060:            private static final int MAXIMUM_ITERATIONS = 15;
061:
062:            /**
063:             * Difference allowed in iterative computations.
064:             */
065:            private static final double ITERATION_TOLERANCE = 1E-10;
066:
067:            /**
068:             * Maximum difference allowed when comparing real numbers.
069:             */
070:            private static final double EPSILON = 1E-6;
071:
072:            /**
073:             * Constants used for the oblique projections. All those constants are completly determined by
074:             * {@link #latitudeOfOrigin}. Concequently, there is no need to test them in {@link #hashCode}
075:             * or {@link #equals} methods.
076:             */
077:            final double k0, sinphi0, cosphi0, chi1, sinChi1, cosChi1;
078:
079:            /**
080:             * Constructs an oblique stereographic projection (USGS equations).
081:             *
082:             * @param  parameters The group of parameter values.
083:             * @throws ParameterNotFoundException if a required parameter was not found.
084:             */
085:            protected StereographicUSGS(final ParameterValueGroup parameters)
086:                    throws ParameterNotFoundException {
087:                this (parameters, Provider.PARAMETERS);
088:            }
089:
090:            /**
091:             * Constructs an oblique stereographic projection (USGS equations).
092:             *
093:             * @param  parameters The group of parameter values.
094:             * @param  descriptor The expected parameter descriptor.
095:             * @throws ParameterNotFoundException if a required parameter was not found.
096:             */
097:            StereographicUSGS(final ParameterValueGroup parameters,
098:                    final ParameterDescriptorGroup descriptor)
099:                    throws ParameterNotFoundException {
100:                super (parameters, descriptor);
101:                if (Math.abs(latitudeOfOrigin) < EPSILON) { // Equatorial
102:                    latitudeOfOrigin = 0;
103:                    cosphi0 = 1.0;
104:                    sinphi0 = 0.0;
105:                    chi1 = 0.0;
106:                    cosChi1 = 1.0;
107:                    sinChi1 = 0.0;
108:                } else { // Oblique
109:                    cosphi0 = Math.cos(latitudeOfOrigin);
110:                    sinphi0 = Math.sin(latitudeOfOrigin);
111:                    chi1 = 2.0 * Math.atan(ssfn(latitudeOfOrigin, sinphi0))
112:                            - (Math.PI / 2);
113:                    cosChi1 = Math.cos(chi1);
114:                    sinChi1 = Math.sin(chi1);
115:                }
116:                // part of (14 - 15)
117:                k0 = 2.0 * msfn(sinphi0, cosphi0);
118:            }
119:
120:            /**
121:             * Transforms the specified (<var>&lambda;</var>,<var>&phi;</var>) coordinates
122:             * (units in radians) and stores the result in {@code ptDst} (linear distance
123:             * on a unit sphere).
124:             */
125:            protected Point2D transformNormalized(double x, double y,
126:                    Point2D ptDst) throws ProjectionException {
127:                final double chi = 2.0 * Math.atan(ssfn(y, Math.sin(y)))
128:                        - (Math.PI / 2);
129:                final double sinChi = Math.sin(chi);
130:                final double cosChi = Math.cos(chi);
131:                final double cosChi_cosLon = cosChi * Math.cos(x);
132:                final double A = k0 / cosChi1
133:                        / (1 + sinChi1 * sinChi + cosChi1 * cosChi_cosLon);
134:                x = A * cosChi * Math.sin(x);
135:                y = A * (cosChi1 * sinChi - sinChi1 * cosChi_cosLon);
136:
137:                if (ptDst != null) {
138:                    ptDst.setLocation(x, y);
139:                    return ptDst;
140:                }
141:                return new Point2D.Double(x, y);
142:            }
143:
144:            /**
145:             * Transforms the specified (<var>x</var>,<var>y</var>) coordinates
146:             * and stores the result in {@code ptDst}.
147:             */
148:            protected Point2D inverseTransformNormalized(double x, double y,
149:                    Point2D ptDst) throws ProjectionException {
150:                final double rho = Math.sqrt(x * x + y * y);
151:                final double ce = 2.0 * Math.atan2(rho * cosChi1, k0);
152:                final double cosce = Math.cos(ce);
153:                final double since = Math.sin(ce);
154:                final boolean rhoIs0 = Math.abs(rho) < EPSILON;
155:                final double chi = rhoIs0 ? chi1 : Math.asin(cosce * sinChi1
156:                        + (y * since * cosChi1 / rho));
157:                final double tp = Math.tan(Math.PI / 4.0 + chi / 2.0);
158:
159:                // parts of (21-36) used to calculate longitude
160:                final double t = x * since;
161:                final double ct = rho * cosChi1 * cosce - y * sinChi1 * since;
162:
163:                // Compute latitude using iterative technique (3-4)
164:                final double halfe = excentricity / 2.0;
165:                double phi0 = chi;
166:                for (int i = MAXIMUM_ITERATIONS;;) {
167:                    final double esinphi = excentricity * Math.sin(phi0);
168:                    final double phi = 2
169:                            * Math.atan(tp
170:                                    * Math.pow((1 + esinphi) / (1 - esinphi),
171:                                            halfe)) - (Math.PI / 2);
172:                    if (Math.abs(phi - phi0) < ITERATION_TOLERANCE) {
173:                        // TODO: checking rho may be redundant
174:                        x = rhoIs0
175:                                || (Math.abs(t) < EPSILON && Math.abs(ct) < EPSILON) ? 0.0
176:                                : Math.atan2(t, ct);
177:                        y = phi;
178:                        break;
179:                    }
180:                    phi0 = phi;
181:                    if (--i < 0) {
182:                        throw new ProjectionException(Errors
183:                                .format(ErrorKeys.NO_CONVERGENCE));
184:                    }
185:                }
186:
187:                if (ptDst != null) {
188:                    ptDst.setLocation(x, y);
189:                    return ptDst;
190:                }
191:                return new Point2D.Double(x, y);
192:            }
193:
194:            /**
195:             * Maximal error (in metres) tolerated for assertions, if enabled.
196:             */
197:            //@Override
198:            protected double getToleranceForAssertions(final double longitude,
199:                    final double latitude) {
200:                final double delta = Math.abs(longitude - centralMeridian) / 2
201:                        + Math.abs(latitude - latitudeOfOrigin);
202:                if (delta > 40) {
203:                    return 0.5;
204:                }
205:                if (delta > 15) {
206:                    return 0.1;
207:                }
208:                return super .getToleranceForAssertions(longitude, latitude);
209:            }
210:
211:            /**
212:             * Computes part of function (3-1) from Snyder.
213:             */
214:            final double ssfn(double phi, double sinphi) {
215:                sinphi *= excentricity;
216:                return Math.tan((Math.PI / 4.0) + phi / 2.0)
217:                        * Math.pow((1 - sinphi) / (1 + sinphi),
218:                                excentricity / 2.0);
219:            }
220:
221:            /**
222:             * Provides the transform equations for the spherical case of the 
223:             * Stereographic projection.
224:             *
225:             * @version $Id: StereographicUSGS.java 24576 2007-02-24 00:07:40Z desruisseaux $
226:             * @author Martin Desruisseaux
227:             * @author Rueben Schulz
228:             */
229:            static final class Spherical extends StereographicUSGS {
230:                /**
231:                 * A constant used in the transformations. This constant hides the {@code k0}
232:                 * constant from the ellipsoidal case. The spherical and ellipsoidal {@code k0}
233:                 * are not computed in the same way, and we preserve the ellipsoidal {@code k0}
234:                 * in {@link Stereographic} in order to allow assertions to work.
235:                 */
236:                private static final double k0 = 2;
237:
238:                /**
239:                 * Constructs a spherical oblique stereographic projection.
240:                 *
241:                 * @param  parameters The group of parameter values.
242:                 * @param  descriptor The expected parameter descriptor.
243:                 * @throws ParameterNotFoundException if a required parameter was not found.
244:                 */
245:                Spherical(final ParameterValueGroup parameters,
246:                        final ParameterDescriptorGroup descriptor)
247:                        throws ParameterNotFoundException {
248:                    super (parameters, descriptor);
249:                    ensureSpherical();
250:                }
251:
252:                /**
253:                 * Transforms the specified (<var>&lambda;</var>,<var>&phi;</var>) coordinates
254:                 * (units in radians) and stores the result in {@code ptDst} (linear distance
255:                 * on a unit sphere).
256:                 */
257:                protected Point2D transformNormalized(double x, double y,
258:                        Point2D ptDst) throws ProjectionException {
259:                    // Compute using ellipsoidal formulas, for comparaison later.
260:                    assert (ptDst = super .transformNormalized(x, y, ptDst)) != null;
261:
262:                    final double coslat = Math.cos(y);
263:                    final double sinlat = Math.sin(y);
264:                    final double coslon = Math.cos(x);
265:                    double f = 1.0 + sinphi0 * sinlat + cosphi0 * coslat
266:                            * coslon; // (21-4)
267:                    if (f < EPSILON) {
268:                        throw new ProjectionException(Errors
269:                                .format(ErrorKeys.VALUE_TEND_TOWARD_INFINITY));
270:                    }
271:                    f = k0 / f;
272:                    x = f * coslat * Math.sin(x); // (21-2)
273:                    y = f * (cosphi0 * sinlat - sinphi0 * coslat * coslon); // (21-3)
274:
275:                    assert checkTransform(x, y, ptDst);
276:                    if (ptDst != null) {
277:                        ptDst.setLocation(x, y);
278:                        return ptDst;
279:                    }
280:                    return new Point2D.Double(x, y);
281:                }
282:
283:                /**
284:                 * Transforms the specified (<var>x</var>,<var>y</var>) coordinates
285:                 * and stores the result in {@code ptDst}.
286:                 */
287:                protected Point2D inverseTransformNormalized(double x,
288:                        double y, Point2D ptDst) throws ProjectionException {
289:                    // Compute using ellipsoidal formulas, for comparaison later.
290:                    assert (ptDst = super .inverseTransformNormalized(x, y,
291:                            ptDst)) != null;
292:
293:                    final double rho = Math.sqrt(x * x + y * y);
294:                    if (Math.abs(rho) < EPSILON) {
295:                        y = latitudeOfOrigin;
296:                        x = 0.0;
297:                    } else {
298:                        final double c = 2.0 * Math.atan(rho / k0);
299:                        final double cosc = Math.cos(c);
300:                        final double sinc = Math.sin(c);
301:                        final double ct = rho * cosphi0 * cosc - y * sinphi0
302:                                * sinc; // (20-15)
303:                        final double t = x * sinc; // (20-15)
304:                        y = Math
305:                                .asin(cosc * sinphi0 + y * sinc * cosphi0 / rho); // (20-14)
306:                        x = (Math.abs(ct) < EPSILON && Math.abs(t) < EPSILON) ? 0.0
307:                                : Math.atan2(t, ct);
308:                    }
309:
310:                    assert checkInverseTransform(x, y, ptDst);
311:                    if (ptDst != null) {
312:                        ptDst.setLocation(x, y);
313:                        return ptDst;
314:                    }
315:                    return new Point2D.Double(x, y);
316:                }
317:            }
318:        }
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