001    // License: GPL. For details, see LICENSE file.
002    package org.openstreetmap.josm.data.projection.proj;
003    
004    import static java.lang.Math.*;
005    
006    import static org.openstreetmap.josm.tools.I18n.tr;
007    
008    import org.openstreetmap.josm.data.projection.Ellipsoid;
009    import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
010    
011    /**
012     * Transverse Mercator projection.
013     *
014     * @author Dirk St??cker
015     * code based on JavaScript from Chuck Taylor
016     *
017     */
018    public class TransverseMercator implements Proj {
019    
020        protected double a, b;
021    
022        @Override
023        public String getName() {
024            return tr("Transverse Mercator");
025        }
026    
027        @Override
028        public String getProj4Id() {
029            return "tmerc";
030        }
031    
032        @Override
033        public void initialize(ProjParameters params) throws ProjectionConfigurationException {
034            this.a = params.ellps.a;
035            this.b = params.ellps.b;
036        }
037    
038        /**
039         * Converts a latitude/longitude pair to x and y coordinates in the
040         * Transverse Mercator projection.  Note that Transverse Mercator is not
041         * the same as UTM; a scale factor is required to convert between them.
042         *
043         * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
044         * GPS: Theory and Practice, 3rd ed.  New York: Springer-Verlag Wien, 1994.
045         *
046         * @param phi Latitude of the point, in radians
047         * @param lambda Longitude of the point, in radians
048         * @return A 2-element array containing the x and y coordinates
049         *         of the computed point
050         */
051        @Override
052        public double[] project(double phi, double lambda) {
053    
054            /* Precalculate ep2 */
055            double ep2 = (pow(a, 2.0) - pow(b, 2.0)) / pow(b, 2.0);
056    
057            /* Precalculate nu2 */
058            double nu2 = ep2 * pow(cos(phi), 2.0);
059    
060            /* Precalculate N / a */
061            double N_a = a / (b * sqrt(1 + nu2));
062    
063            /* Precalculate t */
064            double t = tan(phi);
065            double t2 = t * t;
066    
067            /* Precalculate l */
068            double l = lambda;
069    
070            /* Precalculate coefficients for l**n in the equations below
071               so a normal human being can read the expressions for easting
072               and northing
073               -- l**1 and l**2 have coefficients of 1.0 */
074            double l3coef = 1.0 - t2 + nu2;
075    
076            double l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2);
077    
078            double l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2
079            - 58.0 * t2 * nu2;
080    
081            double l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2
082            - 330.0 * t2 * nu2;
083    
084            double l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2);
085    
086            double l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2);
087    
088            return new double[] {
089                    /* Calculate easting (x) */
090                    N_a * cos(phi) * l
091                    + (N_a / 6.0 * pow(cos(phi), 3.0) * l3coef * pow(l, 3.0))
092                    + (N_a / 120.0 * pow(cos(phi), 5.0) * l5coef * pow(l, 5.0))
093                    + (N_a / 5040.0 * pow(cos(phi), 7.0) * l7coef * pow(l, 7.0)),
094                    /* Calculate northing (y) */
095                    ArcLengthOfMeridian (phi) / a
096                    + (t / 2.0 * N_a * pow(cos(phi), 2.0) * pow(l, 2.0))
097                    + (t / 24.0 * N_a * pow(cos(phi), 4.0) * l4coef * pow(l, 4.0))
098                    + (t / 720.0 * N_a * pow(cos(phi), 6.0) * l6coef * pow(l, 6.0))
099                    + (t / 40320.0 * N_a * pow(cos(phi), 8.0) * l8coef * pow(l, 8.0)) };
100        }
101    
102        /**
103         * Converts x and y coordinates in the Transverse Mercator projection to
104         * a latitude/longitude pair.  Note that Transverse Mercator is not
105         * the same as UTM; a scale factor is required to convert between them.
106         *
107         * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
108         *   GPS: Theory and Practice, 3rd ed.  New York: Springer-Verlag Wien, 1994.
109         *
110         * Remarks:
111         *   The local variables Nf, nuf2, tf, and tf2 serve the same purpose as
112         *   N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
113         *   to the footpoint latitude phif.
114         *
115         *   x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and
116         *   to optimize computations.
117         *
118         * @param x The easting of the point, in meters, divided by the semi major axis of the ellipsoid
119         * @param y The northing of the point, in meters, divided by the semi major axis of the ellipsoid
120         * @return A 2-element containing the latitude and longitude
121         *               in radians
122         */
123        @Override
124        public double[] invproject(double x, double y) {
125            /* Get the value of phif, the footpoint latitude. */
126            double phif = footpointLatitude(y);
127    
128            /* Precalculate ep2 */
129            double ep2 = (a*a - b*b)
130            / (b*b);
131    
132            /* Precalculate cos(phif) */
133            double cf = cos(phif);
134    
135            /* Precalculate nuf2 */
136            double nuf2 = ep2 * pow(cf, 2.0);
137    
138            /* Precalculate Nf / a and initialize Nfpow */
139            double Nf_a = a / (b * sqrt(1 + nuf2));
140            double Nfpow = Nf_a;
141    
142            /* Precalculate tf */
143            double tf = tan(phif);
144            double tf2 = tf * tf;
145            double tf4 = tf2 * tf2;
146    
147            /* Precalculate fractional coefficients for x**n in the equations
148               below to simplify the expressions for latitude and longitude. */
149            double x1frac = 1.0 / (Nfpow * cf);
150    
151            Nfpow *= Nf_a;   /* now equals Nf**2) */
152            double x2frac = tf / (2.0 * Nfpow);
153    
154            Nfpow *= Nf_a;   /* now equals Nf**3) */
155            double x3frac = 1.0 / (6.0 * Nfpow * cf);
156    
157            Nfpow *= Nf_a;   /* now equals Nf**4) */
158            double x4frac = tf / (24.0 * Nfpow);
159    
160            Nfpow *= Nf_a;   /* now equals Nf**5) */
161            double x5frac = 1.0 / (120.0 * Nfpow * cf);
162    
163            Nfpow *= Nf_a;   /* now equals Nf**6) */
164            double x6frac = tf / (720.0 * Nfpow);
165    
166            Nfpow *= Nf_a;   /* now equals Nf**7) */
167            double x7frac = 1.0 / (5040.0 * Nfpow * cf);
168    
169            Nfpow *= Nf_a;   /* now equals Nf**8) */
170            double x8frac = tf / (40320.0 * Nfpow);
171    
172            /* Precalculate polynomial coefficients for x**n.
173               -- x**1 does not have a polynomial coefficient. */
174            double x2poly = -1.0 - nuf2;
175            double x3poly = -1.0 - 2 * tf2 - nuf2;
176            double x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 *nuf2) - 9.0 * tf2 * (nuf2 * nuf2);
177            double x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
178            double x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2;
179            double x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
180            double x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
181    
182            return new double[] {
183                    /* Calculate latitude */
184                            phif + x2frac * x2poly * (x * x)
185                            + x4frac * x4poly * pow(x, 4.0)
186                            + x6frac * x6poly * pow(x, 6.0)
187                            + x8frac * x8poly * pow(x, 8.0),
188                            /* Calculate longitude */
189                            x1frac * x
190                            + x3frac * x3poly * pow(x, 3.0)
191                            + x5frac * x5poly * pow(x, 5.0)
192                            + x7frac * x7poly * pow(x, 7.0) };
193        }
194    
195        /**
196         * ArcLengthOfMeridian
197         *
198         * Computes the ellipsoidal distance from the equator to a point at a
199         * given latitude.
200         *
201         * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
202         * GPS: Theory and Practice, 3rd ed.  New York: Springer-Verlag Wien, 1994.
203         *
204         * @param phi Latitude of the point, in radians
205         * @return The ellipsoidal distance of the point from the equator
206         *         (in meters, divided by the semi major axis of the ellipsoid)
207         */
208        private double ArcLengthOfMeridian(double phi) {
209            /* Precalculate n */
210            double n = (a - b) / (a + b);
211    
212            /* Precalculate alpha */
213            double alpha = ((a + b) / 2.0)
214                * (1.0 + (pow(n, 2.0) / 4.0) + (pow(n, 4.0) / 64.0));
215    
216            /* Precalculate beta */
217            double beta = (-3.0 * n / 2.0) + (9.0 * pow(n, 3.0) / 16.0)
218                + (-3.0 * pow(n, 5.0) / 32.0);
219    
220            /* Precalculate gamma */
221            double gamma = (15.0 * pow(n, 2.0) / 16.0)
222                + (-15.0 * pow(n, 4.0) / 32.0);
223    
224            /* Precalculate delta */
225            double delta = (-35.0 * pow(n, 3.0) / 48.0)
226                + (105.0 * pow(n, 5.0) / 256.0);
227    
228            /* Precalculate epsilon */
229            double epsilon = (315.0 * pow(n, 4.0) / 512.0);
230    
231            /* Now calculate the sum of the series and return */
232            return alpha
233                * (phi + (beta * sin(2.0 * phi))
234                        + (gamma * sin(4.0 * phi))
235                        + (delta * sin(6.0 * phi))
236                        + (epsilon * sin(8.0 * phi)));
237        }
238    
239        /**
240         * FootpointLatitude
241         *
242         * Computes the footpoint latitude for use in converting transverse
243         * Mercator coordinates to ellipsoidal coordinates.
244         *
245         * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
246         *   GPS: Theory and Practice, 3rd ed.  New York: Springer-Verlag Wien, 1994.
247         *
248         * @param y northing coordinate, in meters, divided by the semi major axis of the ellipsoid
249         * @return The footpoint latitude, in radians
250         */
251        private double footpointLatitude(double y) {
252            /* Precalculate n (Eq. 10.18) */
253            double n = (a - b) / (a + b);
254    
255            /* Precalculate alpha_ (Eq. 10.22) */
256            /* (Same as alpha in Eq. 10.17) */
257            double alpha_ = ((a + b) / 2.0)
258                * (1 + (pow(n, 2.0) / 4) + (pow(n, 4.0) / 64));
259    
260            /* Precalculate y_ (Eq. 10.23) */
261            double y_ = y / alpha_ * a;
262    
263            /* Precalculate beta_ (Eq. 10.22) */
264            double beta_ = (3.0 * n / 2.0) + (-27.0 * pow(n, 3.0) / 32.0)
265                + (269.0 * pow(n, 5.0) / 512.0);
266    
267            /* Precalculate gamma_ (Eq. 10.22) */
268            double gamma_ = (21.0 * pow(n, 2.0) / 16.0)
269                + (-55.0 * pow(n, 4.0) / 32.0);
270    
271            /* Precalculate delta_ (Eq. 10.22) */
272            double delta_ = (151.0 * pow(n, 3.0) / 96.0)
273                + (-417.0 * pow(n, 5.0) / 128.0);
274    
275            /* Precalculate epsilon_ (Eq. 10.22) */
276            double epsilon_ = (1097.0 * pow(n, 4.0) / 512.0);
277    
278            /* Now calculate the sum of the series (Eq. 10.21) */
279            return y_ + (beta_ * sin(2.0 * y_))
280                + (gamma_ * sin(4.0 * y_))
281                + (delta_ * sin(6.0 * y_))
282                + (epsilon_ * sin(8.0 * y_));
283        }
284    
285    }