source: josm/trunk/src/org/openstreetmap/josm/data/projection/proj/TransverseMercator.java@ 5237

Last change on this file since 5237 was 5066, checked in by bastiK, 12 years ago

Proj parameter refactoring (see #7495)
  • Property svn:eol-style set to native
File size: 10.2 KB
Line 
1// License: GPL. For details, see LICENSE file.
2package org.openstreetmap.josm.data.projection.proj;
3
4import static java.lang.Math.*;
5
6import static org.openstreetmap.josm.tools.I18n.tr;
7
8import org.openstreetmap.josm.data.projection.Ellipsoid;
9import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
10
11/**
12 * Transverse Mercator projection.
13 *
14 * @author Dirk Stöcker
15 * code based on JavaScript from Chuck Taylor
16 *
17 */
18public class TransverseMercator implements Proj {
19
20 protected double a, b;
21
22 @Override
23 public String getName() {
24 return tr("Transverse Mercator");
25 }
26
27 @Override
28 public String getProj4Id() {
29 return "tmerc";
30 }
31
32 @Override
33 public void initialize(ProjParameters params) throws ProjectionConfigurationException {
34 this.a = params.ellps.a;
35 this.b = params.ellps.b;
36 }
37
38 /**
39 * Converts a latitude/longitude pair to x and y coordinates in the
40 * Transverse Mercator projection. Note that Transverse Mercator is not
41 * the same as UTM; a scale factor is required to convert between them.
42 *
43 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
44 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
45 *
46 * @param phi Latitude of the point, in radians
47 * @param lambda Longitude of the point, in radians
48 * @return A 2-element array containing the x and y coordinates
49 * of the computed point
50 */
51 @Override
52 public double[] project(double phi, double lambda) {
53
54 /* Precalculate ep2 */
55 double ep2 = (pow(a, 2.0) - pow(b, 2.0)) / pow(b, 2.0);
56
57 /* Precalculate nu2 */
58 double nu2 = ep2 * pow(cos(phi), 2.0);
59
60 /* Precalculate N / a */
61 double N_a = a / (b * sqrt(1 + nu2));
62
63 /* Precalculate t */
64 double t = tan(phi);
65 double t2 = t * t;
66
67 /* Precalculate l */
68 double l = lambda;
69
70 /* Precalculate coefficients for l**n in the equations below
71 so a normal human being can read the expressions for easting
72 and northing
73 -- l**1 and l**2 have coefficients of 1.0 */
74 double l3coef = 1.0 - t2 + nu2;
75
76 double l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2);
77
78 double l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2
79 - 58.0 * t2 * nu2;
80
81 double l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2
82 - 330.0 * t2 * nu2;
83
84 double l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2);
85
86 double l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2);
87
88 return new double[] {
89 /* Calculate easting (x) */
90 N_a * cos(phi) * l
91 + (N_a / 6.0 * pow(cos(phi), 3.0) * l3coef * pow(l, 3.0))
92 + (N_a / 120.0 * pow(cos(phi), 5.0) * l5coef * pow(l, 5.0))
93 + (N_a / 5040.0 * pow(cos(phi), 7.0) * l7coef * pow(l, 7.0)),
94 /* Calculate northing (y) */
95 ArcLengthOfMeridian (phi) / a
96 + (t / 2.0 * N_a * pow(cos(phi), 2.0) * pow(l, 2.0))
97 + (t / 24.0 * N_a * pow(cos(phi), 4.0) * l4coef * pow(l, 4.0))
98 + (t / 720.0 * N_a * pow(cos(phi), 6.0) * l6coef * pow(l, 6.0))
99 + (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}
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