source: josm/trunk/src/org/openstreetmap/josm/data/projection/proj/TransverseMercator.java@ 6362

Last change on this file since 6362 was 6362, checked in by Don-vip, 10 years ago

Checkstyle:

  • private constructors for util classes
  • final classes
  • missing "else" statements
  • import cleanup
  • Property svn:eol-style set to native
File size: 10.3 KB
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1// License: GPL. For details, see LICENSE file.
2package org.openstreetmap.josm.data.projection.proj;
3
4import static java.lang.Math.cos;
5import static java.lang.Math.pow;
6import static java.lang.Math.sin;
7import static java.lang.Math.sqrt;
8import static java.lang.Math.tan;
9import static org.openstreetmap.josm.tools.I18n.tr;
10
11import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
12
13/**
14 * Transverse Mercator projection.
15 *
16 * @author Dirk Stöcker
17 * code based on JavaScript from Chuck Taylor
18 *
19 */
20public class TransverseMercator implements Proj {
21
22 protected double a, b;
23
24 @Override
25 public String getName() {
26 return tr("Transverse Mercator");
27 }
28
29 @Override
30 public String getProj4Id() {
31 return "tmerc";
32 }
33
34 @Override
35 public void initialize(ProjParameters params) throws ProjectionConfigurationException {
36 this.a = params.ellps.a;
37 this.b = params.ellps.b;
38 }
39
40 /**
41 * Converts a latitude/longitude pair to x and y coordinates in the
42 * Transverse Mercator projection. Note that Transverse Mercator is not
43 * the same as UTM; a scale factor is required to convert between them.
44 *
45 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
46 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
47 *
48 * @param phi Latitude of the point, in radians
49 * @param lambda Longitude of the point, in radians
50 * @return A 2-element array containing the x and y coordinates
51 * of the computed point
52 */
53 @Override
54 public double[] project(double phi, double lambda) {
55
56 /* Precalculate ep2 */
57 double ep2 = (pow(a, 2.0) - pow(b, 2.0)) / pow(b, 2.0);
58
59 /* Precalculate nu2 */
60 double nu2 = ep2 * pow(cos(phi), 2.0);
61
62 /* Precalculate N / a */
63 double N_a = a / (b * sqrt(1 + nu2));
64
65 /* Precalculate t */
66 double t = tan(phi);
67 double t2 = t * t;
68
69 /* Precalculate l */
70 double l = lambda;
71
72 /* Precalculate coefficients for l**n in the equations below
73 so a normal human being can read the expressions for easting
74 and northing
75 -- l**1 and l**2 have coefficients of 1.0 */
76 double l3coef = 1.0 - t2 + nu2;
77
78 double l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2);
79
80 double l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2
81 - 58.0 * t2 * nu2;
82
83 double l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2
84 - 330.0 * t2 * nu2;
85
86 double l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2);
87
88 double l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2);
89
90 return new double[] {
91 /* Calculate easting (x) */
92 N_a * cos(phi) * l
93 + (N_a / 6.0 * pow(cos(phi), 3.0) * l3coef * pow(l, 3.0))
94 + (N_a / 120.0 * pow(cos(phi), 5.0) * l5coef * pow(l, 5.0))
95 + (N_a / 5040.0 * pow(cos(phi), 7.0) * l7coef * pow(l, 7.0)),
96 /* Calculate northing (y) */
97 ArcLengthOfMeridian (phi) / a
98 + (t / 2.0 * N_a * pow(cos(phi), 2.0) * pow(l, 2.0))
99 + (t / 24.0 * N_a * pow(cos(phi), 4.0) * l4coef * pow(l, 4.0))
100 + (t / 720.0 * N_a * pow(cos(phi), 6.0) * l6coef * pow(l, 6.0))
101 + (t / 40320.0 * N_a * pow(cos(phi), 8.0) * l8coef * pow(l, 8.0)) };
102 }
103
104 /**
105 * Converts x and y coordinates in the Transverse Mercator projection to
106 * a latitude/longitude pair. Note that Transverse Mercator is not
107 * the same as UTM; a scale factor is required to convert between them.
108 *
109 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
110 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
111 *
112 * Remarks:
113 * The local variables Nf, nuf2, tf, and tf2 serve the same purpose as
114 * N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
115 * to the footpoint latitude phif.
116 *
117 * x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and
118 * to optimize computations.
119 *
120 * @param x The easting of the point, in meters, divided by the semi major axis of the ellipsoid
121 * @param y The northing of the point, in meters, divided by the semi major axis of the ellipsoid
122 * @return A 2-element containing the latitude and longitude
123 * in radians
124 */
125 @Override
126 public double[] invproject(double x, double y) {
127 /* Get the value of phif, the footpoint latitude. */
128 double phif = footpointLatitude(y);
129
130 /* Precalculate ep2 */
131 double ep2 = (a*a - b*b)
132 / (b*b);
133
134 /* Precalculate cos(phif) */
135 double cf = cos(phif);
136
137 /* Precalculate nuf2 */
138 double nuf2 = ep2 * pow(cf, 2.0);
139
140 /* Precalculate Nf / a and initialize Nfpow */
141 double Nf_a = a / (b * sqrt(1 + nuf2));
142 double Nfpow = Nf_a;
143
144 /* Precalculate tf */
145 double tf = tan(phif);
146 double tf2 = tf * tf;
147 double tf4 = tf2 * tf2;
148
149 /* Precalculate fractional coefficients for x**n in the equations
150 below to simplify the expressions for latitude and longitude. */
151 double x1frac = 1.0 / (Nfpow * cf);
152
153 Nfpow *= Nf_a; /* now equals Nf**2) */
154 double x2frac = tf / (2.0 * Nfpow);
155
156 Nfpow *= Nf_a; /* now equals Nf**3) */
157 double x3frac = 1.0 / (6.0 * Nfpow * cf);
158
159 Nfpow *= Nf_a; /* now equals Nf**4) */
160 double x4frac = tf / (24.0 * Nfpow);
161
162 Nfpow *= Nf_a; /* now equals Nf**5) */
163 double x5frac = 1.0 / (120.0 * Nfpow * cf);
164
165 Nfpow *= Nf_a; /* now equals Nf**6) */
166 double x6frac = tf / (720.0 * Nfpow);
167
168 Nfpow *= Nf_a; /* now equals Nf**7) */
169 double x7frac = 1.0 / (5040.0 * Nfpow * cf);
170
171 Nfpow *= Nf_a; /* now equals Nf**8) */
172 double x8frac = tf / (40320.0 * Nfpow);
173
174 /* Precalculate polynomial coefficients for x**n.
175 -- x**1 does not have a polynomial coefficient. */
176 double x2poly = -1.0 - nuf2;
177 double x3poly = -1.0 - 2 * tf2 - nuf2;
178 double x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 *nuf2) - 9.0 * tf2 * (nuf2 * nuf2);
179 double x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
180 double x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2;
181 double x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
182 double x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
183
184 return new double[] {
185 /* Calculate latitude */
186 phif + x2frac * x2poly * (x * x)
187 + x4frac * x4poly * pow(x, 4.0)
188 + x6frac * x6poly * pow(x, 6.0)
189 + x8frac * x8poly * pow(x, 8.0),
190 /* Calculate longitude */
191 x1frac * x
192 + x3frac * x3poly * pow(x, 3.0)
193 + x5frac * x5poly * pow(x, 5.0)
194 + x7frac * x7poly * pow(x, 7.0) };
195 }
196
197 /**
198 * ArcLengthOfMeridian
199 *
200 * Computes the ellipsoidal distance from the equator to a point at a
201 * given latitude.
202 *
203 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
204 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
205 *
206 * @param phi Latitude of the point, in radians
207 * @return The ellipsoidal distance of the point from the equator
208 * (in meters, divided by the semi major axis of the ellipsoid)
209 */
210 private double ArcLengthOfMeridian(double phi) {
211 /* Precalculate n */
212 double n = (a - b) / (a + b);
213
214 /* Precalculate alpha */
215 double alpha = ((a + b) / 2.0)
216 * (1.0 + (pow(n, 2.0) / 4.0) + (pow(n, 4.0) / 64.0));
217
218 /* Precalculate beta */
219 double beta = (-3.0 * n / 2.0) + (9.0 * pow(n, 3.0) / 16.0)
220 + (-3.0 * pow(n, 5.0) / 32.0);
221
222 /* Precalculate gamma */
223 double gamma = (15.0 * pow(n, 2.0) / 16.0)
224 + (-15.0 * pow(n, 4.0) / 32.0);
225
226 /* Precalculate delta */
227 double delta = (-35.0 * pow(n, 3.0) / 48.0)
228 + (105.0 * pow(n, 5.0) / 256.0);
229
230 /* Precalculate epsilon */
231 double epsilon = (315.0 * pow(n, 4.0) / 512.0);
232
233 /* Now calculate the sum of the series and return */
234 return alpha
235 * (phi + (beta * sin(2.0 * phi))
236 + (gamma * sin(4.0 * phi))
237 + (delta * sin(6.0 * phi))
238 + (epsilon * sin(8.0 * phi)));
239 }
240
241 /**
242 * FootpointLatitude
243 *
244 * Computes the footpoint latitude for use in converting transverse
245 * Mercator coordinates to ellipsoidal coordinates.
246 *
247 * Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
248 * GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
249 *
250 * @param y northing coordinate, in meters, divided by the semi major axis of the ellipsoid
251 * @return The footpoint latitude, in radians
252 */
253 private double footpointLatitude(double y) {
254 /* Precalculate n (Eq. 10.18) */
255 double n = (a - b) / (a + b);
256
257 /* Precalculate alpha_ (Eq. 10.22) */
258 /* (Same as alpha in Eq. 10.17) */
259 double alpha_ = ((a + b) / 2.0)
260 * (1 + (pow(n, 2.0) / 4) + (pow(n, 4.0) / 64));
261
262 /* Precalculate y_ (Eq. 10.23) */
263 double y_ = y / alpha_ * a;
264
265 /* Precalculate beta_ (Eq. 10.22) */
266 double beta_ = (3.0 * n / 2.0) + (-27.0 * pow(n, 3.0) / 32.0)
267 + (269.0 * pow(n, 5.0) / 512.0);
268
269 /* Precalculate gamma_ (Eq. 10.22) */
270 double gamma_ = (21.0 * pow(n, 2.0) / 16.0)
271 + (-55.0 * pow(n, 4.0) / 32.0);
272
273 /* Precalculate delta_ (Eq. 10.22) */
274 double delta_ = (151.0 * pow(n, 3.0) / 96.0)
275 + (-417.0 * pow(n, 5.0) / 128.0);
276
277 /* Precalculate epsilon_ (Eq. 10.22) */
278 double epsilon_ = (1097.0 * pow(n, 4.0) / 512.0);
279
280 /* Now calculate the sum of the series (Eq. 10.21) */
281 return y_ + (beta_ * sin(2.0 * y_))
282 + (gamma_ * sin(4.0 * y_))
283 + (delta_ * sin(6.0 * y_))
284 + (epsilon_ * sin(8.0 * y_));
285 }
286
287}
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