source: josm/trunk/src/org/openstreetmap/josm/data/projection/proj/LambertAzimuthalEqualArea.java@ 9950

Last change on this file since 9950 was 9636, checked in by bastiK, 8 years ago

remove unnecessary assignment (see #12186)
  • Property svn:eol-style set to native
File size: 9.2 KB
Line 
1// License: GPL. For details, see LICENSE file.
2package org.openstreetmap.josm.data.projection.proj;
3
4import static org.openstreetmap.josm.tools.I18n.tr;
5
6import org.openstreetmap.josm.data.Bounds;
7import org.openstreetmap.josm.data.projection.ProjectionConfigurationException;
8
9/**
10 * Lambert Azimuthal Equal Area (EPSG code 9820).
11 * <p>
12 * This class has been derived from the implementation of the Geotools project;
13 * git 8cbf52d, org.geotools.referencing.operation.projection.LambertAzimuthalEqualArea
14 * at the time of migration.
15 * <p>
16 * <b>References:</b>
17 * <ul>
18 * <li> A. Annoni, C. Luzet, E.Gubler and J. Ihde - Map Projections for Europe</li>
19 * <li> John P. Snyder (Map Projections - A Working Manual,
20 * U.S. Geological Survey Professional Paper 1395)</li>
21 * </ul>
22 *
23 * @author Gerald Evenden (for original code in Proj4)
24 * @author Beate Stollberg
25 * @author Martin Desruisseaux
26 *
27 * @see <A HREF="http://mathworld.wolfram.com/LambertAzimuthalEqual-AreaProjection.html">Lambert Azimuthal Equal-Area Projection</A>
28 * @see <A HREF="http://www.remotesensing.org/geotiff/proj_list/lambert_azimuthal_equal_area.html">"Lambert_Azimuthal_Equal_Area"</A>
29 */
30public class LambertAzimuthalEqualArea extends AbstractProj {
31
32 /** Maximum difference allowed when comparing real numbers. */
33 private static final double EPSILON = 1E-7;
34
35 /** Epsilon for the comparison of small quantities. */
36 private static final double FINE_EPSILON = 1E-10;
37
38 /** Epsilon for the comparison of latitudes. */
39 private static final double EPSILON_LATITUDE = 1E-10;
40
41 /** Constants for authalic latitude. */
42 private static final double P00 = 0.33333333333333333333;
43 private static final double P01 = 0.17222222222222222222;
44 private static final double P02 = 0.10257936507936507936;
45 private static final double P10 = 0.06388888888888888888;
46 private static final double P11 = 0.06640211640211640211;
47 private static final double P20 = 0.01641501294219154443;
48
49 /** The projection mode. */
50 private enum Mode { OBLIQUE, EQUATORIAL, NORTH_POLE, SOUTH_POLE }
51
52 /** The projection mode for this particular instance. */
53 private Mode mode;
54
55 /** Constant parameters. */
56 private double sinb1, cosb1, xmf, ymf, mmf, qp, dd, rq;
57
58 /** Coefficients for authalic latitude. */
59 private double APA0, APA1, APA2;
60
61 private double latitudeOfOrigin;
62
63 @Override
64 public String getName() {
65 return tr("Lambert Azimuthal Equal Area");
66 }
67
68 @Override
69 public String getProj4Id() {
70 return "laea";
71 }
72
73 @Override
74 public void initialize(ProjParameters params) throws ProjectionConfigurationException {
75 super.initialize(params);
76
77 if (params.lat0 == null)
78 throw new ProjectionConfigurationException(tr("Parameter ''{0}'' required.", "lat_0"));
79
80 latitudeOfOrigin = Math.toRadians(params.lat0);
81 /*
82 * Detects the mode (oblique, etc.).
83 */
84 final double t = Math.abs(latitudeOfOrigin);
85 if (Math.abs(t - Math.PI/2) < EPSILON_LATITUDE) {
86 mode = latitudeOfOrigin < 0.0 ? Mode.SOUTH_POLE : Mode.NORTH_POLE;
87 } else if (Math.abs(t) < EPSILON_LATITUDE) {
88 mode = Mode.EQUATORIAL;
89 } else {
90 mode = Mode.OBLIQUE;
91 }
92 /*
93 * Computes the constants for authalic latitude.
94 */
95 final double es2 = e2 * e2;
96 final double es3 = e2 * es2;
97 APA0 = P02 * es3 + P01 * es2 + P00 * e2;
98 APA1 = P11 * es3 + P10 * es2;
99 APA2 = P20 * es3;
100
101 final double sinphi;
102 qp = qsfn(1);
103 rq = Math.sqrt(0.5 * qp);
104 mmf = 0.5 / (1 - e2);
105 sinphi = Math.sin(latitudeOfOrigin);
106 sinb1 = qsfn(sinphi) / qp;
107 cosb1 = Math.sqrt(1.0 - sinb1 * sinb1);
108 switch (mode) {
109 case NORTH_POLE: // Fall through
110 case SOUTH_POLE: {
111 dd = 1.0;
112 xmf = ymf = rq;
113 break;
114 }
115 case EQUATORIAL: {
116 dd = 1.0 / rq;
117 xmf = 1.0;
118 ymf = 0.5 * qp;
119 break;
120 }
121 case OBLIQUE: {
122 dd = Math.cos(latitudeOfOrigin) /
123 (Math.sqrt(1.0 - e2 * sinphi * sinphi) * rq * cosb1);
124 xmf = rq * dd;
125 ymf = rq / dd;
126 break;
127 }
128 default: {
129 throw new AssertionError(mode);
130 }
131 }
132 }
133
134 @Override
135 public double[] project(final double phi, final double lambda) {
136 final double coslam = Math.cos(lambda);
137 final double sinlam = Math.sin(lambda);
138 final double sinphi = Math.sin(phi);
139 double q = qsfn(sinphi);
140 final double sinb, cosb, b, c, x, y;
141 switch (mode) {
142 case OBLIQUE: {
143 sinb = q / qp;
144 cosb = Math.sqrt(1.0 - sinb * sinb);
145 c = 1.0 + sinb1 * sinb + cosb1 * cosb * coslam;
146 b = Math.sqrt(2.0 / c);
147 y = ymf * b * (cosb1 * sinb - sinb1 * cosb * coslam);
148 x = xmf * b * cosb * sinlam;
149 break;
150 }
151 case EQUATORIAL: {
152 sinb = q / qp;
153 cosb = Math.sqrt(1.0 - sinb * sinb);
154 c = 1.0 + cosb * coslam;
155 b = Math.sqrt(2.0 / c);
156 y = ymf * b * sinb;
157 x = xmf * b * cosb * sinlam;
158 break;
159 }
160 case NORTH_POLE: {
161 c = (Math.PI / 2) + phi;
162 q = qp - q;
163 if (q >= 0.0) {
164 b = Math.sqrt(q);
165 x = b * sinlam;
166 y = coslam * -b;
167 } else {
168 x = y = 0.;
169 }
170 break;
171 }
172 case SOUTH_POLE: {
173 c = phi - (Math.PI / 2);
174 q = qp + q;
175 if (q >= 0.0) {
176 b = Math.sqrt(q);
177 x = b * sinlam;
178 y = coslam * +b;
179 } else {
180 x = y = 0.;
181 }
182 break;
183 }
184 default: {
185 throw new AssertionError(mode);
186 }
187 }
188 if (Math.abs(c) < EPSILON_LATITUDE) {
189 return new double[] {0, 0}; // this is an error, we should handle it somehow
190 }
191 return new double[] {x, y};
192 }
193
194 @Override
195 public double[] invproject(double x, double y) {
196 final double lambda, phi;
197 switch (mode) {
198 case EQUATORIAL: // Fall through
199 case OBLIQUE: {
200 x /= dd;
201 y *= dd;
202 final double rho = Math.hypot(x, y);
203 if (rho < FINE_EPSILON) {
204 lambda = 0.0;
205 phi = latitudeOfOrigin;
206 } else {
207 double sCe, cCe, ab;
208 sCe = 2.0 * Math.asin(0.5 * rho / rq);
209 cCe = Math.cos(sCe);
210 sCe = Math.sin(sCe);
211 x *= sCe;
212 if (mode == Mode.OBLIQUE) {
213 ab = cCe * sinb1 + y * sCe * cosb1 / rho;
214 y = rho * cosb1 * cCe - y * sinb1 * sCe;
215 } else {
216 ab = y * sCe / rho;
217 y = rho * cCe;
218 }
219 lambda = Math.atan2(x, y);
220 phi = authlat(Math.asin(ab));
221 }
222 break;
223 }
224 case NORTH_POLE: {
225 y = -y;
226 // Fall through
227 }
228 case SOUTH_POLE: {
229 final double q = x*x + y*y;
230 if (q == 0) {
231 lambda = 0.;
232 phi = latitudeOfOrigin;
233 } else {
234 double ab = 1.0 - q / qp;
235 if (mode == Mode.SOUTH_POLE) {
236 ab = -ab;
237 }
238 lambda = Math.atan2(x, y);
239 phi = authlat(Math.asin(ab));
240 }
241 break;
242 }
243 default: {
244 throw new AssertionError(mode);
245 }
246 }
247 return new double[] {phi, lambda};
248 }
249
250
251 /**
252 * Calculates <var>q</var>, Snyder equation (3-12)
253 *
254 * @param sinphi sin of the latitude <var>q</var> is calculated for.
255 * @return <var>q</var> from Snyder equation (3-12).
256 */
257 private double qsfn(final double sinphi) {
258 if (e >= EPSILON) {
259 final double con = e * sinphi;
260 return ((1.0 - e2) * (sinphi / (1.0 - con*con) -
261 (0.5 / e) * Math.log((1.0 - con) / (1.0 + con))));
262 } else {
263 return sinphi + sinphi;
264 }
265 }
266
267 /**
268 * Determines latitude from authalic latitude.
269 * @param beta authalic latitude
270 * @return corresponding latitude
271 */
272 private double authlat(final double beta) {
273 final double t = beta + beta;
274 return beta + APA0 * Math.sin(t) + APA1 * Math.sin(t+t) + APA2 * Math.sin(t+t+t);
275 }
276
277 @Override
278 public Bounds getAlgorithmBounds() {
279 return new Bounds(-89, -174, 89, 174, false);
280 }
281}
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