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1a37e1c @josephg Readded source
josephg authored
1 /******************************************************************************
2 * $Id: PJ_aeqd.c,v 1.3 2002/12/14 19:27:06 warmerda Exp $
3 *
4 * Project: PROJ.4
5 * Purpose: Implementation of the aeqd (Azimuthal Equidistant) projection.
6 * Author: Gerald Evenden
7 *
8 ******************************************************************************
9 * Copyright (c) 1995, Gerald Evenden
10 *
11 * Permission is hereby granted, free of charge, to any person obtaining a
12 * copy of this software and associated documentation files (the "Software"),
13 * to deal in the Software without restriction, including without limitation
14 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
15 * and/or sell copies of the Software, and to permit persons to whom the
16 * Software is furnished to do so, subject to the following conditions:
17 *
18 * The above copyright notice and this permission notice shall be included
19 * in all copies or substantial portions of the Software.
20 *
21 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
22 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
23 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
24 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
25 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
26 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
27 * DEALINGS IN THE SOFTWARE.
28 ******************************************************************************
29 *
30 * $Log: PJ_aeqd.c,v $
31 * Revision 1.3 2002/12/14 19:27:06 warmerda
32 * updated header
33 *
34 */
35
36 #define PROJ_PARMS__ \
37 double sinph0; \
38 double cosph0; \
39 double *en; \
40 double M1; \
41 double N1; \
42 double Mp; \
43 double He; \
44 double G; \
45 int mode;
46 #define PJ_LIB__
47 #include "projects.h"
48
49 PJ_CVSID("$Id: PJ_aeqd.c,v 1.3 2002/12/14 19:27:06 warmerda Exp $");
50
51 PROJ_HEAD(aeqd, "Azimuthal Equidistant") "\n\tAzi, Sph&Ell\n\tlat_0 guam";
52
53 #define EPS10 1.e-10
54 #define TOL 1.e-14
55
56 #define N_POLE 0
57 #define S_POLE 1
58 #define EQUIT 2
59 #define OBLIQ 3
60 FORWARD(e_guam_fwd); /* Guam elliptical */
61 double cosphi, sinphi, t;
62
63 cosphi = cos(lp.phi);
64 sinphi = sin(lp.phi);
65 t = 1. / sqrt(1. - P->es * sinphi * sinphi);
66 xy.x = lp.lam * cosphi * t;
67 xy.y = pj_mlfn(lp.phi, sinphi, cosphi, P->en) - P->M1 +
68 .5 * lp.lam * lp.lam * cosphi * sinphi * t;
69 return (xy);
70 }
71 FORWARD(e_forward); /* elliptical */
72 double coslam, cosphi, sinphi, rho, s, H, H2, c, Az, t, ct, st, cA, sA;
73
74 coslam = cos(lp.lam);
75 cosphi = cos(lp.phi);
76 sinphi = sin(lp.phi);
77 switch (P->mode) {
78 case N_POLE:
79 coslam = - coslam;
80 case S_POLE:
81 xy.x = (rho = fabs(P->Mp - pj_mlfn(lp.phi, sinphi, cosphi, P->en))) *
82 sin(lp.lam);
83 xy.y = rho * coslam;
84 break;
85 case EQUIT:
86 case OBLIQ:
87 if (fabs(lp.lam) < EPS10 && fabs(lp.phi - P->phi0) < EPS10) {
88 xy.x = xy.y = 0.;
89 break;
90 }
91 t = atan2(P->one_es * sinphi + P->es * P->N1 * P->sinph0 *
92 sqrt(1. - P->es * sinphi * sinphi), cosphi);
93 ct = cos(t); st = sin(t);
94 Az = atan2(sin(lp.lam) * ct, P->cosph0 * st - P->sinph0 * coslam * ct);
95 cA = cos(Az); sA = sin(Az);
96 s = aasin( fabs(sA) < TOL ?
97 (P->cosph0 * st - P->sinph0 * coslam * ct) / cA :
98 sin(lp.lam) * ct / sA );
99 H = P->He * cA;
100 H2 = H * H;
101 c = P->N1 * s * (1. + s * s * (- H2 * (1. - H2)/6. +
102 s * ( P->G * H * (1. - 2. * H2 * H2) / 8. +
103 s * ((H2 * (4. - 7. * H2) - 3. * P->G * P->G * (1. - 7. * H2)) /
104 120. - s * P->G * H / 48.))));
105 xy.x = c * sA;
106 xy.y = c * cA;
107 break;
108 }
109 return (xy);
110 }
111 FORWARD(s_forward); /* spherical */
112 double coslam, cosphi, sinphi;
113
114 sinphi = sin(lp.phi);
115 cosphi = cos(lp.phi);
116 coslam = cos(lp.lam);
117 switch (P->mode) {
118 case EQUIT:
119 xy.y = cosphi * coslam;
120 goto oblcon;
121 case OBLIQ:
122 xy.y = P->sinph0 * sinphi + P->cosph0 * cosphi * coslam;
123 oblcon:
124 if (fabs(fabs(xy.y) - 1.) < TOL)
125 if (xy.y < 0.)
126 F_ERROR
127 else
128 xy.x = xy.y = 0.;
129 else {
130 xy.y = acos(xy.y);
131 xy.y /= sin(xy.y);
132 xy.x = xy.y * cosphi * sin(lp.lam);
133 xy.y *= (P->mode == EQUIT) ? sinphi :
134 P->cosph0 * sinphi - P->sinph0 * cosphi * coslam;
135 }
136 break;
137 case N_POLE:
138 lp.phi = -lp.phi;
139 coslam = -coslam;
140 case S_POLE:
141 if (fabs(lp.phi - HALFPI) < EPS10) F_ERROR;
142 xy.x = (xy.y = (HALFPI + lp.phi)) * sin(lp.lam);
143 xy.y *= coslam;
144 break;
145 }
146 return (xy);
147 }
148 INVERSE(e_guam_inv); /* Guam elliptical */
149 double x2, t;
150 int i;
151
152 x2 = 0.5 * xy.x * xy.x;
153 lp.phi = P->phi0;
154 for (i = 0; i < 3; ++i) {
155 t = P->e * sin(lp.phi);
156 lp.phi = pj_inv_mlfn(P->M1 + xy.y -
157 x2 * tan(lp.phi) * (t = sqrt(1. - t * t)), P->es, P->en);
158 }
159 lp.lam = xy.x * t / cos(lp.phi);
160 return (lp);
161 }
162 INVERSE(e_inverse); /* elliptical */
163 double c, Az, cosAz, A, B, D, E, F, psi, t;
164
165 if ((c = hypot(xy.x, xy.y)) < EPS10) {
166 lp.phi = P->phi0;
167 lp.lam = 0.;
168 return (lp);
169 }
170 if (P->mode == OBLIQ || P->mode == EQUIT) {
171 cosAz = cos(Az = atan2(xy.x, xy.y));
172 t = P->cosph0 * cosAz;
173 B = P->es * t / P->one_es;
174 A = - B * t;
175 B *= 3. * (1. - A) * P->sinph0;
176 D = c / P->N1;
177 E = D * (1. - D * D * (A * (1. + A) / 6. + B * (1. + 3.*A) * D / 24.));
178 F = 1. - E * E * (A / 2. + B * E / 6.);
179 psi = aasin(P->sinph0 * cos(E) + t * sin(E));
180 lp.lam = aasin(sin(Az) * sin(E) / cos(psi));
181 if ((t = fabs(psi)) < EPS10)
182 lp.phi = 0.;
183 else if (fabs(t - HALFPI) < 0.)
184 lp.phi = HALFPI;
185 else
186 lp.phi = atan((1. - P->es * F * P->sinph0 / sin(psi)) * tan(psi) /
187 P->one_es);
188 } else { /* Polar */
189 lp.phi = pj_inv_mlfn(P->mode == N_POLE ? P->Mp - c : P->Mp + c,
190 P->es, P->en);
191 lp.lam = atan2(xy.x, P->mode == N_POLE ? -xy.y : xy.y);
192 }
193 return (lp);
194 }
195 INVERSE(s_inverse); /* spherical */
196 double cosc, c_rh, sinc;
197
198 if ((c_rh = hypot(xy.x, xy.y)) > PI) {
199 if (c_rh - EPS10 > PI) I_ERROR;
200 c_rh = PI;
201 } else if (c_rh < EPS10) {
202 lp.phi = P->phi0;
203 lp.lam = 0.;
204 return (lp);
205 }
206 if (P->mode == OBLIQ || P->mode == EQUIT) {
207 sinc = sin(c_rh);
208 cosc = cos(c_rh);
209 if (P->mode == EQUIT) {
210 lp.phi = aasin(xy.y * sinc / c_rh);
211 xy.x *= sinc;
212 xy.y = cosc * c_rh;
213 } else {
214 lp.phi = aasin(cosc * P->sinph0 + xy.y * sinc * P->cosph0 /
215 c_rh);
216 xy.y = (cosc - P->sinph0 * sin(lp.phi)) * c_rh;
217 xy.x *= sinc * P->cosph0;
218 }
219 lp.lam = xy.y == 0. ? 0. : atan2(xy.x, xy.y);
220 } else if (P->mode == N_POLE) {
221 lp.phi = HALFPI - c_rh;
222 lp.lam = atan2(xy.x, -xy.y);
223 } else {
224 lp.phi = c_rh - HALFPI;
225 lp.lam = atan2(xy.x, xy.y);
226 }
227 return (lp);
228 }
229 FREEUP;
230 if (P) {
231 if (P->en)
232 pj_dalloc(P->en);
233 pj_dalloc(P);
234 }
235 }
236 ENTRY1(aeqd, en)
237 P->phi0 = pj_param(P->params, "rlat_0").f;
238 if (fabs(fabs(P->phi0) - HALFPI) < EPS10) {
239 P->mode = P->phi0 < 0. ? S_POLE : N_POLE;
240 P->sinph0 = P->phi0 < 0. ? -1. : 1.;
241 P->cosph0 = 0.;
242 } else if (fabs(P->phi0) < EPS10) {
243 P->mode = EQUIT;
244 P->sinph0 = 0.;
245 P->cosph0 = 1.;
246 } else {
247 P->mode = OBLIQ;
248 P->sinph0 = sin(P->phi0);
249 P->cosph0 = cos(P->phi0);
250 }
251 if (! P->es) {
252 P->inv = s_inverse; P->fwd = s_forward;
253 } else {
254 if (!(P->en = pj_enfn(P->es))) E_ERROR_0;
255 if (pj_param(P->params, "bguam").i) {
256 P->M1 = pj_mlfn(P->phi0, P->sinph0, P->cosph0, P->en);
257 P->inv = e_guam_inv; P->fwd = e_guam_fwd;
258 } else {
259 switch (P->mode) {
260 case N_POLE:
261 P->Mp = pj_mlfn(HALFPI, 1., 0., P->en);
262 break;
263 case S_POLE:
264 P->Mp = pj_mlfn(-HALFPI, -1., 0., P->en);
265 break;
266 case EQUIT:
267 case OBLIQ:
268 P->inv = e_inverse; P->fwd = e_forward;
269 P->N1 = 1. / sqrt(1. - P->es * P->sinph0 * P->sinph0);
270 P->G = P->sinph0 * (P->He = P->e / sqrt(P->one_es));
271 P->He *= P->cosph0;
272 break;
273 }
274 P->inv = e_inverse; P->fwd = e_forward;
275 }
276 }
277 ENDENTRY(P)
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