/Proj4/PJ_aeqd.c

  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
 49PJ_CVSID("$Id: PJ_aeqd.c,v 1.3 2002/12/14 19:27:06 warmerda Exp $");
 50
 51PROJ_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
 60FORWARD(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}
 71FORWARD(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}
111FORWARD(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;
123oblcon:
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}
148INVERSE(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}
162INVERSE(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}
195INVERSE(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}
229FREEUP;
230    if (P) {
231		if (P->en)
232			pj_dalloc(P->en);
233		pj_dalloc(P);
234	}
235}
236ENTRY1(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	}
277ENDENTRY(P)