1 /*
2 * Project: PROJ
3 * Purpose: Implementation of the krovak (Krovak) projection.
4 * Definition: http://www.ihsenergy.com/epsg/guid7.html#1.4.3
5 * Author: Thomas Flemming, tf@ttqv.com
6 *
7 ******************************************************************************
8 * Copyright (c) 2001, Thomas Flemming, tf@ttqv.com
9 *
10 * Permission is hereby granted, free of charge, to any person obtaining a
11 * copy of this software and associated documentation files (the "Software"),
12 * to deal in the Software without restriction, including without limitation
13 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
14 * and/or sell copies of the Software, and to permit persons to whom the
15 * Software is furnished to do so, subject to the following conditions:
16 *
17 * The above copyright notice and this permission notice shall be included
18 * in all copies or substantial portions of the Software.
19 *
20 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
21 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
22 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
23 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
24 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
25 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
26 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
27 * SOFTWARE.
28 ******************************************************************************
29 * A description of the (forward) projection is found in:
30 *
31 * Bohuslav Veverka,
32 *
33 * KROVAK’S PROJECTION AND ITS USE FOR THE
34 * CZECH REPUBLIC AND THE SLOVAK REPUBLIC,
35 *
36 * 50 years of the Research Institute of
37 * and the Slovak Republic Geodesy, Topography and Cartography
38 *
39 * which can be found via the Wayback Machine:
40 *
41 * https://web.archive.org/web/20150216143806/https://www.vugtk.cz/odis/sborniky/sb2005/Sbornik_50_let_VUGTK/Part_1-Scientific_Contribution/16-Veverka.pdf
42 *
43 * Further info, including the inverse projection, is given by EPSG:
44 *
45 * Guidance Note 7 part 2
46 * Coordinate Conversions and Transformations including Formulas
47 *
48 * http://www.iogp.org/pubs/373-07-2.pdf
49 *
50 * Variable names in this file mostly follows what is used in the
51 * paper by Veverka.
52 *
53 * According to EPSG the full Krovak projection method should have
54 * the following parameters. Within PROJ the azimuth, and pseudo
55 * standard parallel are hardcoded in the algorithm and can't be
56 * altered from outside. The others all have defaults to match the
57 * common usage with Krovak projection.
58 *
59 * lat_0 = latitude of centre of the projection
60 *
61 * lon_0 = longitude of centre of the projection
62 *
63 * ** = azimuth (true) of the centre line passing through the
64 * centre of the projection
65 *
66 * ** = latitude of pseudo standard parallel
67 *
68 * k = scale factor on the pseudo standard parallel
69 *
70 * x_0 = False Easting of the centre of the projection at the
71 * apex of the cone
72 *
73 * y_0 = False Northing of the centre of the projection at
74 * the apex of the cone
75 *
76 *****************************************************************************/
77
78 #define PJ_LIB__
79
80 #include <errno.h>
81 #include <math.h>
82
83 #include "proj.h"
84 #include "proj_internal.h"
85
86 PROJ_HEAD(krovak, "Krovak") "\n\tPCyl, Ell";
87
88 #define EPS 1e-15
89 #define UQ 1.04216856380474 /* DU(2, 59, 42, 42.69689) */
90 #define S0 1.37008346281555 /* Latitude of pseudo standard parallel 78deg 30'00" N */
91 /* Not sure at all of the appropriate number for MAX_ITER... */
92 #define MAX_ITER 100
93
94 namespace { // anonymous namespace
95 struct pj_opaque {
96 double alpha;
97 double k;
98 double n;
99 double rho0;
100 double ad;
101 int czech;
102 };
103 } // anonymous namespace
104
105
krovak_e_forward(PJ_LP lp,PJ * P)106 static PJ_XY krovak_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
107 struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
108 PJ_XY xy = {0.0,0.0};
109
110 double gfi, u, deltav, s, d, eps, rho;
111
112 gfi = pow ( (1. + P->e * sin(lp.phi)) / (1. - P->e * sin(lp.phi)), Q->alpha * P->e / 2.);
113
114 u = 2. * (atan(Q->k * pow( tan(lp.phi / 2. + M_PI_4), Q->alpha) / gfi)-M_PI_4);
115 deltav = -lp.lam * Q->alpha;
116
117 s = asin(cos(Q->ad) * sin(u) + sin(Q->ad) * cos(u) * cos(deltav));
118 const double cos_s = cos(s);
119 if( cos_s < 1e-12 )
120 {
121 xy.x = 0;
122 xy.y = 0;
123 return xy;
124 }
125 d = asin(cos(u) * sin(deltav) / cos_s);
126
127 eps = Q->n * d;
128 rho = Q->rho0 * pow(tan(S0 / 2. + M_PI_4) , Q->n) / pow(tan(s / 2. + M_PI_4) , Q->n);
129
130 xy.y = rho * cos(eps);
131 xy.x = rho * sin(eps);
132
133 xy.y *= Q->czech;
134 xy.x *= Q->czech;
135
136 return xy;
137 }
138
139
krovak_e_inverse(PJ_XY xy,PJ * P)140 static PJ_LP krovak_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
141 struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
142 PJ_LP lp = {0.0,0.0};
143
144 double u, deltav, s, d, eps, rho, fi1, xy0;
145 int i;
146
147 xy0 = xy.x;
148 xy.x = xy.y;
149 xy.y = xy0;
150
151 xy.x *= Q->czech;
152 xy.y *= Q->czech;
153
154 rho = sqrt(xy.x * xy.x + xy.y * xy.y);
155 eps = atan2(xy.y, xy.x);
156
157 d = eps / sin(S0);
158 if( rho == 0.0 ) {
159 s = M_PI_2;
160 }
161 else {
162 s = 2. * (atan( pow(Q->rho0 / rho, 1. / Q->n) * tan(S0 / 2. + M_PI_4)) - M_PI_4);
163 }
164
165 u = asin(cos(Q->ad) * sin(s) - sin(Q->ad) * cos(s) * cos(d));
166 deltav = asin(cos(s) * sin(d) / cos(u));
167
168 lp.lam = P->lam0 - deltav / Q->alpha;
169
170 /* ITERATION FOR lp.phi */
171 fi1 = u;
172
173 for (i = MAX_ITER; i ; --i) {
174 lp.phi = 2. * ( atan( pow( Q->k, -1. / Q->alpha) *
175 pow( tan(u / 2. + M_PI_4) , 1. / Q->alpha) *
176 pow( (1. + P->e * sin(fi1)) / (1. - P->e * sin(fi1)) , P->e / 2.)
177 ) - M_PI_4);
178
179 if (fabs(fi1 - lp.phi) < EPS)
180 break;
181 fi1 = lp.phi;
182 }
183 if( i == 0 )
184 pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
185
186 lp.lam -= P->lam0;
187
188 return lp;
189 }
190
191
PROJECTION(krovak)192 PJ *PROJECTION(krovak) {
193 double u0, n0, g;
194 struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
195 if (nullptr==Q)
196 return pj_default_destructor (P, ENOMEM);
197 P->opaque = Q;
198
199 /* we want Bessel as fixed ellipsoid */
200 P->a = 6377397.155;
201 P->es = 0.006674372230614;
202 P->e = sqrt(P->es);
203
204 /* if latitude of projection center is not set, use 49d30'N */
205 if (!pj_param(P->ctx, P->params, "tlat_0").i)
206 P->phi0 = 0.863937979737193;
207
208 /* if center long is not set use 42d30'E of Ferro - 17d40' for Ferro */
209 /* that will correspond to using longitudes relative to greenwich */
210 /* as input and output, instead of lat/long relative to Ferro */
211 if (!pj_param(P->ctx, P->params, "tlon_0").i)
212 P->lam0 = 0.7417649320975901 - 0.308341501185665;
213
214 /* if scale not set default to 0.9999 */
215 if (!pj_param(P->ctx, P->params, "tk").i && !pj_param(P->ctx, P->params, "tk_0").i)
216 P->k0 = 0.9999;
217
218 Q->czech = 1;
219 if( !pj_param(P->ctx, P->params, "tczech").i )
220 Q->czech = -1;
221
222 /* Set up shared parameters between forward and inverse */
223 Q->alpha = sqrt(1. + (P->es * pow(cos(P->phi0), 4)) / (1. - P->es));
224 u0 = asin(sin(P->phi0) / Q->alpha);
225 g = pow( (1. + P->e * sin(P->phi0)) / (1. - P->e * sin(P->phi0)) , Q->alpha * P->e / 2. );
226 double tan_half_phi0_plus_pi_4 = tan(P->phi0 / 2. + M_PI_4);
227 if( tan_half_phi0_plus_pi_4 == 0.0 ) {
228 return pj_default_destructor(P, PJD_ERR_INVALID_ARG);
229 }
230 Q->k = tan( u0 / 2. + M_PI_4) / pow (tan_half_phi0_plus_pi_4 , Q->alpha) * g;
231 n0 = sqrt(1. - P->es) / (1. - P->es * pow(sin(P->phi0), 2));
232 Q->n = sin(S0);
233 Q->rho0 = P->k0 * n0 / tan(S0);
234 Q->ad = M_PI_2 - UQ;
235
236 P->inv = krovak_e_inverse;
237 P->fwd = krovak_e_forward;
238
239 return P;
240 }
241