-
Notifications
You must be signed in to change notification settings - Fork 5
/
PJ_krovak.c
248 lines (185 loc) · 7.3 KB
/
PJ_krovak.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
/******************************************************************************
* $Id$
*
* Project: PROJ.4
* Purpose: Implementation of the krovak (Krovak) projection.
* Definition: http://www.ihsenergy.com/epsg/guid7.html#1.4.3
* Author: Thomas Flemming, [email protected]
*
******************************************************************************
* Copyright (c) 2001, Thomas Flemming, [email protected]
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*****************************************************************************/
#define PROJ_PARMS__ \
double C_x;
#define PJ_LIB__
#include <projects.h>
#include <string.h>
#include <stdio.h>
PROJ_HEAD(krovak, "Krovak") "\n\tPCyl., Ellps.";
/**
NOTES: According to EPSG the full Krovak projection method should have
the following parameters. Within PROJ.4 the azimuth, and pseudo
standard parallel are hardcoded in the algorithm and can't be
altered from outside. The others all have defaults to match the
common usage with Krovak projection.
lat_0 = latitude of centre of the projection
lon_0 = longitude of centre of the projection
** = azimuth (true) of the centre line passing through the centre of the projection
** = latitude of pseudo standard parallel
k = scale factor on the pseudo standard parallel
x_0 = False Easting of the centre of the projection at the apex of the cone
y_0 = False Northing of the centre of the projection at the apex of the cone
**/
FORWARD(e_forward); /* ellipsoid */
/* calculate xy from lat/lon */
/* Constants, identical to inverse transform function */
double s45, s90, e2, e, alfa, uq, u0, g, k, k1, n0, ro0, ad, a, s0, n;
double gfi, u, fi0, deltav, s, d, eps, ro;
s45 = 0.785398163397448; /* 45deg */
s90 = 2 * s45;
fi0 = P->phi0; /* Latitude of projection centre 49deg 30' */
/* Ellipsoid is used as Parameter in for.c and inv.c, therefore a must
be set to 1 here.
Ellipsoid Bessel 1841 a = 6377397.155m 1/f = 299.1528128,
e2=0.006674372230614;
*/
a = 1; /* 6377397.155; */
/* e2 = P->es;*/ /* 0.006674372230614; */
e2 = 0.006674372230614;
e = sqrt(e2);
alfa = sqrt(1. + (e2 * pow(cos(fi0), 4)) / (1. - e2));
uq = 1.04216856380474; /* DU(2, 59, 42, 42.69689) */
u0 = asin(sin(fi0) / alfa);
g = pow( (1. + e * sin(fi0)) / (1. - e * sin(fi0)) , alfa * e / 2. );
k = tan( u0 / 2. + s45) / pow (tan(fi0 / 2. + s45) , alfa) * g;
k1 = P->k0;
n0 = a * sqrt(1. - e2) / (1. - e2 * pow(sin(fi0), 2));
s0 = 1.37008346281555; /* Latitude of pseudo standard parallel 78deg 30'00" N */
n = sin(s0);
ro0 = k1 * n0 / tan(s0);
ad = s90 - uq;
/* Transformation */
gfi =pow ( ((1. + e * sin(lp.phi)) /
(1. - e * sin(lp.phi))) , (alfa * e / 2.));
u= 2. * (atan(k * pow( tan(lp.phi / 2. + s45), alfa) / gfi)-s45);
deltav = - lp.lam * alfa;
s = asin(cos(ad) * sin(u) + sin(ad) * cos(u) * cos(deltav));
d = asin(cos(u) * sin(deltav) / cos(s));
eps = n * d;
ro = ro0 * pow(tan(s0 / 2. + s45) , n) / pow(tan(s / 2. + s45) , n) ;
/* x and y are reverted! */
xy.y = ro * cos(eps) / a;
xy.x = ro * sin(eps) / a;
if( !pj_param(P->ctx, P->params, "tczech").i )
{
xy.y *= -1.0;
xy.x *= -1.0;
}
return (xy);
}
INVERSE(e_inverse); /* ellipsoid */
/* calculate lat/lon from xy */
/* Constants, identisch wie in der Umkehrfunktion */
double s45, s90, fi0, e2, e, alfa, uq, u0, g, k, k1, n0, ro0, ad, a, s0, n;
double u, deltav, s, d, eps, ro, fi1, xy0;
int ok;
s45 = 0.785398163397448; /* 45deg */
s90 = 2 * s45;
fi0 = P->phi0; /* Latitude of projection centre 49deg 30' */
/* Ellipsoid is used as Parameter in for.c and inv.c, therefore a must
be set to 1 here.
Ellipsoid Bessel 1841 a = 6377397.155m 1/f = 299.1528128,
e2=0.006674372230614;
*/
a = 1; /* 6377397.155; */
/* e2 = P->es; */ /* 0.006674372230614; */
e2 = 0.006674372230614;
e = sqrt(e2);
alfa = sqrt(1. + (e2 * pow(cos(fi0), 4)) / (1. - e2));
uq = 1.04216856380474; /* DU(2, 59, 42, 42.69689) */
u0 = asin(sin(fi0) / alfa);
g = pow( (1. + e * sin(fi0)) / (1. - e * sin(fi0)) , alfa * e / 2. );
k = tan( u0 / 2. + s45) / pow (tan(fi0 / 2. + s45) , alfa) * g;
k1 = P->k0;
n0 = a * sqrt(1. - e2) / (1. - e2 * pow(sin(fi0), 2));
s0 = 1.37008346281555; /* Latitude of pseudo standard parallel 78deg 30'00" N */
n = sin(s0);
ro0 = k1 * n0 / tan(s0);
ad = s90 - uq;
/* Transformation */
/* revert y, x*/
xy0=xy.x;
xy.x=xy.y;
xy.y=xy0;
if( !pj_param(P->ctx, P->params, "tczech").i )
{
xy.x *= -1.0;
xy.y *= -1.0;
}
ro = sqrt(xy.x * xy.x + xy.y * xy.y);
eps = atan2(xy.y, xy.x);
d = eps / sin(s0);
s = 2. * (atan( pow(ro0 / ro, 1. / n) * tan(s0 / 2. + s45)) - s45);
u = asin(cos(ad) * sin(s) - sin(ad) * cos(s) * cos(d));
deltav = asin(cos(s) * sin(d) / cos(u));
lp.lam = P->lam0 - deltav / alfa;
/* ITERATION FOR lp.phi */
fi1 = u;
ok = 0;
do
{
lp.phi = 2. * ( atan( pow( k, -1. / alfa) *
pow( tan(u / 2. + s45) , 1. / alfa) *
pow( (1. + e * sin(fi1)) / (1. - e * sin(fi1)) , e / 2.)
) - s45);
if (fabs(fi1 - lp.phi) < 0.000000000000001) ok=1;
fi1 = lp.phi;
}
while (ok==0);
lp.lam -= P->lam0;
return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(krovak)
double ts;
/* read some Parameters,
* here Latitude Truescale */
ts = pj_param(P->ctx, P->params, "rlat_ts").f;
P->C_x = ts;
/* we want Bessel as fixed ellipsoid */
P->a = 6377397.155;
P->e = sqrt(P->es = 0.006674372230614);
/* if latitude of projection center is not set, use 49d30'N */
if (!pj_param(P->ctx, P->params, "tlat_0").i)
P->phi0 = 0.863937979737193;
/* if center long is not set use 42d30'E of Ferro - 17d40' for Ferro */
/* that will correspond to using longitudes relative to greenwich */
/* as input and output, instead of lat/long relative to Ferro */
if (!pj_param(P->ctx, P->params, "tlon_0").i)
P->lam0 = 0.7417649320975901 - 0.308341501185665;
/* if scale not set default to 0.9999 */
if (!pj_param(P->ctx, P->params, "tk").i)
P->k0 = 0.9999;
/* always the same */
P->inv = e_inverse;
P->fwd = e_forward;
ENDENTRY(P)