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
248
249
250
251
252
|
/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2008 Gerald I. Evenden
*/
/*
** 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.
*/
/* The code in this file is largly based upon procedures:
*
* Written by: Knud Poder and Karsten Engsager
*
* Based on math from: R.Koenig and K.H. Weise, "Mathematische
* Grundlagen der hoeheren Geodaesie und Kartographie,
* Springer-Verlag, Berlin/Goettingen" Heidelberg, 1951.
*
* Modified and used here by permission of Reference Networks
* Division, Kort og Matrikelstyrelsen (KMS), Copenhagen, Denmark
*/
#define PROJ_PARMS__ \
double Qn; /* Merid. quad., scaled to the projection */ \
double Zb; /* Radius vector in polar coord. systems */ \
double cgb[5]; /* Constants for Gauss -> Geo lat */ \
double cbg[5]; /* Constants for Geo lat -> Gauss */ \
double utg[5]; /* Constants for transv. merc. -> geo */ \
double gtu[5]; /* Constants for geo -> transv. merc. */
#define PROJ_LIB__
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(etmerc, "Extended Transverse Mercator")
"\n\tCyl, Sph\n\tlat_ts=(0)\nlat_0=(0)";
#define FABS(x) ((x)<0?-(x):(x))
#ifdef _GNU_SOURCE
inline
#endif
static double
gatg(double *p1, int len_p1, double B) {
double *p;
double h = 0., h1, h2 = 0., cos_2B;
cos_2B = 2.*cos(2.0*B);
for (p = p1 + len_p1, h1 = *--p; p - p1; h2 = h1, h1 = h)
h = -h2 + cos_2B*h1 + *--p;
return (B + h*sin(2.0*B));
}
#ifdef _GNU_SOURCE
inline
#endif
static double
clenS(double *a, int size, double arg_r, double arg_i, double *R, double *I) {
double *p, r, i, hr, hr1, hr2, hi, hi1, hi2;
double sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i;
double exp_arg_i, pxe_arg_i;
/* arguments */
p = a + size;
#ifdef _GNU_SOURCE
sincos(arg_r, &sin_arg_r, &cos_arg_r);
#else
sin_arg_r = sin(arg_r);
cos_arg_r = cos(arg_r);
#endif
exp_arg_i = exp( arg_i);
pxe_arg_i = exp(-arg_i);
sinh_arg_i = (exp_arg_i-pxe_arg_i)/2;
cosh_arg_i = (exp_arg_i+pxe_arg_i)/2;
r = 2.0*cos_arg_r*cosh_arg_i;
i = -2.0*sin_arg_r*sinh_arg_i;
/* summation loop */
for (hi1 = hr1 = hi = 0.0, hr = *--p; a - p;) {
hr2 = hr1;
hi2 = hi1;
hr1 = hr;
hi1 = hi;
hr = -hr2 + r*hr1 - i*hi1 + *--p;
hi = -hi2 + i*hr1 + r*hi1;
}
r = sin_arg_r*cosh_arg_i;
i = cos_arg_r*sinh_arg_i;
*R = r*hr - i*hi;
*I = r*hi + i*hr;
return(*R);
}
static double
clens(double *a, int size, double arg_r) {
double *p, r, hr, hr1, hr2, cos_arg_r;
p = a + size;
cos_arg_r = cos(arg_r);
r = 2.0*cos_arg_r;
/* summation loop */
for (hr1 = 0.0, hr = *--p; a - p;) {
hr2 = hr1;
hr1 = hr;
hr = -hr2 + r*hr1 + *--p;
}
return(sin(arg_r)*hr);
}
FORWARD(e_forward); /* ellipsoid */
double sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
double Cn = lp.phi, Ce = lp.lam;
/* ell. LAT, LNG -> Gaussian LAT, LNG */
Cn = gatg(P->cbg, 5, Cn);
/* Gaussian LAT, LNG -> compl. sph. LAT */
#ifdef _GNU_SOURCE
sincos(Cn, &sin_Cn, &cos_Cn);
sincos(Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
sin_Ce = sin(Ce);
cos_Ce = cos(Ce);
#endif
Cn = atan2(sin_Cn, cos_Ce*cos_Cn);
Ce = atan2(sin_Ce*cos_Cn, hypot(sin_Cn, cos_Cn*cos_Ce));
/* compl. sph. N, E -> ell. norm. N, E */
Ce = log(tan(FORTPI + Ce*0.5));
Cn += clenS(P->gtu, 5, 2.*Cn, 2.*Ce, &dCn, &dCe);
Ce += dCe;
if (FABS(Ce) <= 2.623395162778) {
xy.y = P->Qn * Cn + P->Zb; /* Northing */
xy.x = P->Qn * Ce; /* Easting */
} else
xy.x = xy.y = HUGE_VAL;
return (xy);
}
INVERSE(e_inverse); /* ellipsoid */
double sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
double Cn = xy.y, Ce = xy.x;
/* normalize N, E */
Cn = (Cn - P->Zb)/P->Qn;
Ce = Ce/P->Qn;
if (FABS(Ce) <= 2.623395162778) { /* 150 degrees */
/* norm. N, E -> compl. sph. LAT, LNG */
Cn += clenS(P->utg, 5, 2.*Cn, 2.*Ce, &dCn, &dCe);
Ce += dCe;
Ce = 2.0*(atan(exp(Ce)) - FORTPI);
/* compl. sph. LAT -> Gaussian LAT, LNG */
#ifdef _GNU_SOURCE
sincos(Cn, &sin_Cn, &cos_Cn);
sincos(Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
sin_Ce = sin(Ce);
cos_Ce = cos(Ce);
#endif
Ce = atan2(sin_Ce, cos_Ce*cos_Cn);
Cn = atan2(sin_Cn*cos_Ce, hypot(sin_Ce, cos_Ce*cos_Cn));
/* Gaussian LAT, LNG -> ell. LAT, LNG */
lp.phi = gatg(P->cgb, 5, Cn);
lp.lam = Ce;
}
else
lp.phi = lp.lam = HUGE_VAL;
return (lp);
}
FREEUP; if (P) free(P); }
ENTRY0(etmerc)
double f, n, np, Z;
if (P->es <= 0.) E_ERROR(-34);
f = 1. - sqrt(1. - P->es);
/* third flattening */
np = n = f/(2.0 - f);
/* COEF. OF TRIG SERIES GEO <-> GAUSS */
/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
/* 5 degree : Engsager and Poder: ICC2007 */
P->cgb[0] = n*( 2.0 + n*(-2.0/3.0 + n*(-2.0 + n*(116.0/45.0 + n*(26.0/45.0)))));
P->cbg[0] = n*(-2.0 + n*( 2.0/3.0 + n*( 4.0/3.0 + n*(-82.0/45.0 + n*(32.0/45.0)))));
np *= n;
P->cgb[1] = np*(7.0/3.0 + n*( -8.0/5.0 + n*(-227.0/45.0 + n*(2704.0/315.0))));
P->cbg[1] = np*(5.0/3.0 + n*(-16.0/15.0 + n*( -13.0/ 9.0 + n*( 904.0/315.0))));
np *= n;
P->cgb[2] = np*( 56.0/15.0 + n*(-136.0/35.0 + n*(1262.0/105.0)));
P->cbg[2] = np*(-26.0/15.0 + n*( 34.0/21.0 + n*( 8.0/ 5.0)));
np *= n;
P->cgb[3] = np*(4279.0/630.0 + n*(-322.0/35.0));
P->cbg[3] = np*(1237.0/630.0 + n*( -12.0/ 5.0));
np *= n;
P->cgb[4] = np*(4174.0/315.0);
P->cbg[4] = np*(-734.0/315.0);
/* Constants of the projections */
/* Transverse Mercator (UTM, ITM, etc) */
np = n*n;
/* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
P->Qn = P->k0/(1 + n) * (1. + np*(1./4.0 + np*(1./64.0 + np/256.0)));
/* coef of trig series */
/* utg := ell. N, E -> sph. N, E, KW p194 (65) */
/* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
P->utg[0] = n*(-0.5 + n*( 2.0/3.0 + n*(-37.0/96.0 + n*( 1.0/360.0 + n*( 81.0/512.0)))));
P->gtu[0] = n*( 0.5 + n*(-2.0/3.0 + n*( 5.0/16.0 + n*(41.0/180.0 + n*(-127.0/288.0)))));
P->utg[1] = np*(-1.0/48.0 + n*(-1.0/15.0 + n*(437.0/1440.0 + n*(-46.0/105.0))));
P->gtu[1] = np*(13.0/48.0 + n*(-3.0/5.0 + n*(557.0/1440.0 + n*(281.0/630.0))));
np *= n;
P->utg[2] = np*(-17.0/480.0 + n*( 37.0/840.0 + n*( 209.0/ 4480.0)));
P->gtu[2] = np*( 61.0/240.0 + n*(-103.0/140.0 + n*(15061.0/26880.0)));
np *= n;
P->utg[3] = np*(-4397.0/161280.0 + n*( 11.0/504.0));
P->gtu[3] = np*(49561.0/161280.0 + n*(-179.0/168.0));
np *= n;
P->utg[4] = np*(-4583.0/161280.0);
P->gtu[4] = np*(34729.0/ 80640.0);
/* Gaussian latitude value of the origin latitude */
Z = gatg(P->cbg, 5, P->phi0);
/* Origin northing minus true northing at the origin latitude */
/* i.e. true northing = N - P->Zb */
P->Zb = - P->Qn*(Z + clens(P->gtu, 5, 2.0*Z));
P->inv = e_inverse;
P->fwd = e_forward;
ENDENTRY(P)
|
