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
253
254
255
256
257
258
259
|
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(moll, "Mollweide") "\n\tPCyl., Sph.";
PROJ_HEAD(wag4, "Wagner IV") "\n\tPCyl., Sph.";
PROJ_HEAD(wag5, "Wagner V") "\n\tPCyl., Sph.";
#define MAX_ITER 10
#define LOOP_TOL 1e-7
struct pj_opaque {
double C_x, C_y, C_p;
};
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double k, V;
int i;
k = Q->C_p * sin(lp.phi);
for (i = MAX_ITER; i ; --i) {
lp.phi -= V = (lp.phi + sin(lp.phi) - k) /
(1. + cos(lp.phi));
if (fabs(V) < LOOP_TOL)
break;
}
if (!i)
lp.phi = (lp.phi < 0.) ? -M_HALFPI : M_HALFPI;
else
lp.phi *= 0.5;
xy.x = Q->C_x * lp.lam * cos(lp.phi);
xy.y = Q->C_y * sin(lp.phi);
return xy;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
lp.phi = aasin(P->ctx, xy.y / Q->C_y);
lp.lam = xy.x / (Q->C_x * cos(lp.phi));
if (fabs(lp.lam) < M_PI) {
lp.phi += lp.phi;
lp.phi = aasin(P->ctx, (lp.phi + sin(lp.phi)) / Q->C_p);
} else {
lp.lam = lp.phi = HUGE_VAL;
}
return lp;
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_dealloc (P);
pj_dealloc (P->opaque);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
static PJ * setup(PJ *P, double p) {
struct pj_opaque *Q = P->opaque;
double r, sp, p2 = p + p;
P->es = 0;
sp = sin(p);
r = sqrt(M_TWOPI * sp / (p2 + sin(p2)));
Q->C_x = 2. * r / M_PI;
Q->C_y = r / sp;
Q->C_p = p2 + sin(p2);
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
PJ *PROJECTION(moll) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
return setup(P, M_HALFPI);
}
PJ *PROJECTION(wag4) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
return setup(P, M_PI/3.);
}
PJ *PROJECTION(wag5) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
P->es = 0;
Q->C_x = 0.90977;
Q->C_y = 1.65014;
Q->C_p = 3.00896;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
#ifndef PJ_SELFTEST
int pj_moll_selftest (void) {return 0;}
#else
int pj_moll_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=moll +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{201113.698641813244, 124066.283433859542},
{201113.698641813244, -124066.283433859542},
{-201113.698641813244, 124066.283433859542},
{-201113.698641813244, -124066.283433859542},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{0.00198873782220854774, 0.000806005080362811612},
{0.00198873782220854774, -0.000806005080362811612},
{-0.00198873782220854774, 0.000806005080362811612},
{-0.00198873782220854774, -0.000806005080362811612},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, inv_in, 0, s_inv_expect);
}
#endif
#ifndef PJ_SELFTEST
int pj_wag4_selftest (void) {return 0;}
#else
int pj_wag4_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=wag4 +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{ 192801.218662384286, 129416.216394802992},
{ 192801.218662384286, -129416.216394802992},
{-192801.218662384286, 129416.216394802992},
{-192801.218662384286, -129416.216394802992},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{ 0.00207450259783523421, 0.000772682950537716476},
{ 0.00207450259783523421, -0.000772682950537716476},
{-0.00207450259783523421, 0.000772682950537716476},
{-0.00207450259783523421, -0.000772682950537716476},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, inv_in, 0, s_inv_expect);
}
#endif
#ifndef PJ_SELFTEST
int pj_wag5_selftest (void) {return 0;}
#else
int pj_wag5_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=wag5 +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{ 203227.05192532466, 138651.631442713202},
{ 203227.05192532466, -138651.631442713202},
{-203227.05192532466, 138651.631442713202},
{-203227.05192532466, -138651.631442713202},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{ 0.00196807227086416396, 0.00072121615041701424},
{ 0.00196807227086416396, -0.00072121615041701424},
{-0.00196807227086416396, 0.00072121615041701424},
{-0.00196807227086416396, -0.00072121615041701424},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, inv_in, 0, s_inv_expect);
}
#endif
|
