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
|
/* based upon Snyder and Linck, USGS-NMD */
#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "projects.h"
PROJ_HEAD(lsat, "Space oblique for LANDSAT")
"\n\tCyl, Sph&Ell\n\tlsat= path=";
#define TOL 1e-7
struct pj_opaque {
double a2, a4, b, c1, c3;
double q, t, u, w, p22, sa, ca, xj, rlm, rlm2;
};
static void seraz0(double lam, double mult, PJ *P) {
struct pj_opaque *Q = P->opaque;
double sdsq, h, s, fc, sd, sq, d__1 = 0;
lam *= DEG_TO_RAD;
sd = sin(lam);
sdsq = sd * sd;
s = Q->p22 * Q->sa * cos(lam) * sqrt((1. + Q->t * sdsq)
/ ((1. + Q->w * sdsq) * (1. + Q->q * sdsq)));
d__1 = 1. + Q->q * sdsq;
h = sqrt((1. + Q->q * sdsq) / (1. + Q->w * sdsq)) * ((1. + Q->w * sdsq)
/ (d__1 * d__1) - Q->p22 * Q->ca);
sq = sqrt(Q->xj * Q->xj + s * s);
fc = mult * (h * Q->xj - s * s) / sq;
Q->b += fc;
Q->a2 += fc * cos(lam + lam);
Q->a4 += fc * cos(lam * 4.);
fc = mult * s * (h + Q->xj) / sq;
Q->c1 += fc * cos(lam);
Q->c3 += fc * cos(lam * 3.);
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
int l, nn;
double lamt = 0.0, xlam, sdsq, c, d, s, lamdp = 0.0, phidp, lampp, tanph;
double lamtp, cl, sd, sp, sav, tanphi;
if (lp.phi > M_HALFPI)
lp.phi = M_HALFPI;
else if (lp.phi < -M_HALFPI)
lp.phi = -M_HALFPI;
if (lp.phi >= 0. )
lampp = M_HALFPI;
else
lampp = M_PI_HALFPI;
tanphi = tan(lp.phi);
for (nn = 0;;) {
double fac;
sav = lampp;
lamtp = lp.lam + Q->p22 * lampp;
cl = cos(lamtp);
if( cl < 0 )
fac = lampp + sin(lampp) * M_HALFPI;
else
fac = lampp - sin(lampp) * M_HALFPI;
for (l = 50; l >= 0; --l) {
lamt = lp.lam + Q->p22 * sav;
c = cos(lamt);
if (fabs(c) < TOL)
lamt -= TOL;
xlam = (P->one_es * tanphi * Q->sa + sin(lamt) * Q->ca) / c;
lamdp = atan(xlam) + fac;
if (fabs(fabs(sav) - fabs(lamdp)) < TOL)
break;
sav = lamdp;
}
if (!l || ++nn >= 3 || (lamdp > Q->rlm && lamdp < Q->rlm2))
break;
if (lamdp <= Q->rlm)
lampp = M_TWOPI_HALFPI;
else if (lamdp >= Q->rlm2)
lampp = M_HALFPI;
}
if (l) {
sp = sin(lp.phi);
phidp = aasin(P->ctx,(P->one_es * Q->ca * sp - Q->sa * cos(lp.phi) *
sin(lamt)) / sqrt(1. - P->es * sp * sp));
tanph = log(tan(M_FORTPI + .5 * phidp));
sd = sin(lamdp);
sdsq = sd * sd;
s = Q->p22 * Q->sa * cos(lamdp) * sqrt((1. + Q->t * sdsq)
/ ((1. + Q->w * sdsq) * (1. + Q->q * sdsq)));
d = sqrt(Q->xj * Q->xj + s * s);
xy.x = Q->b * lamdp + Q->a2 * sin(2. * lamdp) + Q->a4 *
sin(lamdp * 4.) - tanph * s / d;
xy.y = Q->c1 * sd + Q->c3 * sin(lamdp * 3.) + tanph * Q->xj / d;
} else
xy.x = xy.y = HUGE_VAL;
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
int nn;
double lamt, sdsq, s, lamdp, phidp, sppsq, dd, sd, sl, fac, scl, sav, spp;
lamdp = xy.x / Q->b;
nn = 50;
do {
sav = lamdp;
sd = sin(lamdp);
sdsq = sd * sd;
s = Q->p22 * Q->sa * cos(lamdp) * sqrt((1. + Q->t * sdsq)
/ ((1. + Q->w * sdsq) * (1. + Q->q * sdsq)));
lamdp = xy.x + xy.y * s / Q->xj - Q->a2 * sin(
2. * lamdp) - Q->a4 * sin(lamdp * 4.) - s / Q->xj * (
Q->c1 * sin(lamdp) + Q->c3 * sin(lamdp * 3.));
lamdp /= Q->b;
} while (fabs(lamdp - sav) >= TOL && --nn);
sl = sin(lamdp);
fac = exp(sqrt(1. + s * s / Q->xj / Q->xj) * (xy.y -
Q->c1 * sl - Q->c3 * sin(lamdp * 3.)));
phidp = 2. * (atan(fac) - M_FORTPI);
dd = sl * sl;
if (fabs(cos(lamdp)) < TOL)
lamdp -= TOL;
spp = sin(phidp);
sppsq = spp * spp;
lamt = atan(((1. - sppsq * P->rone_es) * tan(lamdp) *
Q->ca - spp * Q->sa * sqrt((1. + Q->q * dd) * (
1. - sppsq) - sppsq * Q->u) / cos(lamdp)) / (1. - sppsq
* (1. + Q->u)));
sl = lamt >= 0. ? 1. : -1.;
scl = cos(lamdp) >= 0. ? 1. : -1;
lamt -= M_HALFPI * (1. - scl) * sl;
lp.lam = lamt - Q->p22 * lamdp;
if (fabs(Q->sa) < TOL)
lp.phi = aasin(P->ctx,spp / sqrt(P->one_es * P->one_es + P->es * sppsq));
else
lp.phi = atan((tan(lamdp) * cos(lamt) - Q->ca * sin(lamt)) /
(P->one_es * Q->sa));
return lp;
}
PJ *PROJECTION(lsat) {
int land, path;
double lam, alf, esc, ess;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor(P, ENOMEM);
P->opaque = Q;
land = pj_param(P->ctx, P->params, "ilsat").i;
if (land <= 0 || land > 5)
return pj_default_destructor(P, PJD_ERR_LSAT_NOT_IN_RANGE);
path = pj_param(P->ctx, P->params, "ipath").i;
if (path <= 0 || path > (land <= 3 ? 251 : 233))
return pj_default_destructor(P, PJD_ERR_PATH_NOT_IN_RANGE);
if (land <= 3) {
P->lam0 = DEG_TO_RAD * 128.87 - M_TWOPI / 251. * path;
Q->p22 = 103.2669323;
alf = DEG_TO_RAD * 99.092;
} else {
P->lam0 = DEG_TO_RAD * 129.3 - M_TWOPI / 233. * path;
Q->p22 = 98.8841202;
alf = DEG_TO_RAD * 98.2;
}
Q->p22 /= 1440.;
Q->sa = sin(alf);
Q->ca = cos(alf);
if (fabs(Q->ca) < 1e-9)
Q->ca = 1e-9;
esc = P->es * Q->ca * Q->ca;
ess = P->es * Q->sa * Q->sa;
Q->w = (1. - esc) * P->rone_es;
Q->w = Q->w * Q->w - 1.;
Q->q = ess * P->rone_es;
Q->t = ess * (2. - P->es) * P->rone_es * P->rone_es;
Q->u = esc * P->rone_es;
Q->xj = P->one_es * P->one_es * P->one_es;
Q->rlm = M_PI * (1. / 248. + .5161290322580645);
Q->rlm2 = Q->rlm + M_TWOPI;
Q->a2 = Q->a4 = Q->b = Q->c1 = Q->c3 = 0.;
seraz0(0., 1., P);
for (lam = 9.; lam <= 81.0001; lam += 18.)
seraz0(lam, 4., P);
for (lam = 18; lam <= 72.0001; lam += 18.)
seraz0(lam, 2., P);
seraz0(90., 1., P);
Q->a2 /= 30.;
Q->a4 /= 60.;
Q->b /= 30.;
Q->c1 /= 15.;
Q->c3 /= 45.;
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}
|
