PJ_lsat.c
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/* based upon Snyder and Linck, USGS-NMD */
#define PROJ_PARMS__ \
double a2, a4, b, c1, c3; \
double q, t, u, w, p22, sa, ca, xj, rlm, rlm2;
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(lsat, "Space oblique for LANDSAT")
"\n\tCyl, Sph&Ell\n\tlsat= path=";
#define TOL 1e-7
#define PI_HALFPI 4.71238898038468985766
#define TWOPI_HALFPI 7.85398163397448309610
static void
seraz0(double lam, double mult, PJ *P) {
double sdsq, h, s, fc, sd, sq, d__1;
lam *= DEG_TO_RAD;
sd = sin(lam);
sdsq = sd * sd;
s = P->p22 * P->sa * cos(lam) * sqrt((1. + P->t * sdsq) / ((
1. + P->w * sdsq) * (1. + P->q * sdsq)));
d__1 = 1. + P->q * sdsq;
h = sqrt((1. + P->q * sdsq) / (1. + P->w * sdsq)) * ((1. +
P->w * sdsq) / (d__1 * d__1) - P->p22 * P->ca);
sq = sqrt(P->xj * P->xj + s * s);
P->b += fc = mult * (h * P->xj - s * s) / sq;
P->a2 += fc * cos(lam + lam);
P->a4 += fc * cos(lam * 4.);
fc = mult * s * (h + P->xj) / sq;
P->c1 += fc * cos(lam);
P->c3 += fc * cos(lam * 3.);
}
FORWARD(e_forward); /* ellipsoid */
int l, nn;
double lamt, xlam, sdsq, c, d, s, lamdp, phidp, lampp, tanph,
lamtp, cl, sd, sp, fac, sav, tanphi;
if (lp.phi > HALFPI)
lp.phi = HALFPI;
else if (lp.phi < -HALFPI)
lp.phi = -HALFPI;
lampp = lp.phi >= 0. ? HALFPI : PI_HALFPI;
tanphi = tan(lp.phi);
for (nn = 0;;) {
sav = lampp;
lamtp = lp.lam + P->p22 * lampp;
cl = cos(lamtp);
if (fabs(cl) < TOL)
lamtp -= TOL;
fac = lampp - sin(lampp) * (cl < 0. ? -HALFPI : HALFPI);
for (l = 50; l; --l) {
lamt = lp.lam + P->p22 * sav;
if (fabs(c = cos(lamt)) < TOL)
lamt -= TOL;
xlam = (P->one_es * tanphi * P->sa + sin(lamt) * P->ca) / c;
lamdp = atan(xlam) + fac;
if (fabs(fabs(sav) - fabs(lamdp)) < TOL)
break;
sav = lamdp;
}
if (!l || ++nn >= 3 || (lamdp > P->rlm && lamdp < P->rlm2))
break;
if (lamdp <= P->rlm)
lampp = TWOPI_HALFPI;
else if (lamdp >= P->rlm2)
lampp = HALFPI;
}
if (l) {
sp = sin(lp.phi);
phidp = aasin((P->one_es * P->ca * sp - P->sa * cos(lp.phi) *
sin(lamt)) / sqrt(1. - P->es * sp * sp));
tanph = log(tan(FORTPI + .5 * phidp));
sd = sin(lamdp);
sdsq = sd * sd;
s = P->p22 * P->sa * cos(lamdp) * sqrt((1. + P->t * sdsq)
/ ((1. + P->w * sdsq) * (1. + P->q * sdsq)));
d = sqrt(P->xj * P->xj + s * s);
xy.x = P->b * lamdp + P->a2 * sin(2. * lamdp) + P->a4 *
sin(lamdp * 4.) - tanph * s / d;
xy.y = P->c1 * sd + P->c3 * sin(lamdp * 3.) + tanph * P->xj / d;
} else
xy.x = xy.y = HUGE_VAL;
return xy;
}
INVERSE(e_inverse); /* ellipsoid */
int nn;
double lamt, sdsq, s, lamdp, phidp, sppsq, dd, sd, sl, fac, scl, sav, spp;
lamdp = xy.x / P->b;
nn = 50;
do {
sav = lamdp;
sd = sin(lamdp);
sdsq = sd * sd;
s = P->p22 * P->sa * cos(lamdp) * sqrt((1. + P->t * sdsq)
/ ((1. + P->w * sdsq) * (1. + P->q * sdsq)));
lamdp = xy.x + xy.y * s / P->xj - P->a2 * sin(
2. * lamdp) - P->a4 * sin(lamdp * 4.) - s / P->xj * (
P->c1 * sin(lamdp) + P->c3 * sin(lamdp * 3.));
lamdp /= P->b;
} while (fabs(lamdp - sav) >= TOL && --nn);
sl = sin(lamdp);
fac = exp(sqrt(1. + s * s / P->xj / P->xj) * (xy.y -
P->c1 * sl - P->c3 * sin(lamdp * 3.)));
phidp = 2. * (atan(fac) - 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) *
P->ca - spp * P->sa * sqrt((1. + P->q * dd) * (
1. - sppsq) - sppsq * P->u) / cos(lamdp)) / (1. - sppsq
* (1. + P->u)));
sl = lamt >= 0. ? 1. : -1.;
scl = cos(lamdp) >= 0. ? 1. : -1;
lamt -= HALFPI * (1. - scl) * sl;
lp.lam = lamt - P->p22 * lamdp;
if (fabs(P->sa) < TOL)
lp.phi = aasin(spp / sqrt(P->one_es * P->one_es + P->es * sppsq));
else
lp.phi = atan((tan(lamdp) * cos(lamt) - P->ca * sin(lamt)) /
(P->one_es * P->sa));
return lp;
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(lsat)
int land, path;
double lam, alf, esc, ess;
land = pj_param(P->params, "ilsat").i;
if (land <= 0 || land > 5) E_ERROR(-28);
path = pj_param(P->params, "ipath").i;
if (path <= 0 || path > (land <= 3 ? 251 : 233)) E_ERROR(-29);
if (land <= 3) {
P->lam0 = DEG_TO_RAD * 128.87 - TWOPI / 251. * path;
P->p22 = 103.2669323;
alf = DEG_TO_RAD * 99.092;
} else {
P->lam0 = DEG_TO_RAD * 129.3 - TWOPI / 233. * path;
P->p22 = 98.8841202;
alf = DEG_TO_RAD * 98.2;
}
P->p22 /= 1440.;
P->sa = sin(alf);
P->ca = cos(alf);
if (fabs(P->ca) < 1e-9)
P->ca = 1e-9;
esc = P->es * P->ca * P->ca;
ess = P->es * P->sa * P->sa;
P->w = (1. - esc) * P->rone_es;
P->w = P->w * P->w - 1.;
P->q = ess * P->rone_es;
P->t = ess * (2. - P->es) * P->rone_es * P->rone_es;
P->u = esc * P->rone_es;
P->xj = P->one_es * P->one_es * P->one_es;
P->rlm = PI * (1. / 248. + .5161290322580645);
P->rlm2 = P->rlm + TWOPI;
P->a2 = P->a4 = P->b = P->c1 = P->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);
P->a2 /= 30.;
P->a4 /= 60.;
P->b /= 30.;
P->c1 /= 15.;
P->c3 /= 45.;
P->inv = e_inverse; P->fwd = e_forward;
ENDENTRY(P)