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/******************************************************************************
* This implements Space Oblique Mercator (SOM) projection, used by the
* Multi-angle Imaging SpectroRadiometer (MISR) products, from the NASA EOS Terra
* platform.
*
* The code is identical to that of Landsat SOM (PJ_lsat.c) with the following
* parameter changes:
*
* inclination angle = 98.30382 degrees
* period of revolution = 98.88 minutes
* ascending longitude = 129.3056 degrees - (360 / 233) * path_number
*
* and the following code change:
*
* Q->rlm = PI * (1. / 248. + .5161290322580645);
*
* changed to:
*
* Q->rlm = 0
*
*****************************************************************************/
/* based upon Snyder and Linck, USGS-NMD */
#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
PROJ_HEAD(misrsom, "Space oblique for MISR")
"\n\tCyl, Sph&Ell\n\tpath=";
#define TOL 1e-7
namespace { // anonymous namespace
struct pj_opaque {
double a2, a4, b, c1, c3;
double q, t, u, w, p22, sa, ca, xj, rlm, rlm2;
};
} // anonymous namespace
static void seraz0(double lam, double mult, PJ *P) {
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double sdsq, h, s, fc, sd, sq, d__1;
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 PJ_XY misrsom_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(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; --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 PJ_LP misrsom_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(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;
const double denom = 1. - sppsq * (1. + Q->u);
if( denom == 0.0 ) {
proj_errno_set(P, PJD_ERR_NON_CONVERGENT);
return proj_coord_error().lp;
}
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)) / denom);
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(misrsom) {
int path;
double lam, alf, esc, ess;
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
path = pj_param(P->ctx, P->params, "ipath").i;
if (path <= 0 || path > 233)
return pj_default_destructor(P, PJD_ERR_PATH_NOT_IN_RANGE);
P->lam0 = DEG_TO_RAD * 129.3056 - M_TWOPI / 233. * path;
alf = 98.30382 * DEG_TO_RAD;
Q->p22 = 98.88 / 1440.0;
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 = 0;
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 = misrsom_e_inverse;
P->fwd = misrsom_e_forward;
return P;
}
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