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/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2003, 2006 Gerald I. Evenden
*/
static const char
LIBPROJ_ID[] = "Id";
/*
** 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.
*/
#define PROJ_PARMS__ \
double esp; \
double ml0; \
void *en;
#define PROJ_LIB__
#include <lib_proj.h>
PROJ_HEAD(tmerc, "Transverse Mercator") "\n\tCyl, Sph&Ell";
PROJ_HEAD(utm, "Universal Transverse Mercator (UTM)")
"\n\tCyl, Sph\n\tzone= south";
#define EPS10 1.e-10
#define aks0 P->esp
#define aks5 P->ml0
#define FC1 1.
#define FC2 .5
#define FC3 .16666666666666666666
#define FC4 .08333333333333333333
#define FC5 .05
#define FC6 .03333333333333333333
#define FC7 .02380952380952380952
#define FC8 .01785714285714285714
FORWARD(e_forward); /* ellipse */
double al, als, n, cosphi, sinphi, t;
sinphi = sin(lp.phi); cosphi = cos(lp.phi);
t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
t *= t;
al = cosphi * lp.lam;
als = al * al;
al /= sqrt(1. - P->es * sinphi * sinphi);
n = P->esp * cosphi * cosphi;
xy.x = P->k0 * al * (FC1 +
FC3 * als * (1. - t + n +
FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t +
n * (13. - 64. * t + n * (4. - 24 * t)))
+ FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
)));
xy.y = P->k0 * (proj_mdist(lp.phi, sinphi, cosphi, P->en) - P->ml0 +
sinphi * al * lp.lam * FC2 * ( 1. +
FC4 * als * (5. - t + n * (9. + 4. * n) +
FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t +
n * (445. - 680. * t + n * (324. - 600. * t + n * (88. - 192. * t))))
+ FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
))));
return (xy);
}
FORWARD(s_forward); /* sphere */
double b, cosphi;
b = (cosphi = cos(lp.phi)) * sin(lp.lam);
if (fabs(fabs(b) - 1.) <= EPS10) F_ERROR;
xy.x = aks5 * log((1. + b) / (1. - b));
if ((b = fabs( xy.y = cosphi * cos(lp.lam) / sqrt(1. - b * b) )) >= 1.) {
if ((b - 1.) > EPS10) F_ERROR
else xy.y = 0.;
} else
xy.y = acos(xy.y);
if (lp.phi < 0.) xy.y = -xy.y;
xy.y = aks0 * (xy.y - P->phi0);
return (xy);
}
INVERSE(e_inverse); /* ellipsoid */
double n, con, cosphi, d, ds, sinphi, t;
lp.phi = proj_inv_mdist(P->ml0 + xy.y / P->k0, P->en);
if (fabs(lp.phi) >= HALFPI) {
lp.phi = xy.y < 0. ? -HALFPI : HALFPI;
lp.lam = 0.;
} else {
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
n = P->esp * cosphi * cosphi;
d = xy.x * sqrt(con = 1. - P->es * sinphi * sinphi) / P->k0;
con *= t;
t *= t;
ds = d * d;
lp.phi -= (con * ds / (1.-P->es)) * FC2 * (1. -
ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -
ds * FC6*(61. + t*(90. - n*(252. + 90.*t) +
45.*t) + n*(46. + n*(-3. + t*(-66. + 225.*t) +
n*(100. + 84.*t + n*(88. - 192.*t))))
- ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
)));
lp.lam = d*(FC1 -
ds*FC3*( 1. + 2.*t + n -
ds*FC5*(5. + t*(28. + 8.*n + 24.*t) + n * (6. + n*(- 3. +
4.*t + n*(-4. + 24.*t)))
- ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
))) / cosphi;
}
return (lp);
}
INVERSE(s_inverse); /* sphere */
double D = xy.y / aks0 + P->phi0, xp = xy.x / aks0;
lp.phi = asin(sin(D) / cosh(xp));
lp.lam = atan2(sinh(xp), cos(D));
return (lp);
}
FREEUP;
if (P) {
if (P->en)
free(P->en);
free(P);
}
}
static PROJ *
setup(PROJ *P) { /* general initialization */
if (P->es) {
if (!((P->en = proj_mdist_ini(P->es))))
E_ERROR_0;
P->ml0 = proj_mdist(P->phi0, sin(P->phi0), cos(P->phi0), P->en);
P->esp = P->es / (1. - P->es);
P->inv = e_inverse;
P->fwd = e_forward;
} else {
aks0 = P->k0;
aks5 = .5 * aks0;
P->inv = s_inverse;
P->fwd = s_forward;
}
return P;
}
ENTRY1(tmerc, en)
ENDENTRY(setup(P))
ENTRY1(utm, en)
int zone;
if (!P->es) E_ERROR(-34);
P->y0 = proj_param(P->params, "bsouth").i ? 10000000. : 0.;
P->x0 = 500000.;
if (proj_param(P->params, "tzone").i) /* zone input ? */
if ((zone = proj_param(P->params, "izone").i) > 0 && zone <= 60)
--zone;
else
E_ERROR(-35)
else /* nearest central meridian input */
if (((zone = (int)floor((proj_adjlon(P->lam0) + PI) * 30. / PI))) < 0)
zone = 0;
else if (zone >= 60)
zone = 59;
P->lam0 = (zone + .5) * PI / 30. - PI;
P->k0 = 0.9996;
P->phi0 = 0.;
ENDENTRY(setup(P))
/*
** Log: proj_tmerc.c
** Revision 3.2 2008/06/28 15:10:58 gie
** Corrected error in inverse.
** Updated precision to comply with USC&GS Sp. Pub. #251 and
** DMA publication DMATM 8358.2.
** Effects of both error correction and precision update are
** only noticeable in the mm range.
**
** Revision 3.1 2006/01/11 01:38:18 gie
** Initial
**
*/
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