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/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2008 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.
*/
/* The code in this file is largly based upon procedures:
*
* Written by: Knud Poder and Karsten Engsager
*
* Base upon math from: R.Koenig and K.H. Weise, "Mathematische
* Grundlagen der hoeheren Geodaesie und Kartographie,
* Springer-Verlag, Berlin/Goettingen" Heidelberg, 1951.
*
* Modified and used here by permission of Reference Networks
* Division, Kort og Matrikelstyrelsen (KMS), Copenhagen, Denmark
*/
#define PROJ_PARMS__ \
double Qn; /* Merid. quad., scaled to the projection */ \
double Zb; /* Radius vector in polar coord. systems */ \
double cgb[5]; /* Constants for Gauss -> Geo lat */ \
double cbg[5]; /* Constants for Geo lat -> Gauss */ \
double utg[5]; /* Constants for transv. merc. -> geo */ \
double gtu[5]; /* Constants for geo -> transv. merc. */
#define PROJ_LIB__
# include <lib_proj.h>
#ifndef M_PI
# define M_PI 3.14159265358979323846
#endif /* M_PI */
#ifndef M_PI_4
# define M_PI_4 ( M_PI / 4. )
#endif /* M_PI_4 */
PROJ_HEAD(etmerc, "Extended Transverse Mercator")
"\n\tCyl, Ellips\n\tlat_ts=(0)\nlat_0=(0)";
static double
gatg(double *p1, int len_p1, double B) {
double *p;
double h = 0., h1, h2 = 0., cos_2B;
cos_2B = 2.*cos(2.0*B);
for (p = p1 + len_p1, h1 = *--p; p - p1; h2 = h1, h1 = h)
h = -h2 + cos_2B*h1 + *--p;
return (B + h*sin(2.0*B));
}
static double
clenS(double *a, int size, double arg_r, double arg_i, double *R, double *I) {
double *p, r, i, hr, hr1, hr2, hi, hi1, hi2;
double sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i;
/* arguments */
p = a + size;
sin_arg_r = sin(arg_r);
cos_arg_r = cos(arg_r);
sinh_arg_i = sinh(arg_i);
cosh_arg_i = cosh(arg_i);
r = 2.0*cos_arg_r*cosh_arg_i;
i = -2.0*sin_arg_r*sinh_arg_i;
/* summation loop */
for (hi1 = hr1 = hi = 0.0, hr = *--p; a - p;) {
hr2 = hr1;
hi2 = hi1;
hr1 = hr;
hi1 = hi;
hr = -hr2 + r*hr1 - i*hi1 + *--p;
hi = -hi2 + i*hr1 + r*hi1;
}
r = sin_arg_r*cosh_arg_i;
i = cos_arg_r*sinh_arg_i;
*R = r*hr - i*hi;
*I = r*hi + i*hr;
return(*R);
}
static double
clens(double *a, int size, double arg_r) {
double *p, r, hr, hr1, hr2, cos_arg_r;
p = a + size;
cos_arg_r = cos(arg_r);
r = 2.0*cos_arg_r;
/* summation loop */
for (hr1 = 0.0, hr = *--p; a - p;) {
hr2 = hr1;
hr1 = hr;
hr = -hr2 + r*hr1 + *--p;
}
return(sin(arg_r)*hr);
}
FORWARD(e_forward); /* ellipsoid */
double sin_Cn, cos_Cn, cos_Ce, dCn, dCe;
double Cn = lp.phi, Ce = lp.lam;
/* ell. LAT, LNG -> Gaussian LAT, LNG */
Cn = gatg(P->cbg, 5, Cn);
/* Gaussian LAT, LNG -> compl. sph. LAT */
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
cos_Ce = cos(Ce);
Cn = atan2(sin_Cn, cos_Ce*cos_Cn);
Ce = atan2(sin(Ce)*cos_Cn, hypot(sin_Cn, cos_Cn*cos_Ce));
/* compl. sph. N, E -> ell. norm. N, E */
Ce = log(tan(M_PI_4 + Ce*0.5));
Cn += clenS(P->gtu, 5, 2.*Cn, 2.*Ce, &dCn, &dCe);
Ce += dCe;
if (fabs(Ce) <= 2.623395162778) {
xy.y = P->Qn * Cn + P->Zb; /* Northing */
xy.x = P->Qn * Ce; /* Easting */
} else
xy.x = xy.y = HUGE_VAL;
return (xy);
}
INVERSE(e_inverse); /* ellipsoid */
double sin_Ce, cos_Ce, cos_Cn, dCn, dCe;
double Cn = xy.y, Ce = xy.x;
/* normalize N, E */
Cn = (Cn - P->Zb)/P->Qn;
Ce = Ce/P->Qn;
if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */
/* norm. N, E -> compl. sph. LAT, LNG */
Cn += clenS(P->utg, 5, 2.*Cn, 2.*Ce, &dCn, &dCe);
Ce += dCe;
Ce = 2.0*(atan(exp(Ce)) - M_PI_4);
/* compl. sph. LAT -> Gaussian LAT, LNG */
cos_Cn = cos(Cn);
sin_Ce = sin(Ce);
cos_Ce = cos(Ce);
Ce = atan2(sin_Ce, cos_Ce*cos_Cn);
Cn = atan2(sin(Cn)*cos_Ce, hypot(sin_Ce, cos_Ce*cos_Cn));
/* Gaussian LAT, LNG -> ell. LAT, LNG */
lp.phi = gatg(P->cgb, 5, Cn);
lp.lam = Ce;
}
else
lp.phi = lp.lam = HUGE_VAL;
return (lp);
}
FREEUP; if (P) free(P); }
ENTRY0(etmerc)
double f, n, np, Z;
if (P->es <= 0.) E_ERROR(-34);
f = 1. - sqrt(1. - P->es);
/* third flattening */
np = n = f/(2.0 - f);
/* COEF. OF TRIG SERIES GEO <-> GAUSS */
/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
/* 5 degree : Engsager and Poder: ICC2007 */
P->cgb[0] = n*( 2.0 + n*(-2.0/3.0 + n*(-2.0 + n*(116.0/45.0 + n*(26.0/45.0)))));
P->cbg[0] = n*(-2.0 + n*( 2.0/3.0 + n*( 4.0/3.0 + n*(-82.0/45.0 + n*(32.0/45.0)))));
np *= n;
P->cgb[1] = np*(7.0/3.0 + n*( -8.0/5.0 + n*(-227.0/45.0 + n*(2704.0/315.0))));
P->cbg[1] = np*(5.0/3.0 + n*(-16.0/15.0 + n*( -13.0/ 9.0 + n*( 904.0/315.0))));
np *= n;
P->cgb[2] = np*( 56.0/15.0 + n*(-136.0/35.0 + n*(1262.0/105.0)));
P->cbg[2] = np*(-26.0/15.0 + n*( 34.0/21.0 + n*( 8.0/ 5.0)));
np *= n;
P->cgb[3] = np*(4279.0/630.0 + n*(-322.0/35.0));
P->cbg[3] = np*(1237.0/630.0 + n*( -12.0/ 5.0));
np *= n;
P->cgb[4] = np*(4174.0/315.0);
P->cbg[4] = np*(-734.0/315.0);
/* Constants of the projections */
/* Transverse Mercator (UTM, ITM, etc) */
np = n*n;
/* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
P->Qn = P->k0/(1 + n) * (1. + np*(1./4.0 + np*(1./64.0 + np/256.0)));
/* coef of trig series */
/* utg := ell. N, E -> sph. N, E, KW p194 (65) */
/* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
P->utg[0] = n*(-0.5 + n*( 2.0/3.0 + n*(-37.0/96.0 + n*( 1.0/360.0 + n*( 81.0/512.0)))));
P->gtu[0] = n*( 0.5 + n*(-2.0/3.0 + n*( 5.0/16.0 + n*(41.0/180.0 + n*(-127.0/288.0)))));
P->utg[1] = np*(-1.0/48.0 + n*(-1.0/15.0 + n*(437.0/1440.0 + n*(-46.0/105.0))));
P->gtu[1] = np*(13.0/48.0 + n*(-3.0/5.0 + n*(557.0/1440.0 + n*(281.0/630.0))));
np *= n;
P->utg[2] = np*(-17.0/480.0 + n*( 37.0/840.0 + n*( 209.0/ 4480.0)));
P->gtu[2] = np*( 61.0/240.0 + n*(-103.0/140.0 + n*(15061.0/26880.0)));
np *= n;
P->utg[3] = np*(-4397.0/161280.0 + n*( 11.0/504.0));
P->gtu[3] = np*(49561.0/161280.0 + n*(-179.0/168.0));
np *= n;
P->utg[4] = np*(-4583.0/161280.0);
P->gtu[4] = np*(34729.0/ 80640.0);
/* Gaussian latitude value of the origin latitude */
Z = gatg(P->cbg, 5, P->phi0);
/* Origin northing minus true northing at the origin latitude */
/* i.e. true northing = N - P->Zb */
P->Zb = - P->Qn*(Z + clens(P->gtu, 5, 2.0*Z));
P->inv = e_inverse;
P->fwd = e_forward;
ENDENTRY(P)
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