/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2008 Gerald I. Evenden
*/
/*
** 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
*
* Based on 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[6]; /* Constants for Gauss -> Geo lat */ \
double cbg[6]; /* Constants for Geo lat -> Gauss */ \
double utg[6]; /* Constants for transv. merc. -> geo */ \
double gtu[6]; /* Constants for geo -> transv. merc. */
#define PROJ_LIB__
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(etmerc, "Extended Transverse Mercator")
"\n\tCyl, Sph\n\tlat_ts=(0)\nlat_0=(0)";
#define PROJ_ETMERC_ORDER 6
#ifdef _GNU_SOURCE
inline
#endif
static double
log1py(double x) { /* Compute log(1+x) accurately */
volatile double
y = 1 + x,
z = y - 1;
/* Here's the explanation for this magic: y = 1 + z, exactly, and z
* approx x, thus log(y)/z (which is nearly constant near z = 0) returns
* a good approximation to the true log(1 + x)/x. The multiplication x *
* (log(y)/z) introduces little additional error. */
return z == 0 ? x : x * log(y) / z;
}
#ifdef _GNU_SOURCE
inline
#endif
static double
asinhy(double x) { /* Compute asinh(x) accurately */
double y = fabs(x); /* Enforce odd parity */
y = log1py(y * (1 + y/(hypot(1.0, y) + 1)));
return x < 0 ? -y : y;
}
#ifdef _GNU_SOURCE
inline
#endif
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*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*B));
}
#ifdef _GNU_SOURCE
inline
#endif
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;
#ifdef _GNU_SOURCE
sincos(arg_r, &sin_arg_r, &cos_arg_r);
#else
sin_arg_r = sin(arg_r);
cos_arg_r = cos(arg_r);
#endif
sinh_arg_i = sinh(arg_i);
cosh_arg_i = cosh(arg_i);
r = 2*cos_arg_r*cosh_arg_i;
i = -2*sin_arg_r*sinh_arg_i;
/* summation loop */
for (hi1 = hr1 = hi = 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*cos_arg_r;
/* summation loop */
for (hr1 = 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, sin_Ce, dCn, dCe;
double Cn = lp.phi, Ce = lp.lam;
/* ell. LAT, LNG -> Gaussian LAT, LNG */
Cn = gatg(P->cbg, PROJ_ETMERC_ORDER, Cn);
/* Gaussian LAT, LNG -> compl. sph. LAT */
#ifdef _GNU_SOURCE
sincos(Cn, &sin_Cn, &cos_Cn);
sincos(Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
sin_Ce = sin(Ce);
cos_Ce = cos(Ce);
#endif
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 = asinhy(tan(Ce)); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
Cn += clenS(P->gtu, PROJ_ETMERC_ORDER, 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_Cn, cos_Cn, cos_Ce, sin_Ce, 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, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe);
Ce += dCe;
Ce = atan(sinh(Ce)); /* Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI); */
/* compl. sph. LAT -> Gaussian LAT, LNG */
#ifdef _GNU_SOURCE
sincos(Cn, &sin_Cn, &cos_Cn);
sincos(Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
sin_Ce = sin(Ce);
cos_Ce = cos(Ce);
#endif
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, PROJ_ETMERC_ORDER, 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 = P->es / (1 + sqrt(1 - P->es)); /* Replaces: f = 1 - sqrt(1-P->es); */
/* third flattening */
np = n = f/(2 - f);
/* COEF. OF TRIG SERIES GEO <-> GAUSS */
/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
/* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */
P->cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 +
n*(-2854/675.0 ))))));
P->cbg[0] = n*(-2 + n*( 2/3.0 + n*( 4/3.0 + n*(-82/45.0 + n*(32/45.0 +
n*( 4642/4725.0))))));
np *= n;
P->cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 +
n*( 2323/945.0)))));
P->cbg[1] = np*(5/3.0 + n*(-16/15.0 + n*( -13/9.0 + n*( 904/315.0 +
n*(-1522/945.0)))));
np *= n;
/* n^5 coeff corrected from 1262/105 -> -1262/105 */
P->cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 +
n*( 73814/2835.0))));
P->cbg[2] = np*(-26/15.0 + n*( 34/21.0 + n*( 8/5.0 +
n*(-12686/2835.0))));
np *= n;
/* n^5 coeff corrected from 322/35 -> 332/35 */
P->cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0)));
P->cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0)));
np *= n;
P->cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 ));
P->cbg[4] = np*(-734/315.0 + n*( 109598/31185.0));
np *= n;
P->cgb[5] = np*(601676/22275.0 );
P->cbg[5] = np*(444337/155925.0);
/* 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*( 2/3.0 + n*(-37/96.0 + n*( 1/360.0 +
n*( 81/512.0 + n*(-96199/604800.0))))));
P->gtu[0] = n*( 0.5 + n*(-2/3.0 + n*( 5/16.0 + n*(41/180.0 +
n*(-127/288.0 + n*( 7891/37800.0 ))))));
P->utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 +
n*( 1118711/3870720.0)))));
P->gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 +
n*(-1983433/1935360.0)))));
np *= n;
P->utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 +
n*( -5569/90720.0 ))));
P->gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 +
n*(167603/181440.0))));
np *= n;
P->utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0)));
P->gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0)));
np *= n;
P->utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0));
P->gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0));
np *= n;
P->utg[5] = np*(-20648693/638668800.0);
P->gtu[5] = np*(212378941/319334400.0);
/* Gaussian latitude value of the origin latitude */
Z = gatg(P->cbg, PROJ_ETMERC_ORDER, 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, PROJ_ETMERC_ORDER, 2*Z));
P->inv = e_inverse;
P->fwd = e_forward;
ENDENTRY(P)