EVOLUTION-MANAGER

Edit File: proj_etmerc.c

/* ** 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[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__ #define PJ_LIB__ #include <projects.h> PROJ_HEAD(etmerc, "Extended Transverse Mercator") "\n\tCyl, Sph\n\tlat_ts=(0)\nlat_0=(0)"; #define FABS(x) ((x)<0?-(x):(x)) #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(2.0*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)); } #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; double exp_arg_i, pxe_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 exp_arg_i = exp( arg_i); pxe_arg_i = exp(-arg_i); sinh_arg_i = (exp_arg_i-pxe_arg_i)/2; cosh_arg_i = (exp_arg_i+pxe_arg_i)/2; 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, sin_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 */ #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 = log(tan(FORTPI + 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_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, 5, 2.*Cn, 2.*Ce, &dCn, &dCe); Ce += dCe; Ce = 2.0*(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, 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)