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 PJ_LIB__ #include <errno.h> #include "proj.h" #include "projects.h" #include "proj_math.h" struct pj_opaque { 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. */ }; PROJ_HEAD(etmerc, "Extended Transverse Mercator") "\n\tCyl, Sph\n\tlat_ts=(0)\nlat_0=(0)"; PROJ_HEAD(utm, "Universal Transverse Mercator (UTM)") "\n\tCyl, Sph\n\tzone= south"; #define PROJ_ETMERC_ORDER 6 #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); p = p1 + len_p1; h1 = *--p; while (p - p1) { h = -h2 + cos_2B*h1 + *--p; h2 = h1; h1 = h; } return (B + h*sin(2*B)); } /* Complex Clenshaw summation */ #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 */ hi1 = hr1 = hi = 0; hr = *--p; for (; 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; } /* Real Clenshaw summation */ 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 */ hr1 = 0; hr = *--p; for (; a - p;) { hr2 = hr1; hr1 = hr; hr = -hr2 + r*hr1 + *--p; } return sin (arg_r)*hr; } static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */ XY xy = {0.0,0.0}; struct pj_opaque *Q = P->opaque; 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 (Q->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 = asinh ( tan (Ce) ); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */ Cn += clenS (Q->gtu, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe); Ce += dCe; if (fabs (Ce) <= 2.623395162778) { xy.y = Q->Qn * Cn + Q->Zb; /* Northing */ xy.x = Q->Qn * Ce; /* Easting */ } else xy.x = xy.y = HUGE_VAL; return xy; } static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */ LP lp = {0.0,0.0}; struct pj_opaque *Q = P->opaque; double sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe; double Cn = xy.y, Ce = xy.x; /* normalize N, E */ Cn = (Cn - Q->Zb)/Q->Qn; Ce = Ce/Q->Qn; if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */ /* norm. N, E -> compl. sph. LAT, LNG */ Cn += clenS(Q->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 (Q->cgb, PROJ_ETMERC_ORDER, Cn); lp.lam = Ce; } else lp.phi = lp.lam = HUGE_VAL; return lp; } static PJ *setup(PJ *P) { /* general initialization */ double f, n, np, Z; struct pj_opaque *Q = P->opaque; if (P->es <= 0) { return pj_default_destructor(P, PJD_ERR_ELLIPSOID_USE_REQUIRED); } /* flattening */ 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 */ Q->cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 + n*(-2854/675.0 )))))); Q->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; Q->cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 + n*( 2323/945.0))))); Q->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 */ Q->cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 + n*( 73814/2835.0)))); Q->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 */ Q->cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0))); Q->cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0))); np *= n; Q->cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 )); Q->cbg[4] = np*(-734/315.0 + n*( 109598/31185.0)); np *= n; Q->cgb[5] = np*(601676/22275.0 ); Q->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) */ Q->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) */ Q->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)))))); Q->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 )))))); Q->utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 + n*( 1118711/3870720.0))))); Q->gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 + n*(-1983433/1935360.0))))); np *= n; Q->utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 + n*( -5569/90720.0 )))); Q->gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 + n*(167603/181440.0)))); np *= n; Q->utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0))); Q->gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0))); np *= n; Q->utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0)); Q->gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0)); np *= n; Q->utg[5] = np*(-20648693/638668800.0); Q->gtu[5] = np*(212378941/319334400.0); /* Gaussian latitude value of the origin latitude */ Z = gatg (Q->cbg, PROJ_ETMERC_ORDER, P->phi0); /* Origin northing minus true northing at the origin latitude */ /* i.e. true northing = N - P->Zb */ Q->Zb = - Q->Qn*(Z + clens(Q->gtu, PROJ_ETMERC_ORDER, 2*Z)); P->inv = e_inverse; P->fwd = e_forward; return P; } PJ *PROJECTION(etmerc) { struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque)); if (0==Q) return pj_default_destructor (P, ENOMEM); P->opaque = Q; return setup (P); } /* utm uses etmerc for the underlying projection */ PJ *PROJECTION(utm) { long zone; struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque)); if (0==Q) return pj_default_destructor (P, ENOMEM); P->opaque = Q; if (P->es == 0.0) { proj_errno_set(P, PJD_ERR_ELLIPSOID_USE_REQUIRED); return pj_default_destructor(P, ENOMEM); } if (P->lam0 < -1000.0 || P->lam0 > 1000.0) { return pj_default_destructor(P, PJD_ERR_INVALID_UTM_ZONE); } P->y0 = pj_param (P->ctx, P->params, "bsouth").i ? 10000000. : 0.; P->x0 = 500000.; if (pj_param (P->ctx, P->params, "tzone").i) /* zone input ? */ { zone = pj_param(P->ctx, P->params, "izone").i; if (zone > 0 && zone <= 60) --zone; else { return pj_default_destructor(P, PJD_ERR_INVALID_UTM_ZONE); } } else /* nearest central meridian input */ { zone = lround((floor ((adjlon (P->lam0) + M_PI) * 30. / M_PI))); if (zone < 0) zone = 0; else if (zone >= 60) zone = 59; } P->lam0 = (zone + .5) * M_PI / 30. - M_PI; P->k0 = 0.9996; P->phi0 = 0.; return setup (P); }