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+/*
+** 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"
+
+
+namespace { // anonymous namespace
+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. */
+};
+} // anonymous namespace
+
+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 = static_cast<struct pj_opaque*>(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 = static_cast<struct pj_opaque*>(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 = static_cast<struct pj_opaque*>(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 = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+ if (nullptr==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 = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
+ if (nullptr==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);
+}
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