added extended transverse mercator implementation (#97)

git-svn-id: http://svn.osgeo.org/metacrs/proj/trunk@1976 4e78687f-474d-0410-85f9-8d5e500ac6b2

2 files changed, 253 insertions, 0 deletions

diff --git a/src/pj_list.h b/src/pj_list.h
index b965cc71..1e8df686 100644
--- a/src/pj_list.h
+++ b/src/pj_list.h
@@ -32,6 +32,7 @@ PROJ_HEAD(eck6, "Eckert VI")
 PROJ_HEAD(eqc, "Equidistant Cylindrical (Plate Caree)")
 PROJ_HEAD(eqdc, "Equidistant Conic")
 PROJ_HEAD(euler, "Euler")
+PROJ_HEAD(etmerc, "Extended Transverse Mercator" )
 PROJ_HEAD(fahey, "Fahey")
 PROJ_HEAD(fouc, "Foucaut")
 PROJ_HEAD(fouc_s, "Foucaut Sinusoidal")
diff --git a/src/proj_etmerc.c b/src/proj_etmerc.c
new file mode 100644
index 00000000..4b42f23a
--- /dev/null
+++ b/src/proj_etmerc.c
@@ -0,0 +1,252 @@
+/*
+** 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(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_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)) - M_PI_4);
+		/* 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)