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/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2003, 2006 Gerald I. Evenden
*/
static const char
LIBPROJ_ID[] = "Id";
/*
** 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.
*/
#define N_TOL 1e-6
#define PROJ_LIB__
#ifdef PROJ_HAVE_GSL
#include <gsl/gsl_integration.h>
#define GSL_WORK 1000
#define PROJ_PARMS__ \
double n[2]; \
gsl_function func; \
gsl_integration_workspace *work; \
int mode;
#include <lib_proj.h>
double
mayr_kernel(double x, void * n) {
return (pow(cos(x), *(double*)n));
}
#else
#define PROJ_PARMS__ \
int mode;
#include <lib_proj.h>
#endif
PROJ_HEAD(mayr, "Mayr (Tobler Meridian Geometric Mean)") "\n\tPCyl., Sph., NoInv.";
/* definition of segment bounds for <1e-7 error (unit sphere) */
#define SEG1 1.4
#define SEG2 1.55
#define SEG3 1.57
#define BASE1 1.151132004484049
#define BASE2 1.196140916241303
#define BASE3 1.19812525384759
#define HALFN 4
/* Gauss Legendre weights/abscissa */
double X[] = {
0.96028985649753618,
0.79666647741362673,
0.52553240991632899,
0.18343464249564981 };
double W[] = {
0.10122853629037638,
0.22238103445337443,
0.31370664587788744,
0.36268378337836199 };
/* Mayr kernel */
#define func(v) sqrt(cos(v))
static
double gauss_legendre(double x0, double x1) {
int i = 0;
double s = 0., *x = X, *w = W, xsize, xmean, arg;
xmean = 0.5 * (x1 + x0);
xsize = 0.5 * (x1 - x0);
while ( i++ < HALFN ) {
arg = xsize * *x++;
s += *w++ * (func(xmean - arg) + func(xmean + arg));
};
return xsize * s;
}
static
double integrate(double val) {
double out;
if (val <= SEG1)
out = gauss_legendre(0., val);
else if (val <= SEG2)
out = BASE1 + gauss_legendre(SEG1, val);
else if (val <= SEG3)
out = BASE2 + gauss_legendre(SEG2, val);
else
out = BASE3 + gauss_legendre(SEG3, val);
return out;
}
FORWARD(s_forward); /* spheroid */
(void) P; /* avoid warning */
xy.x = lp.lam * func(lp.phi);
xy.y = integrate(fabs(lp.phi));
if (lp.phi < 0.)
xy.y = -xy.y;
return (xy);
}
#ifdef PROJ_HAVE_GSL
FORWARD(s_forwardg); /* numerical integration n <> 0.5 */
double error;
gsl_integration_qags(&P->func, 0., fabs(lp.phi), 1e-7, 1e-8, GSL_WORK,
P->work, &xy.y, &error);
xy.x = lp.lam * pow(cos(lp.phi), P->n[1]);
if (lp.phi < 0.)
xy.y = -xy.y;
return (xy);
}
#endif
FREEUP;
if (P) {
#if PROJ_HAVE_GSL
if (P->mode)
gsl_integration_workspace_free(P->work);
#endif
free(P);
}
}
ENTRY0(mayr)
P->es = 0;
if (proj_param(P->params, "tn").i) {
#if PROJ_HAVE_GSL
P->n[0] = proj_param(P->params, "dn").f;
if ((P->n[0] < N_TOL) || (P->n[0] > 1.-N_TOL))
E_ERROR(-40)
P->fwd = s_forwardg;
P->n[1] = 1. - P->n[0];
P->func.function = &mayr_kernel;
P->func.params = P->n;
P->work = gsl_integration_workspace_alloc (GSL_WORK);
P->mode = 1;
#else
E_ERROR(-47)
#endif
} else {
P->mode = 0;
P->fwd = s_forward;
}
ENDENTRY(P)
/*
** Log: proj_mayr.c
** Revision 3.2 2006/01/19 01:52:59 gie
** correct some casting ^)*^&^
**
** Revision 3.1 2006/01/11 01:38:18 gie
** Initial
**
*/
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