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/*
* Project: PROJ
* Purpose: Implementation of the krovak (Krovak) projection.
* Definition: http://www.ihsenergy.com/epsg/guid7.html#1.4.3
* Author: Thomas Flemming, tf@ttqv.com
*
******************************************************************************
* Copyright (c) 2001, Thomas Flemming, tf@ttqv.com
*
* 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.
******************************************************************************
* A description of the (forward) projection is found in:
*
* Bohuslav Veverka,
*
* KROVAK’S PROJECTION AND ITS USE FOR THE
* CZECH REPUBLIC AND THE SLOVAK REPUBLIC,
*
* 50 years of the Research Institute of
* and the Slovak Republic Geodesy, Topography and Cartography
*
* which can be found via the Wayback Machine:
*
* https://web.archive.org/web/20150216143806/https://www.vugtk.cz/odis/sborniky/sb2005/Sbornik_50_let_VUGTK/Part_1-Scientific_Contribution/16-Veverka.pdf
*
* Further info, including the inverse projection, is given by EPSG:
*
* Guidance Note 7 part 2
* Coordinate Conversions and Transformations including Formulas
*
* http://www.iogp.org/pubs/373-07-2.pdf
*
* Variable names in this file mostly follows what is used in the
* paper by Veverka.
*
* According to EPSG the full Krovak projection method should have
* the following parameters. Within PROJ the azimuth, and pseudo
* standard parallel are hardcoded in the algorithm and can't be
* altered from outside. The others all have defaults to match the
* common usage with Krovak projection.
*
* lat_0 = latitude of centre of the projection
*
* lon_0 = longitude of centre of the projection
*
* ** = azimuth (true) of the centre line passing through the
* centre of the projection
*
* ** = latitude of pseudo standard parallel
*
* k = scale factor on the pseudo standard parallel
*
* x_0 = False Easting of the centre of the projection at the
* apex of the cone
*
* y_0 = False Northing of the centre of the projection at
* the apex of the cone
*
*****************************************************************************/
#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "projects.h"
PROJ_HEAD(krovak, "Krovak") "\n\tPCyl, Ell";
#define EPS 1e-15
#define UQ 1.04216856380474 /* DU(2, 59, 42, 42.69689) */
#define S0 1.37008346281555 /* Latitude of pseudo standard parallel 78deg 30'00" N */
/* Not sure at all of the appropriate number for MAX_ITER... */
#define MAX_ITER 100
namespace { // anonymous namespace
struct pj_opaque {
double alpha;
double k;
double n;
double rho0;
double ad;
int czech;
};
} // anonymous namespace
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
XY xy = {0.0,0.0};
double gfi, u, deltav, s, d, eps, rho;
gfi = pow ( (1. + P->e * sin(lp.phi)) / (1. - P->e * sin(lp.phi)), Q->alpha * P->e / 2.);
u = 2. * (atan(Q->k * pow( tan(lp.phi / 2. + M_PI_4), Q->alpha) / gfi)-M_PI_4);
deltav = -lp.lam * Q->alpha;
s = asin(cos(Q->ad) * sin(u) + sin(Q->ad) * cos(u) * cos(deltav));
d = asin(cos(u) * sin(deltav) / cos(s));
eps = Q->n * d;
rho = Q->rho0 * pow(tan(S0 / 2. + M_PI_4) , Q->n) / pow(tan(s / 2. + M_PI_4) , Q->n);
xy.y = rho * cos(eps);
xy.x = rho * sin(eps);
xy.y *= Q->czech;
xy.x *= Q->czech;
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
LP lp = {0.0,0.0};
double u, deltav, s, d, eps, rho, fi1, xy0;
int i;
xy0 = xy.x;
xy.x = xy.y;
xy.y = xy0;
xy.x *= Q->czech;
xy.y *= Q->czech;
rho = sqrt(xy.x * xy.x + xy.y * xy.y);
eps = atan2(xy.y, xy.x);
d = eps / sin(S0);
s = 2. * (atan( pow(Q->rho0 / rho, 1. / Q->n) * tan(S0 / 2. + M_PI_4)) - M_PI_4);
u = asin(cos(Q->ad) * sin(s) - sin(Q->ad) * cos(s) * cos(d));
deltav = asin(cos(s) * sin(d) / cos(u));
lp.lam = P->lam0 - deltav / Q->alpha;
/* ITERATION FOR lp.phi */
fi1 = u;
for (i = MAX_ITER; i ; --i) {
lp.phi = 2. * ( atan( pow( Q->k, -1. / Q->alpha) *
pow( tan(u / 2. + M_PI_4) , 1. / Q->alpha) *
pow( (1. + P->e * sin(fi1)) / (1. - P->e * sin(fi1)) , P->e / 2.)
) - M_PI_4);
if (fabs(fi1 - lp.phi) < EPS)
break;
fi1 = lp.phi;
}
if( i == 0 )
pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
lp.lam -= P->lam0;
return lp;
}
PJ *PROJECTION(krovak) {
double u0, n0, g;
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;
/* we want Bessel as fixed ellipsoid */
P->a = 6377397.155;
P->e = sqrt(P->es = 0.006674372230614);
/* if latitude of projection center is not set, use 49d30'N */
if (!pj_param(P->ctx, P->params, "tlat_0").i)
P->phi0 = 0.863937979737193;
/* if center long is not set use 42d30'E of Ferro - 17d40' for Ferro */
/* that will correspond to using longitudes relative to greenwich */
/* as input and output, instead of lat/long relative to Ferro */
if (!pj_param(P->ctx, P->params, "tlon_0").i)
P->lam0 = 0.7417649320975901 - 0.308341501185665;
/* if scale not set default to 0.9999 */
if (!pj_param(P->ctx, P->params, "tk").i && !pj_param(P->ctx, P->params, "tk_0").i)
P->k0 = 0.9999;
Q->czech = 1;
if( !pj_param(P->ctx, P->params, "tczech").i )
Q->czech = -1;
/* Set up shared parameters between forward and inverse */
Q->alpha = sqrt(1. + (P->es * pow(cos(P->phi0), 4)) / (1. - P->es));
u0 = asin(sin(P->phi0) / Q->alpha);
g = pow( (1. + P->e * sin(P->phi0)) / (1. - P->e * sin(P->phi0)) , Q->alpha * P->e / 2. );
Q->k = tan( u0 / 2. + M_PI_4) / pow (tan(P->phi0 / 2. + M_PI_4) , Q->alpha) * g;
n0 = sqrt(1. - P->es) / (1. - P->es * pow(sin(P->phi0), 2));
Q->n = sin(S0);
Q->rho0 = P->k0 * n0 / tan(S0);
Q->ad = M_PI_2 - UQ;
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}
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