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Diffstat (limited to 'src/projections/krovak.cpp')
| -rw-r--r-- | src/projections/krovak.cpp | 222 |
1 files changed, 222 insertions, 0 deletions
diff --git a/src/projections/krovak.cpp b/src/projections/krovak.cpp new file mode 100644 index 00000000..9ecffb89 --- /dev/null +++ b/src/projections/krovak.cpp @@ -0,0 +1,222 @@ + /* + * 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; +} |