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geo.c
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// GK - Converter between Gauss-Krueger/TM and WGS84 coordinates for Slovenia
// Copyright (c) 2014-2016 Matjaz Rihtar <[email protected]>
// All rights reserved.
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published
// by the Free Software Foundation, either version 2.1 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with this program; if not, see http://www.gnu.org/licenses/
//
// geo.c: Collection of coordinate conversion routines
//
#include "common.h"
#include "geo.h"
// Select meridian arc length (L) calculation algorithm
#define L1 //else L2
#undef L3 // alternative
// Select fi0 calculation algorithm (geocentric to geodetic coordinates)
#define FI1 //else FI2
// Select Helmert transformation method
#define H71 // best
#undef H72
#undef H73
//else
// global variables
const double PI = M_PI; //= 4.0*atan(1.0);
// Ellipsoid data
// 0: Bessel 1841, 1: WGS 84, 2: ETRS89
ELLIPSOID ellips[3];
#define ellipsoid ellips[oid]
// Absolute geoid model of Slovenia
// fi: 45°15' - 47°00' = 105'/1.0' = 105
// 45.25° - 47.00°
// x: 13716.729 - 208212.911 (D96/TM)
// x: 13173.078 - 207659.160 (D48/GK)
// la: 13°15' - 16°45' = 210'/1.5' = 140
// 13.25° - 16.75°
// y: 362633.289 - 633083.271 (D96/TM)
// y: 363001.945 - 633454.830 (D48/GK)
// la: 13°15' - 16°45' = 210'/1.0' = 210
double geoid_bes[106][141]; // (doesn't exist) on Bessel 1841 (0)
//double geoid_slo[106][141]; // Slo2000 on WGS 84 (1)
#include "geoid_slo.h"
//double geoid_egm[106][211]; // EGM2008 on WGS 84 (2)
#include "geoid_egm.h"
double gfimin, gfimax, gfiinc1;
double glamin, glamax, glainc15, glainc1;
int gid_wgs; // selected geoid on WGS 84 (via cmd line)
int hsel; // selected output height (via cmd line)
// transformed height(0), copied height(1) or geoid height(2)
// H = ortometric/above sea level height (what we normally use)
// h = elipsoidal height (from GPS)
// Ng = geoid height (from EGM96, EGM2008 or local absolute models)
// H = h - Ng
// h = H + Ng
// Ng for Slovenia:
// 0-5m for Bessel 1841
// 45-48m for WGS 84 (EGM96)
// German expressions:
// Breite = Latitude (N/S)
// Laenge = Longitude (E/W)
// Kennziffer = GK zone = {0°, 3°, 6°, ..., 351°, 354°, 357°} / 3°
// zone = xround(lon.deg / 3.0);
// Gauss-Krueger zones and their limits
GKLM gkzones[] = {
// fimin fimax lamin lamax xmin xmax ymin ymax
{ 40.0, 55.0, -2.0, 2.0, 0.0, 0.0, 0.0, 0.0 }, // 0
{ 40.0, 55.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 }, // 1
{ 40.0, 55.0, 4.0, 8.0, 0.0, 0.0, 0.0, 0.0 }, // 2
{ 40.0, 55.0, 7.0, 11.0, 0.0, 0.0, 0.0, 0.0 }, // 3
{ 40.0, 55.0, 10.0, 14.0, 0.0, 0.0, 0.0, 0.0 }, // 4
{ 40.0, 55.0, 13.0, 17.0, -569400.0, 1097800.0, 329200.0, 628000.0 }, // 5 (Slovenia)
{ 40.0, 55.0, 16.0, 20.0, 0.0, 0.0, 0.0, 0.0 }, // 6
{ 40.0, 55.0, 19.0, 23.0, 0.0, 0.0, 0.0, 0.0 }, // 7
{ 40.0, 55.0, 22.0, 26.0, 0.0, 0.0, 0.0, 0.0 } // 8
};
// Pre-calculated affine transformation tables
#define MAXAFT 1776
//AFT aft_gktm[MAXAFT]; // Affine transformation table from GK to TM for Slovenia
#include "aft_gktm.h"
//AFT aft_tmgk[MAXAFT]; // Affine transformation table from TM to GK for Slovenia
#include "aft_tmgk.h"
int last_tri = -1; // last found triangle
// Distance to triangle segment
#define EPSILON 0.001
#define EPSILON2 EPSILON*EPSILON
// Projection parameters
PROJ tm;
// Parameters for Helmert transformation
HELMERT7 slo7, slo7inv;
#ifdef __cplusplus
extern "C" {
#endif
// ----------------------------------------------------------------------------
// dms2deg
// ----------------------------------------------------------------------------
void dms2deg(DMS dms, double *deg)
{
*deg = dms.deg + (dms.min*60.0 + dms.sec)/3600.0;
} /* dms2deg */
// ----------------------------------------------------------------------------
// dm2deg
// ----------------------------------------------------------------------------
void dm2deg(DMS dms, double *deg)
{
*deg = dms.deg + dms.min*60.0/3600.0;
} /* dm2deg */
// ----------------------------------------------------------------------------
// dms2rad
// ----------------------------------------------------------------------------
void dms2rad(DMS dms, double *rad)
{
*rad = dms.deg + (dms.min*60.0 + dms.sec)/3600.0;
*rad = *rad*PI/180.0; // convert degrees to radians
} /* dms2rad */
// ----------------------------------------------------------------------------
// dm2rad
// ----------------------------------------------------------------------------
void dm2rad(DMS dms, double *rad)
{
*rad = dms.deg + dms.min*60.0/3600.0;
*rad = *rad*PI/180.0; // convert degrees to radians
} /* dm2rad */
// ----------------------------------------------------------------------------
// deg2dms
// ----------------------------------------------------------------------------
void deg2dms(double deg, DMS *dms)
{
dms->deg = xtrunc(deg);
dms->sec = (deg - dms->deg)*60.0;
dms->min = xtrunc(dms->sec);
dms->sec = (dms->sec - dms->min)*60.0;
} /* deg2dms */
// ----------------------------------------------------------------------------
// deg2dm
// ----------------------------------------------------------------------------
void deg2dm(double deg, DMS *dms)
{
dms->deg = xtrunc(deg);
dms->min = (deg - dms->deg)*60.0;
dms->sec = 0.0;
} /* deg2dm */
// ----------------------------------------------------------------------------
// rad2dms
// ----------------------------------------------------------------------------
void rad2dms(double rad, DMS *dms)
{
rad = rad*180.0/PI; // convert radians to degrees
dms->deg = xtrunc(rad);
dms->sec = (rad - dms->deg)*60.0;
dms->min = xtrunc(dms->sec);
dms->sec = (dms->sec - dms->min)*60.0;
} /* rad2dms */
// ----------------------------------------------------------------------------
// rad2dm
// ----------------------------------------------------------------------------
void rad2dm(double rad, DMS *dms)
{
rad = rad*180.0/PI; // convert radians to degrees
dms->deg = xtrunc(rad);
dms->min = (rad - dms->deg)*60.0;
dms->sec = 0.0;
} /* rad2dm */
// ----------------------------------------------------------------------------
// matrix33_mul
// ----------------------------------------------------------------------------
void matrix33_mul(m33 R1, m33 R2, m33 *R12)
{
(*R12)[0][0] = R1[0][0]*R2[0][0] + R1[0][1]*R2[1][0] + R1[0][2]*R2[2][0];
(*R12)[0][1] = R1[0][0]*R2[0][1] + R1[0][1]*R2[1][1] + R1[0][2]*R2[2][1];
(*R12)[0][2] = R1[0][0]*R2[0][2] + R1[0][1]*R2[1][2] + R1[0][2]*R2[2][2];
(*R12)[1][0] = R1[1][0]*R2[0][0] + R1[1][1]*R2[1][0] + R1[1][2]*R2[2][0];
(*R12)[1][1] = R1[1][0]*R2[0][1] + R1[1][1]*R2[1][1] + R1[1][2]*R2[2][1];
(*R12)[1][2] = R1[1][0]*R2[0][2] + R1[1][1]*R2[1][2] + R1[1][2]*R2[2][2];
(*R12)[2][0] = R1[2][0]*R2[0][0] + R1[2][1]*R2[1][0] + R1[2][2]*R2[2][0];
(*R12)[2][1] = R1[2][0]*R2[0][1] + R1[2][1]*R2[1][1] + R1[2][2]*R2[2][1];
(*R12)[2][2] = R1[2][0]*R2[0][2] + R1[2][1]*R2[1][2] + R1[2][2]*R2[2][2];
} /* matrix33_mul */
// ----------------------------------------------------------------------------
// ellipsoid_precalc
// Precalculate some ellipsoid constants
// ----------------------------------------------------------------------------
// http://en.wikipedia.org/wiki/Geodetic_datum
// a = semi-major axis (given)
// f = reciprocal of flattening (given)
// flattening: f = (a - b)/a = 1 - sqrt(1 - e^2)
// b = semi-minor axis
// n = third flattening
// e = first eccentricity
// e' = second eccentricity
// c = polar radius of curvature
// M = meridional radius of curvature
//
// b = a*(1 - f)
// n = (a - b)/(a + b) = f/(2 - f)
// c = a^2/b = a/(1 - f)
// M = b^2/a = a(1 - e^2) = a*(1 - f)^2
// e^2 = 1 - b/c = (a^2 - b^2)/a^2 = 1 - b^2/a^2 = 2f - f^2 = f*(2 - f)
// e'^2 = c/b - 1 = (a^2 - b^2)/b^2 = a^2/b^2 - 1 = e^2/(1 - e^2) = f*(2 - f)/(1 - f)^2
// ----------------------------------------------------------------------------
// Ellipsoid: 0: bessel, 1: wgs84, 2: etrs89
void ellipsoid_precalc(int oid)
{
ellipsoid.a2 = pow(ellipsoid.a,2);
ellipsoid.b = ellipsoid.a*(1 - ellipsoid.f);
ellipsoid.b2 = pow(ellipsoid.b,2);
ellipsoid.n = ellipsoid.f/(2 - ellipsoid.f);
ellipsoid.c = ellipsoid.a/(1 - ellipsoid.f);
ellipsoid.M = ellipsoid.a*pow(1 - ellipsoid.f,2);
ellipsoid.e2 = ellipsoid.f*(2 - ellipsoid.f);
ellipsoid.e2_ = ellipsoid.e2/pow(1 - ellipsoid.f,2);
} /* ellipsoid_precalc */
// ----------------------------------------------------------------------------
// series_precalc
// Precalculate some constants for series used in meridian distance (fi0)
// ----------------------------------------------------------------------------
// Ellipsoid: 0: bessel, 1: wgs84, 2: etrs89
void series_precalc(int oid)
{
double E2, E4, E6, E8, E10;
double N, N2, N3, N4, N5;
// Coefficients for series to determine meridian arc length (L) on ellipsoid
// See "Geodesy - Introduction to Geodetic Datum and Geodetic Systems (Zhiping, 2014), pg. 194"
// for cos() variant
#ifdef L1
// See "Geometrical Geodesy (Hooijberg, 2008), pg. 165(pdf: 183)"
// See "Bundeseinheitliche Transformation für ATKIS"
// for sin() variant (A, ...; more precise)
E2 = ellipsoid.e2_;
E4 = pow(E2,2); E6 = E4*E2; E8 = pow(E4,2); E10 = E6*E4;
ellipsoid.A = 1.0 - 3.0/4.0*E2 + 45.0/64.0*E4 - 175.0/256.0*E6
+ 11025.0/16384.0*E8 - 43659.0/65536.0*E10;
ellipsoid.B = -3.0/4.0*E2 + 15.0/16.0*E4 - 525.0/512.0*E6
+ 2205.0/2048.0*E8 - 72765.0/65536.0*E10;
ellipsoid.C = 15.0/64.0*E4 - 105.0/256.0*E6 + 2205.0/4096.0*E8
- 10395.0/16384.0*E10;
ellipsoid.D = -35.0/512.0*E6 + 315.0/2048.0*E8 - 31185.0/131072.0*E10;
ellipsoid.E = 315.0/16384.0*E8 - 3465.0/65536.0*E10;
ellipsoid.F = -639.0/131072.0*E10;
#else //L2
// See "Stara in nova drzavna kartografska projekcija (2008), pg. 8)"
// See "Digitalni model reliefa (Podobnikar, 2001), pg. 100(pdf: 105)"
// "A General Formula for Calculating Meridian Arc Length (Kawase, 2011)"
E2 = ellipsoid.e2;
E4 = pow(E2,2); E6 = E4*E2; E8 = pow(E4,2); E10 = E6*E4;
ellipsoid.A = 1.0 + 3.0/4.0*E2 + 45.0/64.0*E4 + 175.0/256.0*E6
+ 11025.0/16384.0*E8 + 43659.0/65536.0*E10;
ellipsoid.B = 3.0/4.0*E2 + 15.0/16.0*E4 + 525.0/512.0*E6
+ 2205.0/2048.0*E8 + 72765.0/65536.0*E10;
ellipsoid.C = 15.0/64.0*E4 + 105.0/256.0*E6 + 2205.0/4096.0*E8
+ 10395.0/16384.0*E10;
ellipsoid.D = 35.0/512.0*E6 + 315.0/2048.0*E8 + 31185.0/131072.0*E10;
ellipsoid.E = 315.0/16384.0*E8 + 3465.0/65536.0*E10;
ellipsoid.F = 639.0/131072.0*E10;
#endif
// Coefficients for series to determine fi0 on ellipsoid (alternative way)
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 22-23"
// for sin() variant (alfa, ...; similar to above)
//L3
N = ellipsoid.n; N2 = pow(ellipsoid.n,2); N3 = pow(ellipsoid.n,3);
N4 = pow(ellipsoid.n,4); N5 = pow(ellipsoid.n,5);
ellipsoid.alfa = (ellipsoid.a + ellipsoid.b)/2.0*(1.0 + 1.0/4.0*N2
+ 1.0/64.0*N4);
ellipsoid.beta = 3.0/2.0*N - 27.0/32.0*N3 + 269.0/512.0*N5;
ellipsoid.gama = 21.0/16.0*N2 - 55.0/32.0*N4;
ellipsoid.delta = 151.0/96.0*N3 - 417.0/128.0*N5;
ellipsoid.epsilon = 1097.0/512.0*N4;
} /* series_precalc */
// ----------------------------------------------------------------------------
// ellipsoid_init
// ----------------------------------------------------------------------------
void ellipsoid_init()
{
// http://en.wikipedia.org/wiki/Bessel_ellipsoid
// For Slovenia: http://epsg.io/3911-3917
ellips[0].a = 6377397.155;
ellips[0].f = 1/299.1528128; //0.00334277318217481
//ellips[0].f = 1/299.152815351; // Japan
ellipsoid_precalc(0);
series_precalc(0);
// http://en.wikipedia.org/wiki/World_Geodetic_System (wgs84)
ellips[1].a = 6378137.0;
ellips[1].f = 1/298.257223563; //0.00335281066474748
ellipsoid_precalc(1);
series_precalc(1);
// http://en.wikipedia.org/wiki/European_Terrestrial_Reference_System_1989
// Same as http://en.wikipedia.org/wiki/GRS_80
ellips[2].a = 6378137.0;
ellips[2].f = 1/298.257222101; //0.00335281068118232
ellipsoid_precalc(2);
series_precalc(2);
} /* ellipsoid_init */
// ----------------------------------------------------------------------------
// h7_precalc
// Precalculate rotation matrix for Helmert transformation
// ----------------------------------------------------------------------------
void h7_precalc(HELMERT7 *h7)
{
double alfa, beta, gama;
double sinAlfa, cosAlfa, sinBeta, cosBeta, sinGama, cosGama;
m33 R1, R2, R3, R12;
char *errtxt;
// Angles specified in arc seconds, convert to radians
alfa = (h7->alfa/3600.0)*PI/180.0;
beta = (h7->beta/3600.0)*PI/180.0;
gama = (h7->gama/3600.0)*PI/180.0;
sinAlfa = sin(alfa); cosAlfa = cos(alfa);
sinBeta = sin(beta); cosBeta = cos(beta);
sinGama = sin(gama); cosGama = cos(gama);
#ifdef H71
// See "GNSS - Global Navigation Satellite Systems (Hofmann-Wellenhof, 2008), pg: 294"
// See "Digitalni model reliefa (Podobnikar, 2001), pg. 114(pdf: 119)"
R1[0][0] = cosGama; R1[0][1] = sinGama; R1[0][2] = 0;
R1[1][0] = -sinGama; R1[1][1] = cosGama; R1[1][2] = 0;
R1[2][0] = 0; R1[2][1] = 0; R1[2][2] = 1;
R2[0][0] = cosBeta; R2[0][1] = 0; R2[0][2] = -sinBeta;
R2[1][0] = 0; R2[1][1] = 1; R2[1][2] = 0;
R2[2][0] = sinBeta; R2[2][1] = 0; R2[2][2] = cosBeta;
R3[0][0] = 1; R3[0][1] = 0; R3[0][2] = 0;
R3[1][0] = 0; R3[1][1] = cosAlfa; R3[1][2] = sinAlfa;
R3[2][0] = 0; R3[2][1] = -sinAlfa; R3[2][2] = cosAlfa;
h7->R = (m33 *)malloc(sizeof(m33));
if (h7->R == NULL) {
errtxt = xstrerror();
if (errtxt != NULL) {
fprintf(stderr, "malloc(m33): %s\n", errtxt); free(errtxt);
} else
fprintf(stderr, "malloc(m33): Can't allocate memory\n");
exit(3);
}
matrix33_mul(R1, R2, &R12);
matrix33_mul(R12, R3, h7->R);
#elif defined(H72)
// See "Computing Helmert transformations (Watson, 2005)"
// (different rotations?!)
R1[0][0] = cosAlfa; R1[0][1] = -sinAlfa; R1[0][2] = 0;
R1[1][0] = sinAlfa; R1[1][1] = cosAlfa; R1[1][2] = 0;
R1[2][0] = 0; R1[2][1] = 0; R1[2][2] = 1;
R2[0][0] = cosBeta; R2[0][1] = 0; R2[0][2] = -sinBeta;
R2[1][0] = 0; R2[1][1] = 1; R2[1][2] = 0;
R2[2][0] = sinBeta; R2[2][1] = 0; R2[2][2] = cosBeta;
R3[0][0] = 1; R3[0][1] = 0; R3[0][2] = 0;
R3[1][0] = 0; R3[1][1] = cosGama; R3[1][2] = -sinGama;
R3[2][0] = 0; R3[2][1] = sinGama; R3[2][2] = cosGama;
h7->R = (m33 *)malloc(sizeof(m33));
if (h7->R == NULL) {
errtxt = xstrerror();
if (errtxt != NULL) {
fprintf(stderr, "malloc(m33): %s\n", errtxt); free(errtxt);
} else
fprintf(stderr, "malloc(m33): Can't allocate memory\n");
exit(3);
}
matrix33_mul(R1, R2, &R12);
matrix33_mul(R12, R3, h7->R);
#endif
} /* h7_precalc */
// ----------------------------------------------------------------------------
// params_init
// ----------------------------------------------------------------------------
void params_init()
{
DMS lat, lon;
double dlat, dlon;
// http://en.wikipedia.org/wiki/Helmert_transformation
// Parameters for Slovenia ETRS89 (D48/GK --> D96/TM)
// http://193.2.92.129/SiTraNet2.10-navodila.htm#_Toc214285899 (SLO splosni)
// (Coordinate Frame Transformation)
slo7.dX = 409.545088; // Cx
slo7.dY = 72.164092; // Cy
slo7.dZ = 486.871732; // Cz
slo7.alfa = -3.085957; // rx
slo7.beta = -5.469110; // ry
slo7.gama = 11.020289; // rz
slo7.dm = 17.919665; // s (scale)
// Parameters for Slovenia ETRS89 (D96/TM --> D48/GK, inverse)
// http://193.2.92.129/SiTraNet2.10-navodila.htm#_Toc214285900 (SLO splosni)
slo7inv.dX = -409.520465; // Cx
slo7inv.dY = -72.191827; // Cy
slo7inv.dZ = -486.872387; // Cz
slo7inv.alfa = 3.086250; // rx
slo7inv.beta = 5.468945; // ry
slo7inv.gama = -11.020370; // rz
slo7inv.dm = -17.919456; // s (scale)
// For additional parameters for Slovenia see:
// http://www.transformacije.si/koristno/drzavni-parametri
// Precalculate rotation matrices for Helmert transformation
h7_precalc(&slo7);
h7_precalc(&slo7inv);
// Transverse Mercator projection parameters for Slovenia
// (same for Gauss-Krueger projection)
tm.scale = 0.9999;
tm.false_easting = 500000;
tm.false_northing = -5000000;
tm.meridian = 15; // central meridian for Slovenia
tm.lambda0 = tm.meridian*PI/180.0; //0.26179938779914941
// Absolute geoid model limits
// fi: 45°15' - 47°00', inc: 1.0'
lat.deg = 45; lat.min = 15; lat.sec = 0;
dms2deg(lat, &dlat); gfimin = dlat;
lat.deg = 47; lat.min = 0; lat.sec = 0;
dms2deg(lat, &dlat); gfimax = dlat;
lat.deg = 0; lat.min = 1; lat.sec = 0;
dms2deg(lat, &dlat); gfiinc1 = dlat;
// la: 13°15' - 16°45', inc: 1.5'/1.0'
lon.deg = 13; lon.min = 15; lon.sec = 0;
dms2deg(lon, &dlon); glamin = dlon;
lon.deg = 16; lon.min = 45; lon.sec = 0;
dms2deg(lon, &dlon); glamax = dlon;
lon.deg = 0; lon.min = 1; lon.sec = 30;
dms2deg(lon, &dlon); glainc15 = dlon;
lon.deg = 0; lon.min = 1; lon.sec = 0;
dms2deg(lon, &dlon); glainc1 = dlon;
// There's no data available for geoid on Bessel 1841!
memset(geoid_bes, 0, sizeof(geoid_bes));
} /* params_init */
// ----------------------------------------------------------------------------
// geoid_height (depends on ellipsoid)
// ----------------------------------------------------------------------------
// Geoid: 0: bessel, 1: slo2000/wgs84, 2: egm2008/wgs84
double geoid_height(double fi, double la, int gid)
{
double Ng = 0.0;
double xi, yi; int ix, iy, gixmax, giymax;
double x, y, x1, y1, x2, y2;
double p1, p2, p3, p4;
double R1, R2;
if (fi < gfimin || fi > gfimax || la < glamin || la > glamax) {
// Outside geoid model
return Ng;
}
x = fi; y = la;
xi = (fi - gfimin)/gfiinc1; ix = (int)xtrunc(xi);
if (gid == 2) yi = (la - glamin)/glainc1; //egm2008
else yi = (la - glamin)/glainc15; //slo2000, bessel
iy = (int)xtrunc(yi);
gixmax = 105; giymax = (gid == 2) ? 210 : 140;
if (ix <= 0 || ix >= gixmax || iy <= 0 || iy >= giymax) {
// On geoid model borders
return Ng;
}
if (gid == 1) {
x1 = gfimin + ix*gfiinc1; y1 = glamin + iy*glainc15;
x2 = x1 + gfiinc1; y2 = y1 + glainc15;
p3 = geoid_slo[ix+1][iy]; p4 = geoid_slo[ix+1][iy+1];
p1 = geoid_slo[ix][iy]; p2 = geoid_slo[ix][iy+1];
}
else if (gid == 2) {
x1 = gfimin + ix*gfiinc1; y1 = glamin + iy*glainc15;
x2 = x1 + gfiinc1; y2 = y1 + glainc1;
p3 = geoid_egm[ix+1][iy]; p4 = geoid_egm[ix+1][iy+1];
p1 = geoid_egm[ix][iy]; p2 = geoid_egm[ix][iy+1];
}
else {
x1 = gfimin + ix*gfiinc1; y1 = glamin + iy*glainc15;
x2 = x1 + gfiinc1; y2 = y1 + glainc15;
p3 = geoid_bes[ix+1][iy]; p4 = geoid_bes[ix+1][iy+1];
p1 = geoid_bes[ix][iy]; p2 = geoid_bes[ix][iy+1];
}
if (p1 == 0.0) {
// No data in geoid model (outside Slovenia for slo2000)
return Ng;
}
// Add missing values on Slovenia borders for slo2000
if (p3 == 0.0) p3 = p1; if (p4 == 0.0) p4 = p1;
/* p1 = base value */ if (p2 == 0.0) p2 = p1;
// Bilinear interpolation (from Wiki)
R1 = (y2 - y)/(y2 - y1)*p1 + (y - y1)/(y2 - y1)*p2;
R2 = (y2 - y)/(y2 - y1)*p3 + (y - y1)/(y2 - y1)*p4;
Ng = (x2 - x)/(x2 - x1)*R1 + (x - x1)/(x2 - x1)*R2;
return Ng;
} /* geoid_height */
// ----------------------------------------------------------------------------
// point_in_bounding_box
// ----------------------------------------------------------------------------
int point_in_bounding_box(double x1, double y1, double x2, double y2, double x3, double y3, double x, double y)
{
double xMin, xMax, yMin, yMax;
xMin = xfmin(x1, xfmin(x2, x3)) - EPSILON;
xMax = xfmax(x1, xfmax(x2, x3)) + EPSILON;
yMin = xfmin(y1, xfmin(y2, y3)) - EPSILON;
yMax = xfmax(y1, xfmax(y2, y3)) + EPSILON;
if (x < xMin || x > xMax || y < yMin || y > yMax)
return 0;
else
return 1;
} /* point_in_bounding_box */
// ----------------------------------------------------------------------------
// side
// ----------------------------------------------------------------------------
double side(double x1, double y1, double x2, double y2, double x, double y)
{
return (y2 - y1)*(x - x1) + (-x2 + x1)*(y - y1);
} /* side */
// ----------------------------------------------------------------------------
// point_in_triangle
// ----------------------------------------------------------------------------
int point_in_triangle(double x1, double y1, double x2, double y2, double x3, double y3, double x, double y)
{
int checkSide1, checkSide2, checkSide3;
checkSide1 = side(x1, y1, x2, y2, x, y) >= 0.0;
checkSide2 = side(x2, y2, x3, y3, x, y) >= 0.0;
checkSide3 = side(x3, y3, x1, y1, x, y) >= 0.0;
return checkSide1 && checkSide2 && checkSide3;
} /* point_in_triangle */
// ----------------------------------------------------------------------------
// dist_to_segm
// ----------------------------------------------------------------------------
double dist_to_segm(double x1, double y1, double x2, double y2, double x, double y)
{
double p1_p2_squareLen, p_p1_squareLen;
double dotProduct;
p1_p2_squareLen = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1);
dotProduct = ((x - x1)*(x2 - x1) + (y - y1)*(y2 - y1)) / p1_p2_squareLen;
if (dotProduct < 0.0)
return (x - x1)*(x - x1) + (y - y1)*(y - y1);
else if (dotProduct <= 1.0) {
p_p1_squareLen = (x1 - x)*(x1 - x) + (y1 - y)*(y1 - y);
return p_p1_squareLen - dotProduct * dotProduct * p1_p2_squareLen;
}
else
return (x - x2)*(x - x2) + (y - y2)*(y - y2);
} /* dist_to_segm */
// ----------------------------------------------------------------------------
// coord_in_triangle
// ----------------------------------------------------------------------------
int coord_in_triangle(GEOUTM in, AFT aft)
{
double x, y, x1, y1, x2, y2, x3, y3;
x = in.x; y = in.y;
x1 = aft.src[0].x; y1 = aft.src[0].y;
x2 = aft.src[1].x; y2 = aft.src[1].y;
x3 = aft.src[2].x; y3 = aft.src[2].y;
if (!point_in_bounding_box(x1, y1, x2, y2, x3, y3, x, y))
return 0;
if (point_in_triangle(x1, y1, x2, y2, x3, y3, x, y))
return 1;
if (dist_to_segm(x1, y1, x2, y2, x, y) <= EPSILON2)
return 1;
if (dist_to_segm(x2, y2, x3, y3, x, y) <= EPSILON2)
return 1;
if (dist_to_segm(x3, y3, x1, y1, x, y) <= EPSILON2)
return 1;
return 0;
} /* coord_in_triangle */
// ----------------------------------------------------------------------------
// xy2fila_ellips (height calculated from geoid)
// ----------------------------------------------------------------------------
// Transform from GK/TM x,y,H coordinates to fi,la,h on specified ellipsoid
// ----------------------------------------------------------------------------
// Ellipsoid: 0: bessel, 1: wgs84, 2: etrs89
void xy2fila_ellips(GEOUTM in, GEOGRA *out, int oid)
{
double ab, fi0, dif, L; int n;
double sinFi0, sin2Fi0;
double cosFi0, cos2Fi0;
double tanFi0, tan2Fi0, tan4Fi0, tan6Fi0;
double N, ni2, ni4, Ng;
// Convert from relative to real coordinates
in.x = (in.x - tm.false_northing)/tm.scale;
in.y = (in.y - tm.false_easting)/tm.scale;
// Calculate fi0 - footpoint latitude
// See "Geometrical Geodesy (Hooijberg, 2008), pg. 165(pdf: 183)"
ab = ellipsoid.a + ellipsoid.b;
fi0 = 2.0*in.x/ab; // first estimate
dif = 1.0; n = 15;
while (fabs(dif) >= 1e-18 && n > 0) {
#ifdef L1
L = ellipsoid.c*(ellipsoid.A*fi0 + ellipsoid.B/2.0*sin(2.0*fi0)
+ ellipsoid.C/4.0*sin(4.0*fi0) + ellipsoid.D/6.0*sin(6.0*fi0)
+ ellipsoid.E/8.0*sin(8.0*fi0) + ellipsoid.F/10.0*sin(10.0*fi0));
#else //L2
L = ellipsoid.M*(ellipsoid.A*fi0 - ellipsoid.B/2.0*sin(2.0*fi0)
+ ellipsoid.C/4.0*sin(4.0*fi0) - ellipsoid.D/6.0*sin(6.0*fi0)
+ ellipsoid.E/8.0*sin(8.0*fi0) - ellipsoid.F/10.0*sin(10.0*fi0));
#endif
dif = 2.0*(in.x - L)/ab;
fi0 += dif;
n--;
}
#ifdef L3
// Alternative way of calculating fi0 (similar to above, faster)
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 22-23"
double fiq;
fiq = in.x/ellipsoid.alfa;
fi0 = fiq + ellipsoid.beta*sin(2.0*fiq) + ellipsoid.gama*sin(4.0*fiq)
+ ellipsoid.delta*sin(6.0*fiq) + ellipsoid.epsilon*sin(8.0*fiq);
#endif
sinFi0 = sin(fi0);
sin2Fi0 = pow(sinFi0,2);
cosFi0 = cos(fi0);
cos2Fi0 = pow(cosFi0,2);
tanFi0 = tan(fi0);
tan2Fi0 = pow(tanFi0,2); tan4Fi0 = pow(tanFi0,4); tan6Fi0 = pow(tanFi0,6);
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 22"
N = ellipsoid.c/sqrt(1.0 + ellipsoid.e2_*cos2Fi0);
//N = ellipsoid.a/sqrt(1.0 - ellipsoid.e2*sin2Fi0); // alternative (from java)
//t = tanFi0;
ni2 = ellipsoid.e2_*cos2Fi0;
ni4 = pow(ni2,2);
#if 1
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 41"
// See "Bundeseinheitliche Transformation für ATKIS (BeTA2007), pg. 28"
out->fi = fi0
+ tanFi0/(2.0*pow(N,2))*(-1.0 - ni2)*pow(in.y,2)
+ tanFi0/(24.0*pow(N,4))*(5.0 + 3.0*tan2Fi0 + 6.0*ni2 - 6.0*tan2Fi0*ni2
- 3.0*ni4 - 9.0*tan2Fi0*ni4)*pow(in.y,4)
+ tanFi0/(720.0*pow(N,6))*(-61.0 - 90.0*tan2Fi0 - 45.0*tan4Fi0 - 107.0*ni2
+ 162.0*tan2Fi0*ni2 + 45.0*tan4Fi0*ni2)*pow(in.y,6)
+ tanFi0/(40320.0*pow(N,8))*(1385.0 + 3633.0*tan2Fi0 + 4095.0*tan4Fi0
+ 1575.0*tan6Fi0)*pow(in.y,8);
#else // really identical
// See "Stara in nova drzavna kartografska projekcija (2008), pg. 8)"
// See "Digitalni model reliefa (Podobnikar, 2001), pg. 109(pdf: 114)"
out->fi = fi0
- tanFi0/(2.0*pow(N,2))*(1.0 + ni2)*pow(in.y,2)
+ tanFi0/(24.0*pow(N,4))*(5.0 + 3.0*tan2Fi0 + 6.0*ni2 - 6.0*tan2Fi0*ni2
- 3.0*ni4 - 9.0*tan2Fi0*ni4)*pow(in.y,4)
- tanFi0/(720.0*pow(N,6))*(61.0 + 90.0*tan2Fi0 + 45.0*tan4Fi0 + 107.0*ni2
- 162.0*tan2Fi0*ni2 - 45.0*tan4Fi0*ni2)*pow(in.y,6)
+ tanFi0/(40320.0*pow(N,8))*(1385.0 + 3633.0*tan2Fi0 + 4095.0*tan4Fi0
+ 1575.0*tan6Fi0)*pow(in.y,8);
#endif
#if 0 //xxx
#ifdef L1
L = ellipsoid.c*(ellipsoid.A*out->fi + ellipsoid.B/2.0*sin(2.0*out->fi)
+ ellipsoid.C/4.0*sin(4.0*out->fi) + ellipsoid.D/6.0*sin(6.0*out->fi)
+ ellipsoid.E/8.0*sin(8.0*out->fi) + ellipsoid.F/10.0*sin(10.0*out->fi));
#else //L2
L = ellipsoid.M*(ellipsoid.A*out->fi - ellipsoid.B/2.0*sin(2.0*out->fi)
+ ellipsoid.C/4.0*sin(4.0*out->fi) - ellipsoid.D/6.0*sin(6.0*out->fi)
+ ellipsoid.E/8.0*sin(8.0*out->fi) - ellipsoid.F/10.0*sin(10.0*out->fi));
#endif
printf(">> L: %.10f\n", L);
#endif
#if 1
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 41"
// See "Bundeseinheitliche Transformation für ATKIS (BeTA2007), pg. 28"
out->la = tm.lambda0
+ 1.0/(N*cosFi0)*in.y
+ 1.0/(6.0*pow(N,3)*cosFi0)*(-1.0 - 2.0*tan2Fi0 - ni2)*pow(in.y,3)
+ 1.0/(120.0*pow(N,5)*cosFi0)*(5.0 + 28.0*tan2Fi0 + 24.0*tan4Fi0
+ 8.0*tan2Fi0*ni2 + 6.0*ni2)*pow(in.y,5)
+ 1.0/(5040.0*pow(N,7)*cosFi0)*(-61.0 - 662.0*tan2Fi0 - 1320.0*tan4Fi0
- 720.0*tan6Fi0)*pow(in.y,7);
#else // really identical
// See "Stara in nova drzavna kartografska projekcija (2008), pg. 8)"
// See "Digitalni model reliefa (Podobnikar, 2001), pg. 109(pdf: 114)"
out->la = tm.lambda0
+ 1.0/(N*cosFi0)*in.y
- 1.0/(6.0*pow(N,3)*cosFi0)*(1.0 + 2.0*tan2Fi0 + ni2)*pow(in.y,3)
+ 1.0/(120.0*pow(N,5)*cosFi0)*(5.0 + 28.0*tan2Fi0 + 24.0*tan4Fi0 + 6.0*ni2
+ 8.0*tan2Fi0*ni2)*pow(in.y,5)
- 1.0/(5040.0*pow(N,7)*cosFi0)*(61.0 + 662.0*tan2Fi0 + 1320.0*tan4Fi0
+ 720.0*tan6Fi0)*pow(in.y,7);
#endif
// Convert from radians to degrees
out->fi = out->fi*180.0/PI;
out->la = out->la*180.0/PI;
if (oid == 1 || oid == 2) //wgs84/etrs89
Ng = geoid_height(out->fi, out->la, gid_wgs); //slo2000/egm2008
else //bessel
Ng = geoid_height(out->fi, out->la, 0); //bessel
out->Ng = Ng;
// Geoid height
out->h = in.H + Ng;
} /* xy2fila_ellips */
// ----------------------------------------------------------------------------
// fila_ellips2xy (height calculated from geoid)
// ----------------------------------------------------------------------------
// Transform from fi,la,h to GK/TM x,y,H coordinates on specified ellipsoid
// ----------------------------------------------------------------------------
// Ellipsoid: 0: bessel, 1: wgs84, 2: etrs89
void fila_ellips2xy(GEOGRA in, GEOUTM *out, int oid)
{
double dl, dl2, dl3, dl4, dl5, dl6, dl7, dl8;
double sinFi, sin2Fi;
double cosFi, cos2Fi, cos3Fi, cos4Fi, cos5Fi, cos6Fi, cos7Fi, cos8Fi;
double tanFi, tan2Fi, tan4Fi, tan6Fi;
double N, ni2, ni4, L, Ng;
if (oid == 1 || oid == 2) //wgs84/etrs89
Ng = geoid_height(in.fi, in.la, gid_wgs); //slo2000/egm2008
else //bessel
Ng = geoid_height(in.fi, in.la, 0); //bessel
out->Ng = Ng;
// Convert from degrees to radians
in.fi = in.fi*PI/180.0;
in.la = in.la*PI/180.0;
dl = in.la - tm.lambda0;
dl2 = pow(dl,2); dl3 = pow(dl,3); dl4 = pow(dl,4); dl5 = pow(dl,5);
dl6 = pow(dl,6); dl7 = pow(dl,7); dl8 = pow(dl,8);
sinFi = sin(in.fi);
sin2Fi = pow(sinFi,2);
cosFi = cos(in.fi);
cos2Fi = pow(cosFi,2); cos3Fi = pow(cosFi,3); cos4Fi = pow(cosFi,4);
cos5Fi = pow(cosFi,5); cos6Fi = pow(cosFi,6); cos7Fi = pow(cosFi,7);
cos8Fi = pow(cosFi,8);
tanFi = tan(in.fi);
tan2Fi = pow(tanFi,2); tan4Fi = pow(tanFi,4); tan6Fi = pow(tanFi,6);
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 22"
N = ellipsoid.c/sqrt(1.0 + ellipsoid.e2_*cos2Fi);
//N = ellipsoid.a/sqrt(1.0 - ellipsoid.e2*sin2Fi); // alternative (from java)
//t = tanFi;
ni2 = ellipsoid.e2_*cos2Fi;
ni4 = pow(ni2,2);
#ifdef L1
L = ellipsoid.c*(ellipsoid.A*in.fi + ellipsoid.B/2.0*sin(2.0*in.fi)
+ ellipsoid.C/4.0*sin(4.0*in.fi) + ellipsoid.D/6.0*sin(6.0*in.fi)
+ ellipsoid.E/8.0*sin(8.0*in.fi) + ellipsoid.F/10.0*sin(10.0*in.fi));
#else //L2
L = ellipsoid.M*(ellipsoid.A*in.fi - ellipsoid.B/2.0*sin(2.0*in.fi)
+ ellipsoid.C/4.0*sin(4.0*in.fi) - ellipsoid.D/6.0*sin(6.0*in.fi)
+ ellipsoid.E/8.0*sin(8.0*in.fi) - ellipsoid.F/10.0*sin(10.0*in.fi));
#endif
#if 1
// See "Stara in nova drzavna kartografska projekcija (2008), pg. 8)"
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 40"
out->x = L
+ tanFi/2.0*N*cos2Fi*dl2
+ tanFi/24.0*N*cos4Fi*(5.0 - tan2Fi + 9.0*ni2 + 4.0*ni4)*dl4
+ tanFi/720.0*N*cos6Fi*(61.0 - 58.0*tan2Fi + tan4Fi + 270.0*ni2
- 330.0*tan2Fi*ni2)*dl6
+ tanFi/40320.0*N*cos8Fi*(1385.0 - 3111.0*tan2Fi + 543.0*tan4Fi
- tan6Fi)*dl8;
#else // identical
// See "Digitalni model reliefa (Podobnikar, 2001), pg. 110(pdf: 115)"
out->x = L
+ 1.0/2.0*N*sinFi*cosFi*dl2
+ 1.0/24.0*N*sinFi*cos3Fi*(5.0 - tan2Fi + 9.0*ni2 + 4.0*ni4)*dl4
+ 1.0/720.0*N*sinFi*cos5Fi*(61.0 - 58.0*tan2Fi + tan4Fi)*dl6
+ 1.0/40320.0*N*sinFi*cos7Fi*(1385.0 - 3111.0*tan2Fi + 543.0*tan4Fi
- tan6Fi)*dl8;
#endif
#if 1
// See "Stara in nova drzavna kartografska projekcija (2008), pg. 8)"
// See "Predavanje Geodezija (Univ. Zagreb, 2007), pg. 40"
out->y = N*cosFi*dl
+ 1.0/6.0*N*cos3Fi*(1.0 - tan2Fi + ni2)*dl3
+ 1.0/120.0*N*cos5Fi*(5.0 - 18.0*tan2Fi + tan4Fi + 14.0*ni2
- 58.0*tan2Fi*ni2)*dl5
+ 1.0/5040.0*N*cos7Fi*(61.0 - 479.0*tan2Fi + 179.0*tan4Fi - tan6Fi)*dl7;
#else // really identical
// See "Digitalni model reliefa (Podobnikar, 2001), pg. 110(pdf: 115)"
out->y = N*cosFi*dl
+ 1.0/6.0*N*cos3Fi*(1.0 - tan2Fi + ni2)*dl3
+ 1.0/120.0*N*cos5Fi*(5.0 - 18.0*tan2Fi + tan4Fi + 14.0*ni2
- 58.0*tan2Fi*ni2)*dl5
+ 1.0/5040.0*N*cos7Fi*(61.0 - 479.0*tan2Fi + 179.0*tan4Fi - tan6Fi)*dl7;
#endif
// Convert from real to relative coordinates
out->x = out->x*tm.scale + tm.false_northing;
out->y = out->y*tm.scale + tm.false_easting;
// Geoid height
out->H = in.h - Ng;
} /* fila_ellips2xy */
// ----------------------------------------------------------------------------
// xy2fila_ellips_loop (height calculated from geoid)
// ----------------------------------------------------------------------------
// Transform from GK/TM x,y,H coordinates to fi,la,h on specified ellipsoid
// using loop search over coordinates
// ----------------------------------------------------------------------------
// Ellipsoid: 0: bessel, 1: wgs84, 2: etrs89
int xy2fila_ellips_loop(GEOUTM in, GEOGRA *out, int oid)
{
GEOGRA fl; GEOUTM xy;
double fi_max, fi_inc;
double la_max, la_inc;
long long int rx, ry, rxx, ryy; double prec;
int zone, found;
double Ng;
zone = 5; // Slovenia
fl.fi = gkzones[zone].fimin; fi_max = gkzones[zone].fimax; fi_inc = 0.1;
fl.la = gkzones[zone].lamin; la_max = gkzones[zone].lamax; la_inc = 0.1;
fl.h = 0; // height will be calculated at the end
xy.x = 0; xy.y = 0; xy.H = 0;
prec = 100000000.0; // maximum precision (1e-8)
rx = xllround(in.x*prec); ry = xllround(in.y*prec);
rxx = xllround(xy.x*prec); ryy = xllround(xy.y*prec);
found = 0;
for ( ; ; ) {
for ( ; fl.fi <= fi_max; fl.fi += fi_inc) {
for ( ; fl.la <= la_max; fl.la += la_inc) {
fila_ellips2xy(fl, &xy, oid);
ryy = xllround(xy.y*prec);
if ((ry - ryy) < 0) {
fl.la -= la_inc;
break;
}
else if (ry == ryy) break;
} // for fl.la
rxx = xllround(xy.x*prec);
if ((rx - rxx) < 0) {
fl.fi -= fi_inc;
break;
}
else if (rx == rxx) break;
} // for fl.fi
if (ry == ryy && rx == rxx) { found = 1; break; }
fi_inc /= 10.0; la_inc /= 10.0; // increase precision for next round
if (fi_inc < 1e-18 || la_inc < 1e-18) break;
} // outer loop
fila_ellips2xy(fl, &xy, oid);
out->fi = fl.fi; out->la = fl.la;
if (oid == 1 || oid == 2) //wgs84/etrs89
Ng = geoid_height(out->fi, out->la, gid_wgs); //slo2000/egm2008
else //bessel
Ng = geoid_height(out->fi, out->la, 0); //bessel
out->Ng = Ng;
// Geoid height
out->h = in.H + Ng;
return found;
} /* xy2fila_ellips_loop */
// ----------------------------------------------------------------------------
// fila_ellips2xy_loop (height calculated from geoid)
// ----------------------------------------------------------------------------
// Transform from fi,la,h to GK/TM x,y,H coordinates on specified ellipsoid
// using loop search over coordinates
// ----------------------------------------------------------------------------
// Ellipsoid: 0: bessel, 1: wgs84, 2: etrs89
int fila_ellips2xy_loop(GEOGRA in, GEOUTM *out, int oid)
{
GEOUTM xy; GEOGRA fl;
double x_max, x_inc;
double y_max, y_inc;
long long int rfi, rla, rxfi, rxla; double prec;
int zone, found;
double Ng;
if (oid == 1 || oid == 2) //wgs84/etrs89
Ng = geoid_height(in.fi, in.la, gid_wgs); //slo2000/egm2008
else //bessel
Ng = geoid_height(in.fi, in.la, 0); //bessel
out->Ng = Ng;
zone = 5; // Slovenia
xy.x = gkzones[zone].xmin; x_max = gkzones[zone].xmax; x_inc = 10000;
xy.y = gkzones[zone].ymin; y_max = gkzones[zone].ymax; y_inc = 10000;
xy.H = 0; // height will be calculated at the end
fl.fi = 0; fl.la = 0; fl.h = 0.0;
prec = 100000000.0; // maximum precision (1e-8)
rfi = xllround(in.fi*prec); rla = xllround(in.la*prec);
rxfi = xllround(fl.fi*prec); rxla = xllround(fl.la*prec);
found = 0;
for ( ; ; ) {
for ( ; xy.x <= x_max; xy.x += x_inc) {
for ( ; xy.y <= y_max; xy.y += y_inc) {
xy2fila_ellips(xy, &fl, oid);
rxla = xllround(fl.la*prec);
if ((rla - rxla) < 0) {
xy.y -= y_inc;
break;
}
else if (rla == rxla) break;
} // for xy.y
rxfi = xllround(fl.fi*prec);
if ((rfi - rxfi) < 0) {
xy.x -= x_inc;
break;
}
else if (rfi == rxfi) break;