src/coords.c

   1 /*
   2 coords.c
   3 borrowed from:
   4 http://acme.com/software/coords/
   5 I (Evan Battaglia <viking@greentorch.org>) have only made some small changes such as
   6 renaming functions and defining LatLon and UTM structs.
   7 2004-02-10 -- I also added a function of my own -- a_coords_utm_diff() -- that I felt belonged in coords.c
   8 2004-02-21 -- I also added a_coords_utm_equal().
   9 2005-11-23 -- Added a_coords_dtostr() for lack of a better place.
  10
  11 */
  12 /* coords.h - include file for coords routines
  13 **
  14 ** Copyright © 2001 by Jef Poskanzer <jef@acme.com>.
  15 ** All rights reserved.
  16 **
  17 ** Redistribution and use in source and binary forms, with or without
  18 ** modification, are permitted provided that the following conditions
  19 ** are met:
  20 ** 1. Redistributions of source code must retain the above copyright
  21 **    notice, this list of conditions and the following disclaimer.
  22 ** 2. Redistributions in binary form must reproduce the above copyright
  23 **    notice, this list of conditions and the following disclaimer in the
  24 **    documentation and/or other materials provided with the distribution.
  25 **
  26 ** THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  27 ** ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  28 ** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  29 ** ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  30 ** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  31 ** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  32 ** OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  33 ** HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  34 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  35 ** OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  36 ** SUCH DAMAGE.
  37 */
  38
  39 #include <stdlib.h>
  40 #include <string.h>
  41 #include <math.h>
  42
  43 #include "viking.h"
  44
  45 #ifdef WINDOWS
  46 #define M_PI 3.14159265358979
  47 #endif
  48
  49 /**
  50  * Convert a double to a string WITHOUT LOCALE.
  51  *
  52  * Following GPX specifications, decimal values are xsd:decimal
  53  * So, they must use the period separator, not the localized one.
  54  *
  55  * The returned value must be freed by g_free.
  56  */
  57 char *a_coords_dtostr ( double d )
  58 {
  59   /* In order to ignore locale, we do all the stuff manually */
  60   double integer, decimal;
  61   integer = trunc(d);
  62
  63   /* 6 decimals are sufficient (~0,1m) */
  64   /* Cf. http://www.tbs-sct.gc.ca/rpm-gbi/guides/Latlong_f.asp */
  65   decimal = d - integer;
  66   decimal = decimal * 1000000;
  67   decimal = trunc ( decimal );
  68   decimal = fabs ( decimal );
  69
  70   /* Format */
  71   return g_strdup_printf ( "%g.%06g", integer, decimal );
  72 }
  73
  74 #define PIOVER180 0.01745329252
  75
  76 #define K0 0.9996
  77
  78 /* WGS-84 */
  79 #define EquatorialRadius 6378137
  80 #define EccentricitySquared 0.00669438
  81
  82 static char coords_utm_letter( double latitude );
  83
  84 int a_coords_utm_equal( const struct UTM *utm1, const struct UTM *utm2 )
  85 {
  86   return ( utm1->easting == utm2->easting && utm1->northing == utm2->northing && utm1->zone == utm2->zone );
  87 }
  88
  89 double a_coords_utm_diff( const struct UTM *utm1, const struct UTM *utm2 )
  90 {
  91   static struct LatLon tmp1, tmp2;
  92   if ( utm1->zone == utm2->zone ) {
  93     return sqrt ( pow ( utm1->easting - utm2->easting, 2 ) + pow ( utm1->northing - utm2->northing, 2 ) );
  94   } else {
  95     a_coords_utm_to_latlon ( utm1, &tmp1 );
  96     a_coords_utm_to_latlon ( utm2, &tmp2 );
  97     return a_coords_latlon_diff ( &tmp1, &tmp2 );
  98   }
  99 }
 100
 101 double a_coords_latlon_diff ( const struct LatLon *ll1, const struct LatLon *ll2 )
 102 {
 103   static struct LatLon tmp1, tmp2;
 104   tmp1.lat = ll1->lat * PIOVER180;
 105   tmp1.lon = ll1->lon * PIOVER180;
 106   tmp2.lat = ll2->lat * PIOVER180;
 107   tmp2.lon = ll2->lon * PIOVER180;
 108   return EquatorialRadius * acos(sin(tmp1.lat)*sin(tmp2.lat)+cos(tmp1.lat)*cos(tmp2.lat)*cos(tmp1.lon-tmp2.lon));
 109 }
 110
 111 void a_coords_latlon_to_utm( const struct LatLon *latlon, struct UTM *utm )
 112     {
 113     double latitude;
 114     double longitude;
 115     double lat_rad, long_rad;
 116     double long_origin, long_origin_rad;
 117     double eccPrimeSquared;
 118     double N, T, C, A, M;
 119     int zone;
 120     double northing, easting;
 121
 122     longitude = latlon->lon;
 123     latitude = latlon->lat;
 124
 125     /* We want the longitude within -180..180. */
 126     if ( longitude < -180.0 )
 127         longitude += 360.0;
 128     if ( longitude > 180.0 )
 129         longitude -= 360.0;
 130
 131     /* Now convert. */
 132     lat_rad = latitude * M_PI / 180.0;
 133     long_rad = longitude * M_PI / 180.0;
 134     zone = (int) ( ( longitude + 180 ) / 6 ) + 1;
 135     if ( latitude >= 56.0 && latitude < 64.0 &&
 136          longitude >= 3.0 && longitude < 12.0 )
 137         zone = 32;
 138     /* Special zones for Svalbard. */
 139     if ( latitude >= 72.0 && latitude < 84.0 )
 140         {
 141         if      ( longitude >= 0.0  && longitude <  9.0 ) zone = 31;
 142         else if ( longitude >= 9.0  && longitude < 21.0 ) zone = 33;
 143         else if ( longitude >= 21.0 && longitude < 33.0 ) zone = 35;
 144         else if ( longitude >= 33.0 && longitude < 42.0 ) zone = 37;
 145         }
 146     long_origin = ( zone - 1 ) * 6 - 180 + 3;   /* +3 puts origin in middle of zone */
 147     long_origin_rad = long_origin * M_PI / 180.0;
 148     eccPrimeSquared = EccentricitySquared / ( 1.0 - EccentricitySquared );
 149     N = EquatorialRadius / sqrt( 1.0 - EccentricitySquared * sin( lat_rad ) * sin( lat_rad ) );
 150     T = tan( lat_rad ) * tan( lat_rad );
 151     C = eccPrimeSquared * cos( lat_rad ) * cos( lat_rad );
 152     A = cos( lat_rad ) * ( long_rad - long_origin_rad );
 153     M = EquatorialRadius * ( ( 1.0 - EccentricitySquared / 4 - 3 * EccentricitySquared * EccentricitySquared / 64 - 5 * EccentricitySquared * EccentricitySquared * EccentricitySquared / 256 ) * lat_rad - ( 3 * EccentricitySquared / 8 + 3 * EccentricitySquared * EccentricitySquared / 32 + 45 * EccentricitySquared * EccentricitySquared * EccentricitySquared / 1024 ) * sin( 2 * lat_rad ) + ( 15 * EccentricitySquared * EccentricitySquared / 256 + 45 * EccentricitySquared * EccentricitySquared * EccentricitySquared / 1024 ) * sin( 4 * lat_rad ) - ( 35 * EccentricitySquared * EccentricitySquared * EccentricitySquared / 3072 ) * sin( 6 * lat_rad ) );
 154     easting =
 155         K0 * N * ( A + ( 1 - T + C ) * A * A * A / 6 + ( 5 - 18 * T + T * T + 72 * C - 58 * eccPrimeSquared ) * A * A * A * A * A / 120 ) + 500000.0;
 156     northing =
 157         K0 * ( M + N * tan( lat_rad ) * ( A * A / 2 + ( 5 - T + 9 * C + 4 * C * C ) * A * A * A * A / 24 + ( 61 - 58 * T + T * T + 600 * C - 330 * eccPrimeSquared ) * A * A * A * A * A * A / 720 ) );
 158     if ( latitude < 0.0 )
 159         northing += 10000000.0;  /* 1e7 meter offset for southern hemisphere */
 160
 161     utm->northing = northing;
 162     utm->easting = easting;
 163     utm->zone = zone;
 164     utm->letter = coords_utm_letter( latitude );
 165
 166     /* All done. */
 167     }
 168
 169
 170 static char coords_utm_letter( double latitude )
 171     {
 172     /* This routine determines the correct UTM letter designator for the
 173     ** given latitude.  It returns 'Z' if the latitude is outside the UTM
 174     ** limits of 84N to 80S.
 175     */
 176     if ( latitude <= 84.0 && latitude >= 72.0 ) return 'X';
 177     else if ( latitude < 72.0 && latitude >= 64.0 ) return 'W';
 178     else if ( latitude < 64.0 && latitude >= 56.0 ) return 'V';
 179     else if ( latitude < 56.0 && latitude >= 48.0 ) return 'U';
 180     else if ( latitude < 48.0 && latitude >= 40.0 ) return 'T';
 181     else if ( latitude < 40.0 && latitude >= 32.0 ) return 'S';
 182     else if ( latitude < 32.0 && latitude >= 24.0 ) return 'R';
 183     else if ( latitude < 24.0 && latitude >= 16.0 ) return 'Q';
 184     else if ( latitude < 16.0 && latitude >= 8.0 ) return 'P';
 185     else if ( latitude <  8.0 && latitude >= 0.0 ) return 'N';
 186     else if ( latitude <  0.0 && latitude >= -8.0 ) return 'M';
 187     else if ( latitude < -8.0 && latitude >= -16.0 ) return 'L';
 188     else if ( latitude < -16.0 && latitude >= -24.0 ) return 'K';
 189     else if ( latitude < -24.0 && latitude >= -32.0 ) return 'J';
 190     else if ( latitude < -32.0 && latitude >= -40.0 ) return 'H';
 191     else if ( latitude < -40.0 && latitude >= -48.0 ) return 'G';
 192     else if ( latitude < -48.0 && latitude >= -56.0 ) return 'F';
 193     else if ( latitude < -56.0 && latitude >= -64.0 ) return 'E';
 194     else if ( latitude < -64.0 && latitude >= -72.0 ) return 'D';
 195     else if ( latitude < -72.0 && latitude >= -80.0 ) return 'C';
 196     else return 'Z';
 197     }
 198
 199
 200
 201 void a_coords_utm_to_latlon( const struct UTM *utm, struct LatLon *latlon )
 202     {
 203     double northing, easting;
 204     int zone;
 205     char letter[100];
 206     double x, y;
 207     double eccPrimeSquared;
 208     double e1;
 209     double N1, T1, C1, R1, D, M;
 210     double long_origin;
 211     double mu, phi1_rad;
 212     int northernHemisphere;     /* 1 for northern hemisphere, 0 for southern */
 213     double latitude, longitude;
 214
 215     northing = utm->northing;
 216     easting = utm->easting;
 217     zone = utm->zone;
 218     letter[0] = utm->letter;
 219
 220     /* Now convert. */
 221     x = easting - 500000.0;     /* remove 500000 meter offset */
 222     y = northing;
 223     if ( ( *letter - 'N' ) >= 0 )
 224         northernHemisphere = 1; /* northern hemisphere */
 225     else
 226         {
 227         northernHemisphere = 0; /* southern hemisphere */
 228         y -= 10000000.0;        /* remove 1e7 meter offset */
 229         }
 230     long_origin = ( zone - 1 ) * 6 - 180 + 3;   /* +3 puts origin in middle of zone */
 231     eccPrimeSquared = EccentricitySquared / ( 1.0 - EccentricitySquared );
 232     e1 = ( 1.0 - sqrt( 1.0 - EccentricitySquared ) ) / ( 1.0 + sqrt( 1.0 - EccentricitySquared ) );
 233     M = y / K0;
 234     mu = M / ( EquatorialRadius * ( 1.0 - EccentricitySquared / 4 - 3 * EccentricitySquared * EccentricitySquared / 64 - 5 * EccentricitySquared * EccentricitySquared * EccentricitySquared / 256 ) );
 235     phi1_rad = mu + ( 3 * e1 / 2 - 27 * e1 * e1 * e1 / 32 )* sin( 2 * mu ) + ( 21 * e1 * e1 / 16 - 55 * e1 * e1 * e1 * e1 / 32 ) * sin( 4 * mu ) + ( 151 * e1 * e1 * e1 / 96 ) * sin( 6 *mu );
 236     N1 = EquatorialRadius / sqrt( 1.0 - EccentricitySquared * sin( phi1_rad ) * sin( phi1_rad ) );
 237     T1 = tan( phi1_rad ) * tan( phi1_rad );
 238     C1 = eccPrimeSquared * cos( phi1_rad ) * cos( phi1_rad );
 239     R1 = EquatorialRadius * ( 1.0 - EccentricitySquared ) / pow( 1.0 - EccentricitySquared * sin( phi1_rad ) * sin( phi1_rad ), 1.5 );
 240     D = x / ( N1 * K0 );
 241     latitude = phi1_rad - ( N1 * tan( phi1_rad ) / R1 ) * ( D * D / 2 -( 5 + 3 * T1 + 10 * C1 - 4 * C1 * C1 - 9 * eccPrimeSquared ) * D * D * D * D / 24 + ( 61 + 90 * T1 + 298 * C1 + 45 * T1 * T1 - 252 * eccPrimeSquared - 3 * C1 * C1 ) * D * D * D * D * D * D / 720 );
 242     latitude = latitude * 180.0 / M_PI;
 243     longitude = ( D - ( 1 + 2 * T1 + C1 ) * D * D * D / 6 + ( 5 - 2 * C1 + 28 * T1 - 3 * C1 * C1 + 8 * eccPrimeSquared + 24 * T1 * T1 ) * D * D * D * D * D / 120 ) / cos( phi1_rad );
 244     longitude = long_origin + longitude * 180.0 / M_PI;
 245
 246     /* Show results. */
 247
 248     latlon->lat = latitude;
 249     latlon->lon = longitude;
 250
 251     }