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