robot_localization: navsat_conversions.h Source File

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00001 /*
00002 * Copyright (C) 2010 Austin Robot Technology, and others
00003 * All rights reserved.
00004 *
00005 * Redistribution and use in source and binary forms, with or without
00006 * modification, are permitted provided that the following conditions
00007 * are met:
00008 *
00009 * 1. Redistributions of source code must retain the above copyright
00010 * notice, this list of conditions and the following disclaimer.
00011 * 2. Redistributions in binary form must reproduce the above
00012 * copyright notice, this list of conditions and the following
00013 * disclaimer in the documentation and/or other materials provided
00014 * with the distribution.
00015 * 3. Neither the names of the University of Texas at Austin, nor
00016 * Austin Robot Technology, nor the names of other contributors may
00017 * be used to endorse or promote products derived from this
00018 * software without specific prior written permission.
00019 *
00020 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
00021 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
00022 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
00023 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
00024 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
00025 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
00026 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
00027 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
00028 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
00029 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
00030 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
00031 * POSSIBILITY OF SUCH DAMAGE.
00032 *
00033 * This file contains code from multiple files in the original
00034 * source. The originals can be found here:
00035 *
00036 * https://github.com/austin-robot/utexas-art-ros-pkg/blob/afd147a1eb944fc3dbd138574c39699813f797bf/stacks/art_vehicle/art_common/include/art/UTM.h
00037 * https://github.com/austin-robot/utexas-art-ros-pkg/blob/afd147a1eb944fc3dbd138574c39699813f797bf/stacks/art_vehicle/art_common/include/art/conversions.h
00038 */
00039 
00040 #ifndef ROBOT_LOCALIZATION_NAVSAT_CONVERSIONS_H
00041 #define ROBOT_LOCALIZATION_NAVSAT_CONVERSIONS_H
00042 
00051 #include <cmath>
00052 #include <string>
00053 
00054 #include <stdio.h>
00055 #include <stdlib.h>
00056 
00057 namespace RobotLocalization
00058 {
00059 namespace NavsatConversions
00060 {
00061 
00062 const double RADIANS_PER_DEGREE = M_PI/180.0;
00063 const double DEGREES_PER_RADIAN = 180.0/M_PI;
00064 
00065 // Grid granularity for rounding UTM coordinates to generate MapXY.
00066 const double grid_size = 100000.0;    // 100 km grid
00067 
00068 // WGS84 Parameters
00069 #define WGS84_A   6378137.0   // major axis
00070 #define WGS84_B   6356752.31424518  // minor axis
00071 #define WGS84_F   0.0033528107    // ellipsoid flattening
00072 #define WGS84_E   0.0818191908    // first eccentricity
00073 #define WGS84_EP  0.0820944379    // second eccentricity
00074 
00075 // UTM Parameters
00076 #define UTM_K0    0.9996               // scale factor
00077 #define UTM_FE    500000.0             // false easting
00078 #define UTM_FN_N  0.0                  // false northing, northern hemisphere
00079 #define UTM_FN_S  10000000.0           // false northing, southern hemisphere
00080 #define UTM_E2    (WGS84_E*WGS84_E)    // e^2
00081 #define UTM_E4    (UTM_E2*UTM_E2)      // e^4
00082 #define UTM_E6    (UTM_E4*UTM_E2)      // e^6
00083 #define UTM_EP2   (UTM_E2/(1-UTM_E2))  // e'^2
00084 
00094 static inline void UTM(double lat, double lon, double *x, double *y)
00095 {
00096   // constants
00097   static const double m0 = (1 - UTM_E2/4 - 3*UTM_E4/64 - 5*UTM_E6/256);
00098   static const double m1 = -(3*UTM_E2/8 + 3*UTM_E4/32 + 45*UTM_E6/1024);
00099   static const double m2 = (15*UTM_E4/256 + 45*UTM_E6/1024);
00100   static const double m3 = -(35*UTM_E6/3072);
00101 
00102   // compute the central meridian
00103   int cm = ((lon >= 0.0)
00104     ? (static_cast<int>(lon) - (static_cast<int>(lon)) % 6 + 3)
00105     : (static_cast<int>(lon) - (static_cast<int>(lon)) % 6 - 3));
00106 
00107   // convert degrees into radians
00108   double rlat = lat * RADIANS_PER_DEGREE;
00109   double rlon = lon * RADIANS_PER_DEGREE;
00110   double rlon0 = cm * RADIANS_PER_DEGREE;
00111 
00112   // compute trigonometric functions
00113   double slat = sin(rlat);
00114   double clat = cos(rlat);
00115   double tlat = tan(rlat);
00116 
00117   // decide the false northing at origin
00118   double fn = (lat > 0) ? UTM_FN_N : UTM_FN_S;
00119 
00120   double T = tlat * tlat;
00121   double C = UTM_EP2 * clat * clat;
00122   double A = (rlon - rlon0) * clat;
00123   double M = WGS84_A * (m0*rlat + m1*sin(2*rlat)
00124       + m2*sin(4*rlat) + m3*sin(6*rlat));
00125   double V = WGS84_A / sqrt(1 - UTM_E2*slat*slat);
00126 
00127   // compute the easting-northing coordinates
00128   *x = UTM_FE + UTM_K0 * V * (A + (1-T+C)*pow(A, 3)/6
00129             + (5-18*T+T*T+72*C-58*UTM_EP2)*pow(A, 5)/120);
00130   *y = fn + UTM_K0 * (M + V * tlat * (A*A/2
00131               + (5-T+9*C+4*C*C)*pow(A, 4)/24
00132               + ((61-58*T+T*T+600*C-330*UTM_EP2)
00133            * pow(A, 6)/720)));
00134 
00135   return;
00136 }
00137 
00138 
00147 static inline char UTMLetterDesignator(double Lat)
00148 {
00149   char LetterDesignator;
00150 
00151   if     ((84 >= Lat) && (Lat >= 72))  LetterDesignator = 'X';
00152   else if ((72 > Lat) && (Lat >= 64))  LetterDesignator = 'W';
00153   else if ((64 > Lat) && (Lat >= 56))  LetterDesignator = 'V';
00154   else if ((56 > Lat) && (Lat >= 48))  LetterDesignator = 'U';
00155   else if ((48 > Lat) && (Lat >= 40))  LetterDesignator = 'T';
00156   else if ((40 > Lat) && (Lat >= 32))  LetterDesignator = 'S';
00157   else if ((32 > Lat) && (Lat >= 24))  LetterDesignator = 'R';
00158   else if ((24 > Lat) && (Lat >= 16))  LetterDesignator = 'Q';
00159   else if ((16 > Lat) && (Lat >= 8))   LetterDesignator = 'P';
00160   else if (( 8 > Lat) && (Lat >= 0))   LetterDesignator = 'N';
00161   else if (( 0 > Lat) && (Lat >= -8))  LetterDesignator = 'M';
00162   else if ((-8 > Lat) && (Lat >= -16)) LetterDesignator = 'L';
00163   else if ((-16 > Lat) && (Lat >= -24)) LetterDesignator = 'K';
00164   else if ((-24 > Lat) && (Lat >= -32)) LetterDesignator = 'J';
00165   else if ((-32 > Lat) && (Lat >= -40)) LetterDesignator = 'H';
00166   else if ((-40 > Lat) && (Lat >= -48)) LetterDesignator = 'G';
00167   else if ((-48 > Lat) && (Lat >= -56)) LetterDesignator = 'F';
00168   else if ((-56 > Lat) && (Lat >= -64)) LetterDesignator = 'E';
00169   else if ((-64 > Lat) && (Lat >= -72)) LetterDesignator = 'D';
00170   else if ((-72 > Lat) && (Lat >= -80)) LetterDesignator = 'C';
00171         // 'Z' is an error flag, the Latitude is outside the UTM limits
00172   else LetterDesignator = 'Z';
00173   return LetterDesignator;
00174 }
00175 
00185 static inline void LLtoUTM(const double Lat, const double Long,
00186                            double &UTMNorthing, double &UTMEasting,
00187                            std::string &UTMZone)
00188 {
00189   double a = WGS84_A;
00190   double eccSquared = UTM_E2;
00191   double k0 = UTM_K0;
00192 
00193   double LongOrigin;
00194   double eccPrimeSquared;
00195   double N, T, C, A, M;
00196 
00197   // Make sure the longitude is between -180.00 .. 179.9
00198   double LongTemp = (Long+180)-static_cast<int>((Long+180)/360)*360-180;
00199 
00200   double LatRad = Lat*RADIANS_PER_DEGREE;
00201   double LongRad = LongTemp*RADIANS_PER_DEGREE;
00202   double LongOriginRad;
00203   int    ZoneNumber;
00204 
00205   ZoneNumber = static_cast<int>((LongTemp + 180)/6) + 1;
00206 
00207   if ( Lat >= 56.0 && Lat < 64.0 && LongTemp >= 3.0 && LongTemp < 12.0 )
00208     ZoneNumber = 32;
00209 
00210         // Special zones for Svalbard
00211   if ( Lat >= 72.0 && Lat < 84.0 )
00212   {
00213     if (      LongTemp >= 0.0  && LongTemp <  9.0 ) ZoneNumber = 31;
00214     else if ( LongTemp >= 9.0  && LongTemp < 21.0 ) ZoneNumber = 33;
00215     else if ( LongTemp >= 21.0 && LongTemp < 33.0 ) ZoneNumber = 35;
00216     else if ( LongTemp >= 33.0 && LongTemp < 42.0 ) ZoneNumber = 37;
00217   }
00218         // +3 puts origin in middle of zone
00219   LongOrigin = (ZoneNumber - 1)*6 - 180 + 3;
00220   LongOriginRad = LongOrigin * RADIANS_PER_DEGREE;
00221 
00222   // Compute the UTM Zone from the latitude and longitude
00223   char zone_buf[] = {0, 0, 0, 0};
00224   snprintf(zone_buf, sizeof(zone_buf), "%d%c", ZoneNumber, UTMLetterDesignator(Lat));
00225   UTMZone = std::string(zone_buf);
00226 
00227   eccPrimeSquared = (eccSquared)/(1-eccSquared);
00228 
00229   N = a/sqrt(1-eccSquared*sin(LatRad)*sin(LatRad));
00230   T = tan(LatRad)*tan(LatRad);
00231   C = eccPrimeSquared*cos(LatRad)*cos(LatRad);
00232   A = cos(LatRad)*(LongRad-LongOriginRad);
00233 
00234   M = a*((1 - eccSquared/4 - 3*eccSquared*eccSquared/64
00235                 - 5*eccSquared*eccSquared*eccSquared/256) * LatRad
00236                - (3*eccSquared/8 + 3*eccSquared*eccSquared/32
00237                   + 45*eccSquared*eccSquared*eccSquared/1024)*sin(2*LatRad)
00238                + (15*eccSquared*eccSquared/256
00239                   + 45*eccSquared*eccSquared*eccSquared/1024)*sin(4*LatRad)
00240                - (35*eccSquared*eccSquared*eccSquared/3072)*sin(6*LatRad));
00241 
00242   UTMEasting = static_cast<double>
00243           (k0*N*(A+(1-T+C)*A*A*A/6
00244                  + (5-18*T+T*T+72*C-58*eccPrimeSquared)*A*A*A*A*A/120)
00245            + 500000.0);
00246 
00247   UTMNorthing = static_cast<double>
00248           (k0*(M+N*tan(LatRad)
00249                *(A*A/2+(5-T+9*C+4*C*C)*A*A*A*A/24
00250                  + (61-58*T+T*T+600*C-330*eccPrimeSquared)*A*A*A*A*A*A/720)));
00251 
00252   if (Lat < 0)
00253           {
00254             // 10000000 meter offset for southern hemisphere
00255             UTMNorthing += 10000000.0;
00256           }
00257 }
00258 
00268 static inline void UTMtoLL(const double UTMNorthing, const double UTMEasting,
00269                            const std::string &UTMZone, double& Lat,  double& Long )
00270 {
00271   double k0 = UTM_K0;
00272   double a = WGS84_A;
00273   double eccSquared = UTM_E2;
00274   double eccPrimeSquared;
00275   double e1 = (1-sqrt(1-eccSquared))/(1+sqrt(1-eccSquared));
00276   double N1, T1, C1, R1, D, M;
00277   double LongOrigin;
00278   double mu, phi1Rad;
00279   double x, y;
00280   int ZoneNumber;
00281   char* ZoneLetter;
00282 
00283   x = UTMEasting - 500000.0;  // remove 500,000 meter offset for longitude
00284   y = UTMNorthing;
00285 
00286   ZoneNumber = strtoul(UTMZone.c_str(), &ZoneLetter, 10);
00287   if ((*ZoneLetter - 'N') < 0)
00288           {
00289             // remove 10,000,000 meter offset used for southern hemisphere
00290             y -= 10000000.0;
00291           }
00292 
00293   // +3 puts origin in middle of zone
00294   LongOrigin = (ZoneNumber - 1)*6 - 180 + 3;
00295   eccPrimeSquared = (eccSquared)/(1-eccSquared);
00296 
00297   M = y / k0;
00298   mu = M/(a*(1-eccSquared/4-3*eccSquared*eccSquared/64
00299                    -5*eccSquared*eccSquared*eccSquared/256));
00300 
00301   phi1Rad = mu + ((3*e1/2-27*e1*e1*e1/32)*sin(2*mu)
00302                         + (21*e1*e1/16-55*e1*e1*e1*e1/32)*sin(4*mu)
00303                         + (151*e1*e1*e1/96)*sin(6*mu));
00304 
00305   N1 = a/sqrt(1-eccSquared*sin(phi1Rad)*sin(phi1Rad));
00306   T1 = tan(phi1Rad)*tan(phi1Rad);
00307   C1 = eccPrimeSquared*cos(phi1Rad)*cos(phi1Rad);
00308   R1 = a*(1-eccSquared)/pow(1-eccSquared*sin(phi1Rad)*sin(phi1Rad), 1.5);
00309   D = x/(N1*k0);
00310 
00311   Lat = phi1Rad - ((N1*tan(phi1Rad)/R1)
00312                          *(D*D/2
00313                            -(5+3*T1+10*C1-4*C1*C1-9*eccPrimeSquared)*D*D*D*D/24
00314                            +(61+90*T1+298*C1+45*T1*T1-252*eccPrimeSquared
00315                              -3*C1*C1)*D*D*D*D*D*D/720));
00316 
00317   Lat = Lat * DEGREES_PER_RADIAN;
00318 
00319   Long = ((D-(1+2*T1+C1)*D*D*D/6
00320                  +(5-2*C1+28*T1-3*C1*C1+8*eccPrimeSquared+24*T1*T1)
00321                  *D*D*D*D*D/120)
00322                 / cos(phi1Rad));
00323   Long = LongOrigin + Long * DEGREES_PER_RADIAN;
00324 }
00325 
00326 }  // namespace NavsatConversions
00327 }  // namespace RobotLocalization
00328 
00329 #endif  // ROBOT_LOCALIZATION_NAVSAT_CONVERSIONS_H