Program Listing for File conversions.h
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/* Taken from utexas-art-ros-pkg:art_vehicle/applanix */
/*
* Conversions between coordinate systems.
*
* Includes LatLong<->UTM.
*/
#ifndef _UTM_H
#define _UTM_H
#include <cmath>
#include <cstdio>
#include <cstdlib>
namespace gps_tools
{
const double RADIANS_PER_DEGREE = M_PI/180.0;
const double DEGREES_PER_RADIAN = 180.0/M_PI;
// WGS84 Parameters
const double WGS84_A = 6378137.0; // major axis
const double WGS84_B = 6356752.31424518; // minor axis
const double WGS84_F = 0.0033528107; // ellipsoid flattening
const double WGS84_E = 0.0818191908; // first eccentricity
const double WGS84_EP = 0.0820944379; // second eccentricity
// UTM Parameters
const double UTM_K0 = 0.9996; // scale factor
const double UTM_FE = 500000.0; // false easting
const double UTM_FN_N = 0.0; // false northing on north hemisphere
const double UTM_FN_S = 10000000.0; // false northing on south hemisphere
const double UTM_E2 = (WGS84_E*WGS84_E); // e^2
const double UTM_E4 = (UTM_E2*UTM_E2); // e^4
const double UTM_E6 = (UTM_E4*UTM_E2); // e^6
const double UTM_EP2 = (UTM_E2/(1-UTM_E2)); // e'^2
static inline void UTM(double lat, double lon, double *x, double *y)
{
// constants
const static double m0 = (1 - UTM_E2/4 - 3*UTM_E4/64 - 5*UTM_E6/256);
const static double m1 = -(3*UTM_E2/8 + 3*UTM_E4/32 + 45*UTM_E6/1024);
const static double m2 = (15*UTM_E4/256 + 45*UTM_E6/1024);
const static double m3 = -(35*UTM_E6/3072);
// compute the central meridian
int cm = ((lon >= 0.0)
? ((int)lon - ((int)lon)%6 + 3)
: ((int)lon - ((int)lon)%6 - 3));
// convert degrees into radians
double rlat = lat * RADIANS_PER_DEGREE;
double rlon = lon * RADIANS_PER_DEGREE;
double rlon0 = cm * RADIANS_PER_DEGREE;
// compute trigonometric functions
double slat = sin(rlat);
double clat = cos(rlat);
double tlat = tan(rlat);
// decide the false northing at origin
double fn = (lat > 0) ? UTM_FN_N : UTM_FN_S;
double T = tlat * tlat;
double C = UTM_EP2 * clat * clat;
double A = (rlon - rlon0) * clat;
double M = WGS84_A * (m0*rlat + m1*sin(2*rlat)
+ m2*sin(4*rlat) + m3*sin(6*rlat));
double V = WGS84_A / sqrt(1 - UTM_E2*slat*slat);
// compute the easting-northing coordinates
*x = UTM_FE + UTM_K0 * V * (A + (1-T+C)*pow(A,3)/6
+ (5-18*T+T*T+72*C-58*UTM_EP2)*pow(A,5)/120);
*y = fn + UTM_K0 * (M + V * tlat * (A*A/2
+ (5-T+9*C+4*C*C)*pow(A,4)/24
+ ((61-58*T+T*T+600*C-330*UTM_EP2)
* pow(A,6)/720)));
return;
}
static inline char UTMLetterDesignator(double Lat)
{
char LetterDesignator;
if ((84 >= Lat) && (Lat >= 72)) LetterDesignator = 'X';
else if ((72 > Lat) && (Lat >= 64)) LetterDesignator = 'W';
else if ((64 > Lat) && (Lat >= 56)) LetterDesignator = 'V';
else if ((56 > Lat) && (Lat >= 48)) LetterDesignator = 'U';
else if ((48 > Lat) && (Lat >= 40)) LetterDesignator = 'T';
else if ((40 > Lat) && (Lat >= 32)) LetterDesignator = 'S';
else if ((32 > Lat) && (Lat >= 24)) LetterDesignator = 'R';
else if ((24 > Lat) && (Lat >= 16)) LetterDesignator = 'Q';
else if ((16 > Lat) && (Lat >= 8)) LetterDesignator = 'P';
else if (( 8 > Lat) && (Lat >= 0)) LetterDesignator = 'N';
else if (( 0 > Lat) && (Lat >= -8)) LetterDesignator = 'M';
else if ((-8 > Lat) && (Lat >= -16)) LetterDesignator = 'L';
else if((-16 > Lat) && (Lat >= -24)) LetterDesignator = 'K';
else if((-24 > Lat) && (Lat >= -32)) LetterDesignator = 'J';
else if((-32 > Lat) && (Lat >= -40)) LetterDesignator = 'H';
else if((-40 > Lat) && (Lat >= -48)) LetterDesignator = 'G';
else if((-48 > Lat) && (Lat >= -56)) LetterDesignator = 'F';
else if((-56 > Lat) && (Lat >= -64)) LetterDesignator = 'E';
else if((-64 > Lat) && (Lat >= -72)) LetterDesignator = 'D';
else if((-72 > Lat) && (Lat >= -80)) LetterDesignator = 'C';
// 'Z' is an error flag, the Latitude is outside the UTM limits
else LetterDesignator = 'Z';
return LetterDesignator;
}
static inline void LLtoUTM(const double Lat, const double Long,
double &UTMNorthing, double &UTMEasting,
char* UTMZone)
{
double a = WGS84_A;
double eccSquared = UTM_E2;
double k0 = UTM_K0;
double LongOrigin;
double eccPrimeSquared;
double N, T, C, A, M;
//Make sure the longitude is between -180.00 .. 179.9
double LongTemp = (Long+180)-int((Long+180)/360)*360-180;
double LatRad = Lat*RADIANS_PER_DEGREE;
double LongRad = LongTemp*RADIANS_PER_DEGREE;
double LongOriginRad;
int ZoneNumber;
ZoneNumber = int((LongTemp + 180)/6) + 1;
if( Lat >= 56.0 && Lat < 64.0 && LongTemp >= 3.0 && LongTemp < 12.0 )
ZoneNumber = 32;
// Special zones for Svalbard
if( Lat >= 72.0 && Lat < 84.0 )
{
if( LongTemp >= 0.0 && LongTemp < 9.0 ) ZoneNumber = 31;
else if( LongTemp >= 9.0 && LongTemp < 21.0 ) ZoneNumber = 33;
else if( LongTemp >= 21.0 && LongTemp < 33.0 ) ZoneNumber = 35;
else if( LongTemp >= 33.0 && LongTemp < 42.0 ) ZoneNumber = 37;
}
// +3 puts origin in middle of zone
LongOrigin = (ZoneNumber - 1)*6 - 180 + 3;
LongOriginRad = LongOrigin * RADIANS_PER_DEGREE;
//compute the UTM Zone from the latitude and longitude
snprintf(UTMZone, 13, "%d%c", ZoneNumber, UTMLetterDesignator(Lat));
eccPrimeSquared = (eccSquared)/(1-eccSquared);
N = a/sqrt(1-eccSquared*sin(LatRad)*sin(LatRad));
T = tan(LatRad)*tan(LatRad);
C = eccPrimeSquared*cos(LatRad)*cos(LatRad);
A = cos(LatRad)*(LongRad-LongOriginRad);
M = a*((1 - eccSquared/4 - 3*eccSquared*eccSquared/64 - 5*eccSquared*eccSquared*eccSquared/256)*LatRad
- (3*eccSquared/8 + 3*eccSquared*eccSquared/32 + 45*eccSquared*eccSquared*eccSquared/1024)*sin(2*LatRad)
+ (15*eccSquared*eccSquared/256 + 45*eccSquared*eccSquared*eccSquared/1024)*sin(4*LatRad)
- (35*eccSquared*eccSquared*eccSquared/3072)*sin(6*LatRad));
UTMEasting = (double)(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);
UTMNorthing = (double)(k0*(M+N*tan(LatRad)*(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)));
if(Lat < 0)
UTMNorthing += 10000000.0; //10000000 meter offset for southern hemisphere
}
static inline void LLtoUTM(const double Lat, const double Long,
double &UTMNorthing, double &UTMEasting,
std::string &UTMZone) {
char zone_buf[13] = {0};
LLtoUTM(Lat, Long, UTMNorthing, UTMEasting, zone_buf);
UTMZone = zone_buf;
}
static inline void UTMtoLL(const double UTMNorthing, const double UTMEasting,
const char* UTMZone, double& Lat, double& Long )
{
double k0 = UTM_K0;
double a = WGS84_A;
double eccSquared = UTM_E2;
double eccPrimeSquared;
double e1 = (1-sqrt(1-eccSquared))/(1+sqrt(1-eccSquared));
double N1, T1, C1, R1, D, M;
double LongOrigin;
double mu, phi1Rad;
double x, y;
int ZoneNumber;
char* ZoneLetter;
x = UTMEasting - 500000.0; //remove 500,000 meter offset for longitude
y = UTMNorthing;
ZoneNumber = strtoul(UTMZone, &ZoneLetter, 10);
if((*ZoneLetter - 'N') < 0)
{
y -= 10000000.0;//remove 10,000,000 meter offset used for southern hemisphere
}
LongOrigin = (ZoneNumber - 1)*6 - 180 + 3; //+3 puts origin in middle of zone
eccPrimeSquared = (eccSquared)/(1-eccSquared);
M = y / k0;
mu = M/(a*(1-eccSquared/4-3*eccSquared*eccSquared/64-5*eccSquared*eccSquared*eccSquared/256));
phi1Rad = 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);
N1 = a/sqrt(1-eccSquared*sin(phi1Rad)*sin(phi1Rad));
T1 = tan(phi1Rad)*tan(phi1Rad);
C1 = eccPrimeSquared*cos(phi1Rad)*cos(phi1Rad);
R1 = a*(1-eccSquared)/pow(1-eccSquared*sin(phi1Rad)*sin(phi1Rad), 1.5);
D = x/(N1*k0);
Lat = phi1Rad - (N1*tan(phi1Rad)/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);
Lat = Lat * DEGREES_PER_RADIAN;
Long = (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(phi1Rad);
Long = LongOrigin + Long * DEGREES_PER_RADIAN;
}
static inline void UTMtoLL(const double UTMNorthing, const double UTMEasting,
std::string UTMZone, double& Lat, double& Long) {
UTMtoLL(UTMNorthing, UTMEasting, UTMZone.c_str(), Lat, Long);
}
} // end namespace UTM
#endif // _UTM_H