448 lines
14 KiB
C
448 lines
14 KiB
C
//
|
|
// Created by villuton on 24.03.25.
|
|
//
|
|
#include "Nmea0183_Math.h"
|
|
#include "Nmea0183Parser_Private.h"
|
|
#include <math.h>
|
|
|
|
/**
|
|
* \struct tNmeaMathPos
|
|
* \brief Position data in fractional degrees or radians
|
|
*/
|
|
typedef struct {
|
|
double lat;
|
|
double lon;
|
|
}tNmeaMathPos;
|
|
|
|
/**
|
|
* \fn nmeaDegreeToRadian
|
|
* \brief Convert degree to radian
|
|
*/
|
|
double nmeaDegreeToRadian(double val)
|
|
{ return (val * NMEA_PI180); }
|
|
|
|
/**
|
|
* \fn nmeaRadianToDegree
|
|
* \brief Convert radian to degree
|
|
*/
|
|
double nmeaRadianToDegree(double val)
|
|
{ return (val / NMEA_PI180); }
|
|
|
|
/**
|
|
* \fn nmeaNdegToDegree
|
|
* \brief Convert NDEG (NMEA degree) to fractional degree
|
|
*/
|
|
double nmeaNdegToDegree(double val)
|
|
{
|
|
double deg = ((int)(val / 100));
|
|
val = deg + (val - deg * 100) / 60;
|
|
return val;
|
|
}
|
|
|
|
/**
|
|
* \fn nmeaDegreeToNdeg
|
|
* \brief Convert fractional degree to NDEG (NMEA degree)
|
|
*/
|
|
double nmeaDegreeToNdeg(double val)
|
|
{
|
|
double int_part;
|
|
double fra_part;
|
|
fra_part = modf(val, &int_part);
|
|
val = int_part * 100 + fra_part * 60;
|
|
return val;
|
|
}
|
|
|
|
/**
|
|
* \fn nmeaNdegToRadian
|
|
* \brief Convert NDEG (NMEA degree) to radian
|
|
*/
|
|
double nmeaNdegToRadian(double val)
|
|
{ return nmeaDegreeToRadian(nmeaNdegToDegree(val)); }
|
|
|
|
/**
|
|
* \fn nmeaRadianToNdeg
|
|
* \brief Convert radian to NDEG (NMEA degree)
|
|
*/
|
|
double nmeaRadianToNdeg(double val)
|
|
{ return nmeaDegreeToNdeg(nmeaRadianToDegree(val)); }
|
|
|
|
/**
|
|
* \fn nmeaCalcPdop
|
|
* \brief Calculate PDOP (Position Dilution Of Precision) factor
|
|
*/
|
|
double nmeaCalcPdop(double hdop, double vdop)
|
|
{
|
|
return sqrt(pow(hdop, 2) + pow(vdop, 2));
|
|
}
|
|
|
|
/**
|
|
* \fn nmeaDopToMeters
|
|
* \brief Calculate DOP to meters
|
|
*/
|
|
double nmeaDopToMeters(double dop)
|
|
{ return (dop * NMEA_DOP_FACTOR); }
|
|
|
|
/**
|
|
* \fn nmeaMetersToDop
|
|
* \brief Calculate meters to DOP
|
|
*/
|
|
double nmeaMetersToDop(double meters)
|
|
{ return (meters / NMEA_DOP_FACTOR); }
|
|
|
|
/**
|
|
* \fn nmeaCalcDistance
|
|
* \brief Calculate distance between two points
|
|
* @param from_pos_lat < From position latitude in radians
|
|
* @param from_pos_lon < From position longitude in radians
|
|
* @param to_pos_lat < To position latitude in radians
|
|
* @param to_pos_lon < To position longitude in radians
|
|
* @return Distance in meters
|
|
*/
|
|
double nmeaCalcDistance(
|
|
const double *from_pos_lat, // /**< From position latitude in radians */
|
|
const double *from_pos_lon, // /**< From position longitude in radians */
|
|
const double *to_pos_lat, // /**< To position latitude in radians */
|
|
const double *to_pos_lon // /**< To position longitude in radians */
|
|
)
|
|
{
|
|
tNmeaMathPos from_pos = {
|
|
.lat = *from_pos_lat,
|
|
.lon = *from_pos_lon
|
|
};
|
|
tNmeaMathPos to_pos = {
|
|
.lat = *to_pos_lat,
|
|
.lon = *to_pos_lon
|
|
};
|
|
double dist = ((double)NMEA_EARTHRADIUS_M) * acos(
|
|
sin(to_pos.lat) * sin(from_pos.lat) +
|
|
cos(to_pos.lat) * cos(from_pos.lat) * cos(to_pos.lon - from_pos.lon)
|
|
);
|
|
return dist;
|
|
}
|
|
|
|
/**
|
|
* \fn nmeaCalcDistanceEllipsoid
|
|
* \brief Calculate distance between two points
|
|
* This function uses an algorithm for an oblate spheroid earth model.
|
|
* The algorithm is described here:
|
|
* http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
|
|
* @param from_pos_lat < From position latitude in radians
|
|
* @param from_pos_lon < From position longitude in radians
|
|
* @param to_pos_lat < To position latitude in radians
|
|
* @param to_pos_lon < To position longitude in radians
|
|
* @param from_azimuth < (O) azimuth at "from" position in radians
|
|
* @param to_azimuth < (O) azimuth at "to" position in radians
|
|
* @return Distance in meters
|
|
*/
|
|
double nmeaCalcDistanceEllipsoid(
|
|
const double *from_pos_lat, // /**< From position latitude in radians */
|
|
const double *from_pos_lon, // /**< From position longitude in radians */
|
|
const double *to_pos_lat, // /**< To position latitude in radians */
|
|
const double *to_pos_lon, // /**< To position longitude in radians */
|
|
double *from_azimuth, // /**< (O) azimuth at "from" position in radians */
|
|
double *to_azimuth // /**< (O) azimuth at "to" position in radians */
|
|
)
|
|
{
|
|
/* All variables */
|
|
tNmeaMathPos from_pos = {
|
|
.lat = *from_pos_lat,
|
|
.lon = *from_pos_lon
|
|
};
|
|
tNmeaMathPos to_pos = {
|
|
.lat = *to_pos_lat,
|
|
.lon = *to_pos_lon
|
|
};
|
|
double f, a, b, sqr_a, sqr_b;
|
|
double L, phi1, phi2, U1, U2, sin_U1, sin_U2, cos_U1, cos_U2;
|
|
double sigma, sin_sigma, cos_sigma, cos_2_sigmam, sqr_cos_2_sigmam, sqr_cos_alpha, lambda, sin_lambda, cos_lambda, delta_lambda;
|
|
int remaining_steps;
|
|
double sqr_u, A, B, delta_sigma;
|
|
|
|
/* Check input */
|
|
NMEA_ASSERT(from_pos_lat != NULL)
|
|
NMEA_ASSERT(from_pos_lon != NULL)
|
|
|
|
NMEA_ASSERT(to_pos_lat != NULL)
|
|
NMEA_ASSERT(to_pos_lon != NULL)
|
|
|
|
|
|
if ((from_pos.lat == to_pos.lat) && (from_pos.lon == to_pos.lon))
|
|
{ /* Identical points */
|
|
if ( from_azimuth != 0 )
|
|
*from_azimuth = 0;
|
|
if ( to_azimuth != 0 )
|
|
*to_azimuth = 0;
|
|
return 0;
|
|
} /* Identical points */
|
|
|
|
/* Earth geometry */
|
|
f = NMEA_EARTH_FLATTENING;
|
|
a = NMEA_EARTH_SEMIMAJORAXIS_M;
|
|
b = (1 - f) * a;
|
|
sqr_a = a * a;
|
|
sqr_b = b * b;
|
|
|
|
/* Calculation */
|
|
L = to_pos.lon - from_pos.lon;
|
|
phi1 = from_pos.lat;
|
|
phi2 = to_pos.lat;
|
|
U1 = atan((1 - f) * tan(phi1));
|
|
U2 = atan((1 - f) * tan(phi2));
|
|
sin_U1 = sin(U1);
|
|
sin_U2 = sin(U2);
|
|
cos_U1 = cos(U1);
|
|
cos_U2 = cos(U2);
|
|
|
|
/* Initialize iteration */
|
|
sigma = 0;
|
|
sin_sigma = sin(sigma);
|
|
cos_sigma = cos(sigma);
|
|
cos_2_sigmam = 0;
|
|
sqr_cos_2_sigmam = cos_2_sigmam * cos_2_sigmam;
|
|
sqr_cos_alpha = 0;
|
|
lambda = L;
|
|
sin_lambda = sin(lambda);
|
|
cos_lambda = cos(lambda);
|
|
delta_lambda = lambda;
|
|
remaining_steps = 20;
|
|
|
|
while ((delta_lambda > 1e-12) && (remaining_steps > 0))
|
|
{ /* Iterate */
|
|
/* Variables */
|
|
double tmp1, tmp2, sin_alpha, cos_alpha, C, lambda_prev;
|
|
|
|
/* Calculation */
|
|
tmp1 = cos_U2 * sin_lambda;
|
|
tmp2 = cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda;
|
|
sin_sigma = sqrt(tmp1 * tmp1 + tmp2 * tmp2);
|
|
cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda;
|
|
sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma;
|
|
cos_alpha = cos(asin(sin_alpha));
|
|
sqr_cos_alpha = cos_alpha * cos_alpha;
|
|
cos_2_sigmam = cos_sigma - 2 * sin_U1 * sin_U2 / sqr_cos_alpha;
|
|
sqr_cos_2_sigmam = cos_2_sigmam * cos_2_sigmam;
|
|
C = f / 16 * sqr_cos_alpha * (4 + f * (4 - 3 * sqr_cos_alpha));
|
|
lambda_prev = lambda;
|
|
sigma = asin(sin_sigma);
|
|
lambda = L +
|
|
(1 - C) * f * sin_alpha
|
|
* (sigma + C * sin_sigma * (cos_2_sigmam + C * cos_sigma * (-1 + 2 * sqr_cos_2_sigmam)));
|
|
delta_lambda = lambda_prev - lambda;
|
|
if ( delta_lambda < 0 ) delta_lambda = -delta_lambda;
|
|
sin_lambda = sin(lambda);
|
|
cos_lambda = cos(lambda);
|
|
remaining_steps--;
|
|
} /* Iterate */
|
|
|
|
/* More calculation */
|
|
sqr_u = sqr_cos_alpha * (sqr_a - sqr_b) / sqr_b;
|
|
A = 1 + sqr_u / 16384 * (4096 + sqr_u * (-768 + sqr_u * (320 - 175 * sqr_u)));
|
|
B = sqr_u / 1024 * (256 + sqr_u * (-128 + sqr_u * (74 - 47 * sqr_u)));
|
|
delta_sigma = B * sin_sigma * (
|
|
cos_2_sigmam + B / 4 * (
|
|
cos_sigma * (-1 + 2 * sqr_cos_2_sigmam) -
|
|
B / 6 * cos_2_sigmam * (-3 + 4 * sin_sigma * sin_sigma) * (-3 + 4 * sqr_cos_2_sigmam)
|
|
));
|
|
|
|
/* Calculate result */
|
|
if ( from_azimuth != 0 )
|
|
{
|
|
double tan_alpha_1 = cos_U2 * sin_lambda / (cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda);
|
|
*from_azimuth = atan(tan_alpha_1);
|
|
}
|
|
if ( to_azimuth != 0 )
|
|
{
|
|
double tan_alpha_2 = cos_U1 * sin_lambda / (-sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda);
|
|
*to_azimuth = atan(tan_alpha_2);
|
|
}
|
|
|
|
return b * A * (sigma - delta_sigma);
|
|
}
|
|
|
|
/**
|
|
* \fn nmeaMoveHorz
|
|
* \brief Horizontal move of point position
|
|
* @param start_pos_lat < Start position latitude in radians
|
|
* @param start_pos_lon < Start position longitude in radians
|
|
* @param end_pos_lat < Result position latitude in radians
|
|
* @param end_pos_lon < Result position longitude in radians
|
|
* @param azimuth < Azimuth (degree) [0, 359]
|
|
* @param distance < Distance (km)
|
|
* @return
|
|
*/
|
|
int nmeaMoveHorz(
|
|
const double *start_pos_lat, // /**< Start position latitude in radians */
|
|
const double *start_pos_lon, // /**< Start position longitude in radians */
|
|
double *end_pos_lat, // /**< Result position latitude in radians */
|
|
double *end_pos_lon, // /**< Result position longitude in radians */
|
|
double azimuth, // /**< Azimuth (degree) [0, 359] */
|
|
double distance // /**< Distance (km) */
|
|
)
|
|
{
|
|
tNmeaMathPos p1 = {
|
|
.lat = *start_pos_lat,
|
|
.lon = *start_pos_lon
|
|
};
|
|
int RetVal = 1;
|
|
|
|
distance /= NMEA_EARTHRADIUS_KM; /* Angular distance covered on earth's surface */
|
|
azimuth = nmeaDegreeToRadian(azimuth);
|
|
|
|
*end_pos_lat = asin(
|
|
sin(p1.lat) * cos(distance) + cos(p1.lat) * sin(distance) * cos(azimuth));
|
|
*end_pos_lon = p1.lon + atan2(
|
|
sin(azimuth) * sin(distance) * cos(p1.lat), cos(distance) - sin(p1.lat) * sin(*end_pos_lat));
|
|
|
|
if(isnan(*end_pos_lat) || isnan(*end_pos_lon))
|
|
{
|
|
*end_pos_lat = 0; *end_pos_lon = 0;
|
|
RetVal = 0;
|
|
}
|
|
|
|
return RetVal;
|
|
}
|
|
|
|
/**
|
|
*
|
|
* \brief Horizontal move of point position
|
|
* This function uses an algorithm for an oblate spheroid earth model.
|
|
* The algorithm is described here:
|
|
* http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
|
|
* @param start_pos_lat < Start position latitude in radians
|
|
* @param start_pos_lon < Start position longitude in radians
|
|
* @param end_pos_lat < (O) Result position latitude in radians
|
|
* @param end_pos_lon < (O) Result position longitude in radians
|
|
* @param azimuth < Azimuth in radians
|
|
* @param distance < Distance (km)
|
|
* @param end_azimuth < (O) Azimuth at end position in radians
|
|
* @return
|
|
*/
|
|
int nmeaMoveHorzEllipsoid(
|
|
const double *start_pos_lat, // /**< Start position latitude in radians */
|
|
const double *start_pos_lon, // /**< Start position longitude in radians */
|
|
double *end_pos_lat, // /**< (O) Result position latitude in radians */
|
|
double *end_pos_lon, // /**< (O) Result position longitude in radians */
|
|
double azimuth, // /**< Azimuth in radians */
|
|
double distance, // /**< Distance (km) */
|
|
double *end_azimuth // /**< (O) Azimuth at end position in radians */
|
|
)
|
|
{
|
|
/* Variables */
|
|
double f, a, b, sqr_a, sqr_b;
|
|
double phi1, tan_U1, sin_U1, cos_U1, s, alpha1, sin_alpha1, cos_alpha1;
|
|
double sigma1, sin_alpha, sqr_cos_alpha, sqr_u, A, B;
|
|
double sigma_initial, sigma, sigma_prev, sin_sigma, cos_sigma, cos_2_sigmam, sqr_cos_2_sigmam, delta_sigma;
|
|
int remaining_steps;
|
|
double tmp1, phi2, lambda, C, L;
|
|
|
|
/* Check input */
|
|
NMEA_ASSERT(start_pos_lat != NULL)
|
|
NMEA_ASSERT(start_pos_lon != NULL)
|
|
NMEA_ASSERT(end_pos_lat != NULL)
|
|
NMEA_ASSERT(end_pos_lon != NULL)
|
|
|
|
if (fabs(distance) < 1e-12)
|
|
{ /* No move */
|
|
*end_pos_lat = *start_pos_lat;
|
|
*end_pos_lon = *start_pos_lon;
|
|
if ( end_azimuth != 0 ) *end_azimuth = azimuth;
|
|
return ! (isnan(*end_pos_lat) || isnan(*end_pos_lon));
|
|
} /* No move */
|
|
|
|
/* Earth geometry */
|
|
f = NMEA_EARTH_FLATTENING;
|
|
a = NMEA_EARTH_SEMIMAJORAXIS_M;
|
|
b = (1 - f) * a;
|
|
sqr_a = a * a;
|
|
sqr_b = b * b;
|
|
|
|
/* Calculation */
|
|
phi1 = *start_pos_lat;
|
|
tan_U1 = (1 - f) * tan(phi1);
|
|
cos_U1 = 1 / sqrt(1 + tan_U1 * tan_U1);
|
|
sin_U1 = tan_U1 * cos_U1;
|
|
s = distance;
|
|
alpha1 = azimuth;
|
|
sin_alpha1 = sin(alpha1);
|
|
cos_alpha1 = cos(alpha1);
|
|
sigma1 = atan2(tan_U1, cos_alpha1);
|
|
sin_alpha = cos_U1 * sin_alpha1;
|
|
sqr_cos_alpha = 1 - sin_alpha * sin_alpha;
|
|
sqr_u = sqr_cos_alpha * (sqr_a - sqr_b) / sqr_b;
|
|
A = 1 + sqr_u / 16384 * (4096 + sqr_u * (-768 + sqr_u * (320 - 175 * sqr_u)));
|
|
B = sqr_u / 1024 * (256 + sqr_u * (-128 + sqr_u * (74 - 47 * sqr_u)));
|
|
|
|
/* Initialize iteration */
|
|
sigma_initial = s / (b * A);
|
|
sigma = sigma_initial;
|
|
sin_sigma = sin(sigma);
|
|
cos_sigma = cos(sigma);
|
|
cos_2_sigmam = cos(2 * sigma1 + sigma);
|
|
sqr_cos_2_sigmam = cos_2_sigmam * cos_2_sigmam;
|
|
sigma_prev = 2 * NMEA_PI;
|
|
remaining_steps = 20;
|
|
|
|
while ((fabs(sigma - sigma_prev) > 1e-12) && (remaining_steps > 0))
|
|
{ /* Iterate */
|
|
cos_2_sigmam = cos(2 * sigma1 + sigma);
|
|
sqr_cos_2_sigmam = cos_2_sigmam * cos_2_sigmam;
|
|
sin_sigma = sin(sigma);
|
|
cos_sigma = cos(sigma);
|
|
delta_sigma = B * sin_sigma * (
|
|
cos_2_sigmam + B / 4 * (
|
|
cos_sigma * (-1 + 2 * sqr_cos_2_sigmam) -
|
|
B / 6 * cos_2_sigmam * (-3 + 4 * sin_sigma * sin_sigma) * (-3 + 4 * sqr_cos_2_sigmam)
|
|
));
|
|
sigma_prev = sigma;
|
|
sigma = sigma_initial + delta_sigma;
|
|
remaining_steps --;
|
|
} /* Iterate */
|
|
|
|
/* Calculate result */
|
|
tmp1 = (sin_U1 * sin_sigma - cos_U1 * cos_sigma * cos_alpha1);
|
|
phi2 = atan2(
|
|
sin_U1 * cos_sigma + cos_U1 * sin_sigma * cos_alpha1,
|
|
(1 - f) * sqrt(sin_alpha * sin_alpha + tmp1 * tmp1)
|
|
);
|
|
lambda = atan2(
|
|
sin_sigma * sin_alpha1,
|
|
cos_U1 * cos_sigma - sin_U1 * sin_sigma * cos_alpha1
|
|
);
|
|
C = f / 16 * sqr_cos_alpha * (4 + f * (4 - 3 * sqr_cos_alpha));
|
|
L = lambda -
|
|
(1 - C) * f * sin_alpha * (
|
|
sigma + C * sin_sigma *
|
|
(cos_2_sigmam + C * cos_sigma * (-1 + 2 * sqr_cos_2_sigmam))
|
|
);
|
|
|
|
/* Result */
|
|
*end_pos_lon = *start_pos_lon + L;
|
|
*end_pos_lat = phi2;
|
|
if ( end_azimuth != 0 )
|
|
{
|
|
*end_azimuth = atan2(
|
|
sin_alpha, -sin_U1 * sin_sigma + cos_U1 * cos_sigma * cos_alpha1
|
|
);
|
|
}
|
|
return ! (isnan(*end_pos_lat) || isnan(*end_pos_lon));
|
|
}
|
|
|
|
/** todo перонести в другой модуль */
|
|
|
|
///**
|
|
// * \brief Convert position from INFO to radians position
|
|
// */
|
|
//void nmeaInfoToPos(const nmeaINFO *info, const nmeaPOS *pos)
|
|
//{
|
|
// pos->lat = nmeaNdegToRadian(info->lat);
|
|
// pos->lon = nmeaNdegToRadian(info->lon);
|
|
//}
|
|
//
|
|
///**
|
|
// * \brief Convert radians position to INFOs position
|
|
// */
|
|
//void nmeaPosToInfo(const nmeaPOS *pos, const nmeaINFO *info)
|
|
//{
|
|
// info->lat = nmeaRadianToNdeg(pos->lat);
|
|
// info->lon = nmeaRadianToNdeg(pos->lon);
|
|
//}
|