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Merge branch 'master' of github.com:pixhawk/Firmware

This commit is contained in:
Lorenz Meier 2012-11-05 17:47:11 +01:00
parent e7f2c053c2 242d49402e
commit 706a7e4dd5
2 changed files with 151 additions and 1 deletions
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144
apps/systemlib/geo/geo.c
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@ -47,6 +47,150 @@
#include <systemlib/geo/geo.h>
#include <math.h>
/* values for map projection */
static double phi_1;
static double sin_phi_1;
static double cos_phi_1;
static double lambda_0;
static double scale;
/**
* Initializes the map transformation.
*
* Initializes the transformation between the geographic coordinate system and the azimuthal equidistant plane
* @param lat in degrees (47.1234567°, not 471234567°)
* @param lon in degrees (8.1234567°, not 81234567°)
*/
__EXPORT static void map_projection_init(double lat_0, double lon_0) //lat_0, lon_0 are expected to be in correct format: -> 47.1234567 and not 471234567
{
/* notation and formulas according to: http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html */
phi_1 = lat_0 / 180.0 * M_PI;
lambda_0 = lon_0 / 180.0 * M_PI;
sin_phi_1 = sin(phi_1);
cos_phi_1 = cos(phi_1);
/* calculate local scale by using the relation of true distance and the distance on plane */ //TODO: this is a quick solution, there are probably easier ways to determine the scale
/* 1) calculate true distance d on sphere to a point: http://www.movable-type.co.uk/scripts/latlong.html */
const double r_earth = 6371000;
double lat1 = phi_1;
double lon1 = lambda_0;
double lat2 = phi_1 + 0.5 / 180 * M_PI;
double lon2 = lambda_0 + 0.5 / 180 * M_PI;
double sin_lat_2 = sin(lat2);
double cos_lat_2 = cos(lat2);
double d = acos(sin(lat1) * sin_lat_2 + cos(lat1) * cos_lat_2 * cos(lon2 - lon1)) * r_earth;
/* 2) calculate distance rho on plane */
double k_bar = 0;
double c = acos(sin_phi_1 * sin_lat_2 + cos_phi_1 * cos_lat_2 * cos(lon2 - lambda_0));
if (0 != c)
k_bar = c / sin(c);
double x2 = k_bar * (cos_lat_2 * sin(lon2 - lambda_0)); //Projection of point 2 on plane
double y2 = k_bar * ((cos_phi_1 * sin_lat_2 - sin_phi_1 * cos_lat_2 * cos(lon2 - lambda_0)));
double rho = sqrt(pow(x2, 2) + pow(y2, 2));
scale = d / rho;
}
/**
* Transforms a point in the geographic coordinate system to the local azimuthal equidistant plane
* @param x north
* @param y east
* @param lat in degrees (47.1234567°, not 471234567°)
* @param lon in degrees (8.1234567°, not 81234567°)
*/
__EXPORT static void map_projection_project(double lat, double lon, float *x, float *y)
{
/* notation and formulas accoring to: http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html */
double phi = lat / 180.0 * M_PI;
double lambda = lon / 180.0 * M_PI;
double sin_phi = sin(phi);
double cos_phi = cos(phi);
double k_bar = 0;
/* using small angle approximation (formula in comment is without aproximation) */
double c = acos(sin_phi_1 * sin_phi + cos_phi_1 * cos_phi * (1 - pow((lambda - lambda_0), 2) / 2)); //double c = acos( sin_phi_1 * sin_phi + cos_phi_1 * cos_phi * cos(lambda - lambda_0) );
if (0 != c)
k_bar = c / sin(c);
/* using small angle approximation (formula in comment is without aproximation) */
*y = k_bar * (cos_phi * (lambda - lambda_0)) * scale;//*y = k_bar * (cos_phi * sin(lambda - lambda_0)) * scale;
*x = k_bar * ((cos_phi_1 * sin_phi - sin_phi_1 * cos_phi * (1 - pow((lambda - lambda_0), 2) / 2))) * scale; // *x = k_bar * ((cos_phi_1 * sin_phi - sin_phi_1 * cos_phi * cos(lambda - lambda_0))) * scale;
// printf("%phi_1=%.10f, lambda_0 =%.10f\n", phi_1, lambda_0);
}
/**
* Transforms a point in the local azimuthal equidistant plane to the geographic coordinate system
*
* @param x north
* @param y east
* @param lat in degrees (47.1234567°, not 471234567°)
* @param lon in degrees (8.1234567°, not 81234567°)
*/
__EXPORT static void map_projection_reproject(float x, float y, double *lat, double *lon)
{
/* notation and formulas accoring to: http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html */
double x_descaled = x / scale;
double y_descaled = y / scale;
double c = sqrt(pow(x_descaled, 2) + pow(y_descaled, 2));
double sin_c = sin(c);
double cos_c = cos(c);
double lat_sphere = 0;
if (c != 0)
lat_sphere = asin(cos_c * sin_phi_1 + (x_descaled * sin_c * cos_phi_1) / c);
else
lat_sphere = asin(cos_c * sin_phi_1);
// printf("lat_sphere = %.10f\n",lat_sphere);
double lon_sphere = 0;
if (phi_1 == M_PI / 2) {
//using small angle approximation (formula in comment is without aproximation)
lon_sphere = (lambda_0 - y_descaled / x_descaled); //lon_sphere = (lambda_0 + atan2(-y_descaled, x_descaled));
} else if (phi_1 == -M_PI / 2) {
//using small angle approximation (formula in comment is without aproximation)
lon_sphere = (lambda_0 + y_descaled / x_descaled); //lon_sphere = (lambda_0 + atan2(y_descaled, x_descaled));
} else {
lon_sphere = (lambda_0 + atan2(y_descaled * sin_c , c * cos_phi_1 * cos_c - x_descaled * sin_phi_1 * sin_c));
//using small angle approximation
// double denominator = (c * cos_phi_1 * cos_c - x_descaled * sin_phi_1 * sin_c);
// if(denominator != 0)
// {
// lon_sphere = (lambda_0 + (y_descaled * sin_c) / denominator);
// }
// else
// {
// ...
// }
}
// printf("lon_sphere = %.10f\n",lon_sphere);
*lat = lat_sphere * 180.0 / M_PI;
*lon = lon_sphere * 180.0 / M_PI;
}
__EXPORT float get_distance_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next)
{
double lat_now_rad = lat_now / 180.0d * M_PI;

8
apps/systemlib/geo/geo.h
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@ -55,6 +55,12 @@ typedef struct {
float bearing; // Bearing in radians to closest point on line/arc
} crosstrack_error_s;
__EXPORT static void map_projection_init(double lat_0, double lon_0);
__EXPORT static void map_projection_project(double lat, double lon, float *x, float *y);
__EXPORT static void map_projection_reproject(float x, float y, double *lat, double *lon);
__EXPORT float get_distance_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next);
__EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next);
@ -69,4 +75,4 @@ __EXPORT crosstrack_error_s get_distance_to_arc(double lat_now, double lon_now,
float _wrap180(float bearing);
float _wrap360(float bearing);
float _wrapPI(float bearing);
float _wrap2PI(float bearing);
float _wrap2PI(float bearing);