/****************************************************************************
*
* Copyright (C) 2012 PX4 Development Team. All rights reserved.
* Author: Thomas Gubler <thomasgubler@student.ethz.ch>
* Julian Oes <joes@student.ethz.ch>
* Lorenz Meier <lm@inf.ethz.ch>
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* 3. Neither the name PX4 nor the names of its contributors may be
* used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
****************************************************************************/
/**
* @file geo.c
*
* Geo / math functions to perform geodesic calculations
*
* @author Thomas Gubler <thomasgubler@student.ethz.ch>
* @author Julian Oes <joes@student.ethz.ch>
* @author Lorenz Meier <lm@inf.ethz.ch>
*/
#include <systemlib/geo/geo.h>
#include <nuttx/config.h>
//#include <unistd.h>
#include <pthread.h>
#include <stdio.h>
#include <math.h>
#include <stdbool.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;
__EXPORT 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;
}
__EXPORT 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);
}
__EXPORT 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;
double lon_now_rad = lon_now / 180.0d * M_PI;
double lat_next_rad = lat_next / 180.0d * M_PI;
double lon_next_rad = lon_next / 180.0d * M_PI;
double d_lat = lat_next_rad - lat_now_rad;
double d_lon = lon_next_rad - lon_now_rad;
double a = sin(d_lat / 2.0d) * sin(d_lat / 2.0d) + sin(d_lon / 2.0d) * sin(d_lon / 2.0d) * cos(lat_now_rad) * cos(lat_next_rad);
double c = 2.0d * atan2(sqrt(a), sqrt(1.0d - a));
const double radius_earth = 6371000.0d;
printf("DIST: %.4f\n", radius_earth * c);
return radius_earth * c;
}
__EXPORT float get_bearing_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next)
{
double lat_now_rad = lat_now * M_DEG_TO_RAD;
double lon_now_rad = lon_now * M_DEG_TO_RAD;
double lat_next_rad = lat_next * M_DEG_TO_RAD;
double lon_next_rad = lon_next * M_DEG_TO_RAD;
double d_lat = lat_next_rad - lat_now_rad;
double d_lon = lon_next_rad - lon_now_rad;
/* conscious mix of double and float trig function to maximize speed and efficiency */
float theta = atan2f(sin(d_lon) * cos(lat_next_rad) , cos(lat_now_rad) * sin(lat_next_rad) - sin(lat_now_rad) * cos(lat_next_rad) * cos(d_lon));
theta = _wrap_pi(theta);
return theta;
}
// Additional functions - @author Doug Weibel <douglas.weibel@colorado.edu>
__EXPORT int get_distance_to_line(struct crosstrack_error_s * crosstrack_error, double lat_now, double lon_now, double lat_start, double lon_start, double lat_end, double lon_end)
{
// This function returns the distance to the nearest point on the track line. Distance is positive if current
// position is right of the track and negative if left of the track as seen from a point on the track line
// headed towards the end point.
float dist_to_end;
float bearing_end;
float bearing_track;
float bearing_diff;
int return_value = ERROR; // Set error flag, cleared when valid result calculated.
crosstrack_error->past_end = false;
crosstrack_error->distance = 0.0f;
crosstrack_error->bearing = 0.0f;
// Return error if arguments are bad
if (lat_now == 0.0d || lon_now == 0.0d || lat_start == 0.0d || lon_start == 0.0d || lat_end == 0.0d || lon_end == 0.0d) return return_value;
bearing_end = get_bearing_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
bearing_track = get_bearing_to_next_waypoint(lat_start, lon_start, lat_end, lon_end);
bearing_diff = bearing_track - bearing_end;
bearing_diff = _wrap_pi(bearing_diff);
// Return past_end = true if past end point of line
if (bearing_diff > M_PI_2_F || bearing_diff < -M_PI_2_F) {
crosstrack_error->past_end = true;
return_value = OK;
return return_value;
}
dist_to_end = get_distance_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
crosstrack_error->distance = (dist_to_end) * sin(bearing_diff);
if (sin(bearing_diff) >= 0) {
crosstrack_error->bearing = _wrap_pi(bearing_track - M_PI_2_F);
} else {
crosstrack_error->bearing = _wrap_pi(bearing_track + M_PI_2_F);
}
return_value = OK;
return return_value;
}
__EXPORT int get_distance_to_arc(struct crosstrack_error_s * crosstrack_error, double lat_now, double lon_now, double lat_center, double lon_center,
float radius, float arc_start_bearing, float arc_sweep)
{
// This function returns the distance to the nearest point on the track arc. Distance is positive if current
// position is right of the arc and negative if left of the arc as seen from the closest point on the arc and
// headed towards the end point.
// Determine if the current position is inside or outside the sector between the line from the center
// to the arc start and the line from the center to the arc end
float bearing_sector_start;
float bearing_sector_end;
float bearing_now = get_bearing_to_next_waypoint(lat_now, lon_now, lat_center, lon_center);
bool in_sector;
int return_value = ERROR; // Set error flag, cleared when valid result calculated.
crosstrack_error->past_end = false;
crosstrack_error->distance = 0.0f;
crosstrack_error->bearing = 0.0f;
// Return error if arguments are bad
if (lat_now == 0.0d || lon_now == 0.0d || lat_center == 0.0d || lon_center == 0.0d || radius == 0.0d) return return_value;
if (arc_sweep >= 0) {
bearing_sector_start = arc_start_bearing;
bearing_sector_end = arc_start_bearing + arc_sweep;
if (bearing_sector_end > 2.0f * M_PI_F) bearing_sector_end -= M_TWOPI_F;
} else {
bearing_sector_end = arc_start_bearing;
bearing_sector_start = arc_start_bearing - arc_sweep;
if (bearing_sector_start < 0.0f) bearing_sector_start += M_TWOPI_F;
}
in_sector = false;
// Case where sector does not span zero
if (bearing_sector_end >= bearing_sector_start && bearing_now >= bearing_sector_start && bearing_now <= bearing_sector_end) in_sector = true;
// Case where sector does span zero
if (bearing_sector_end < bearing_sector_start && (bearing_now > bearing_sector_start || bearing_now < bearing_sector_end)) in_sector = true;
// If in the sector then calculate distance and bearing to closest point
if (in_sector) {
crosstrack_error->past_end = false;
float dist_to_center = get_distance_to_next_waypoint(lat_now, lon_now, lat_center, lon_center);
if (dist_to_center <= radius) {
crosstrack_error->distance = radius - dist_to_center;
crosstrack_error->bearing = bearing_now + M_PI_F;
} else {
crosstrack_error->distance = dist_to_center - radius;
crosstrack_error->bearing = bearing_now;
}
// If out of the sector then calculate dist and bearing to start or end point
} else {
// Use the approximation that 111,111 meters in the y direction is 1 degree (of latitude)
// and 111,111 * cos(latitude) meters in the x direction is 1 degree (of longitude) to
// calculate the position of the start and end points. We should not be doing this often
// as this function generally will not be called repeatedly when we are out of the sector.
// TO DO - this is messed up and won't compile
float start_disp_x = radius * sin(arc_start_bearing);
float start_disp_y = radius * cos(arc_start_bearing);
float end_disp_x = radius * sin(_wrapPI(arc_start_bearing + arc_sweep));
float end_disp_y = radius * cos(_wrapPI(arc_start_bearing + arc_sweep));
float lon_start = lon_now + start_disp_x / 111111.0d;
float lat_start = lat_now + start_disp_y * cos(lat_now) / 111111.0d;
float lon_end = lon_now + end_disp_x / 111111.0d;
float lat_end = lat_now + end_disp_y * cos(lat_now) / 111111.0d;
float dist_to_start = get_distance_to_next_waypoint(lat_now, lon_now, lat_start, lon_start);
float dist_to_end = get_distance_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
if (dist_to_start < dist_to_end) {
crosstrack_error->distance = dist_to_start;
crosstrack_error->bearing = get_bearing_to_next_waypoint(lat_now, lon_now, lat_start, lon_start);
} else {
crosstrack_error->past_end = true;
crosstrack_error->distance = dist_to_end;
crosstrack_error->bearing = get_bearing_to_next_waypoint(lat_now, lon_now, lat_end, lon_end);
}
}
crosstrack_error->bearing = _wrapPI(crosstrack_error->bearing);
return_value = OK;
return return_value;
}
__EXPORT float _wrap_pi(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing) || bearing == 0) {
return bearing;
}
int c = 0;
while (bearing > M_PI_F && c < 30) {
bearing -= M_TWOPI_F;
c++;
}
c = 0;
while (bearing <= -M_PI_F && c < 30) {
bearing += M_TWOPI_F;
c++;
}
return bearing;
}
__EXPORT float _wrap_2pi(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
while (bearing >= M_TWOPI_F) {
bearing = bearing - M_TWOPI_F;
}
while (bearing < 0.0f) {
bearing = bearing + M_TWOPI_F;
}
return bearing;
}
__EXPORT float _wrap_180(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
while (bearing > 180.0f) {
bearing = bearing - 360.0f;
}
while (bearing <= -180.0f) {
bearing = bearing + 360.0f;
}
return bearing;
}
__EXPORT float _wrap_360(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
while (bearing >= 360.0f) {
bearing = bearing - 360.0f;
}
while (bearing < 0.0f) {
bearing = bearing + 360.0f;
}
return bearing;
}