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-/****************************************************************************
- *
- * 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
- * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
- * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
- * 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 / 2.0) + 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;
-
- 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;
-}
-
-
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