1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
|
/****************************************************************************
*
* Copyright (C) 2012, 2014 PX4 Development Team. All rights reserved.
*
* 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>
* @author Anton Babushkin <anton.babushkin@me.com>
*/
#include <geo/geo.h>
#include <nuttx/config.h>
#include <unistd.h>
#include <pthread.h>
#include <stdio.h>
#include <math.h>
#include <stdbool.h>
/*
* Azimuthal Equidistant Projection
* formulas according to: http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html
*/
struct map_projection_reference_s mp_ref;
__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
{
mp_ref.lat = lat_0 / 180.0 * M_PI;
mp_ref.lon = lon_0 / 180.0 * M_PI;
mp_ref.sin_lat = sin(mp_ref.lat);
mp_ref.cos_lat = cos(mp_ref.lat);
mp_ref.init_done = true;
}
__EXPORT bool map_projection_project(double lat, double lon, float *x, float *y)
{
if (!mp_ref.init_done) {
return false;
}
double lat_rad = lat / 180.0 * M_PI;
double lon_rad = lon / 180.0 * M_PI;
double sin_lat = sin(lat_rad);
double cos_lat = cos(lat_rad);
double cos_d_lon = cos(lon_rad - mp_ref.lon);
double c = acos(mp_ref.sin_lat * sin_lat + mp_ref.cos_lat * cos_lat * cos_d_lon);
double k = (c == 0.0) ? 1.0 : (c / sin(c));
*x = k * (mp_ref.cos_lat * sin_lat - mp_ref.sin_lat * cos_lat * cos_d_lon) * CONSTANTS_RADIUS_OF_EARTH;
*y = k * cos_lat * sin(lon_rad - mp_ref.lon) * CONSTANTS_RADIUS_OF_EARTH;
return true;
}
__EXPORT bool map_projection_reproject(float x, float y, double *lat, double *lon)
{
if (!mp_ref.init_done) {
return false;
}
float x_rad = x / CONSTANTS_RADIUS_OF_EARTH;
float y_rad = y / CONSTANTS_RADIUS_OF_EARTH;
double c = sqrtf(x_rad * x_rad + y_rad * y_rad);
double sin_c = sin(c);
double cos_c = cos(c);
double lat_rad;
double lon_rad;
if (c != 0.0) {
lat_rad = asin(cos_c * mp_ref.sin_lat + (x_rad * sin_c * mp_ref.cos_lat) / c);
lon_rad = (mp_ref.lon + atan2(y_rad * sin_c, c * mp_ref.cos_lat * cos_c - x_rad * mp_ref.sin_lat * sin_c));
} else {
lat_rad = mp_ref.lat;
lon_rad = mp_ref.lon;
}
*lat = lat_rad * 180.0 / M_PI;
*lon = lon_rad * 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));
return CONSTANTS_RADIUS_OF_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_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;
}
__EXPORT void get_vector_to_next_waypoint(double lat_now, double lon_now, double lat_next, double lon_next, float *v_n, float *v_e)
{
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 */
*v_n = CONSTANTS_RADIUS_OF_EARTH * (cos(lat_now_rad) * sin(lat_next_rad) - sin(lat_now_rad) * cos(lat_next_rad) * cos(d_lon));
*v_e = CONSTANTS_RADIUS_OF_EARTH * sin(d_lon) * cos(lat_next_rad);
}
__EXPORT void get_vector_to_next_waypoint_fast(double lat_now, double lon_now, double lat_next, double lon_next, float *v_n, float *v_e)
{
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 */
*v_n = CONSTANTS_RADIUS_OF_EARTH * d_lat;
*v_e = CONSTANTS_RADIUS_OF_EARTH * d_lon * cos(lat_now_rad);
}
__EXPORT void add_vector_to_global_position(double lat_now, double lon_now, float v_n, float v_e, double *lat_res, double *lon_res)
{
double lat_now_rad = lat_now * M_DEG_TO_RAD;
double lon_now_rad = lon_now * M_DEG_TO_RAD;
*lat_res = (lat_now_rad + v_n / CONSTANTS_RADIUS_OF_EARTH) * M_RAD_TO_DEG;
*lon_res = (lon_now_rad + v_e / (CONSTANTS_RADIUS_OF_EARTH * cos(lat_now_rad))) * M_RAD_TO_DEG;
}
// 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 get_distance_to_point_global_wgs84(double lat_now, double lon_now, float alt_now,
double lat_next, double lon_next, float alt_next,
float *dist_xy, float *dist_z)
{
double current_x_rad = lat_next / 180.0 * M_PI;
double current_y_rad = lon_next / 180.0 * M_PI;
double x_rad = lat_now / 180.0 * M_PI;
double y_rad = lon_now / 180.0 * M_PI;
double d_lat = x_rad - current_x_rad;
double d_lon = y_rad - current_y_rad;
double a = sin(d_lat / 2.0) * sin(d_lat / 2.0) + sin(d_lon / 2.0) * sin(d_lon / 2.0f) * cos(current_x_rad) * cos(x_rad);
double c = 2 * atan2(sqrt(a), sqrt(1 - a));
float dxy = CONSTANTS_RADIUS_OF_EARTH * c;
float dz = alt_now - alt_next;
*dist_xy = fabsf(dxy);
*dist_z = fabsf(dz);
return sqrtf(dxy * dxy + dz * dz);
}
__EXPORT float mavlink_wpm_distance_to_point_local(float x_now, float y_now, float z_now,
float x_next, float y_next, float z_next,
float *dist_xy, float *dist_z)
{
float dx = x_now - x_next;
float dy = y_now - y_next;
float dz = z_now - z_next;
*dist_xy = sqrtf(dx * dx + dy * dy);
*dist_z = fabsf(dz);
return sqrtf(dx * dx + dy * dy + dz * dz);
}
__EXPORT float _wrap_pi(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
int c = 0;
while (bearing >= M_PI_F) {
bearing -= M_TWOPI_F;
if (c++ > 3) {
return NAN;
}
}
c = 0;
while (bearing < -M_PI_F) {
bearing += M_TWOPI_F;
if (c++ > 3) {
return NAN;
}
}
return bearing;
}
__EXPORT float _wrap_2pi(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
int c = 0;
while (bearing >= M_TWOPI_F) {
bearing -= M_TWOPI_F;
if (c++ > 3) {
return NAN;
}
}
c = 0;
while (bearing < 0.0f) {
bearing += M_TWOPI_F;
if (c++ > 3) {
return NAN;
}
}
return bearing;
}
__EXPORT float _wrap_180(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
int c = 0;
while (bearing >= 180.0f) {
bearing -= 360.0f;
if (c++ > 3) {
return NAN;
}
}
c = 0;
while (bearing < -180.0f) {
bearing += 360.0f;
if (c++ > 3) {
return NAN;
}
}
return bearing;
}
__EXPORT float _wrap_360(float bearing)
{
/* value is inf or NaN */
if (!isfinite(bearing)) {
return bearing;
}
int c = 0;
while (bearing >= 360.0f) {
bearing -= 360.0f;
if (c++ > 3) {
return NAN;
}
}
c = 0;
while (bearing < 0.0f) {
bearing += 360.0f;
if (c++ > 3) {
return NAN;
}
}
return bearing;
}
|