Fix a problem with the normals.
[tcxmerge] / opt.cc
1 #include <stdio.h>
2 #include <vector>
3 #include "ceres/ceres.h"
4 #include "gflags/gflags.h"
5 #include "glog/logging.h"
6 #include "LatLong-UTMconversion.h"
7 #include "constants.h"
8
9 #define GPS_SIGMA 20.0
10 #define GPS_EXTRA_SIGMA_PER_SECOND 1.0
11
12 #define KD_LEAF_SIZE 5
13
14 using namespace ceres;
15 using std::vector;
16
17 struct Coord {
18         double x, y;
19 };
20 struct TCXPoint {
21         int time;
22         double lat, lon, alt;
23         int hr;
24
25         // computed
26         double utm_north, utm_east;
27         char utm_zone[16];
28 };
29 struct FootPoint {
30         int time;
31         int hr;
32         int cadence;
33         double speed;
34         double distance;
35 };
36
37 struct LineSegment {
38         Coord from, to;
39
40         // computed
41         double wv_x, wv_y;
42         double len_sq, inv_len_sq;
43 };
44 vector<LineSegment> roads;
45
46 struct BSPTreeNode {
47         bool is_leaf;
48         double a, b, d;  // split plane
49         vector<int> roads_this_node;
50         BSPTreeNode *left, *right;
51 };
52 BSPTreeNode *root = NULL;
53
54 double signed_distance(double a, double b, double d, Coord c)
55 {
56         return a * c.x + b * c.y + d;
57 }
58
59 double split_cost(const vector<int>& remaining_roads, double a, double b, double d)
60 {
61         unsigned in_left = 0, in_right = 0, in_both = 0;
62         for (int i = 0; i < remaining_roads.size(); ++i) {
63                 double dist_from = signed_distance(a, b, d, roads[remaining_roads[i]].from);
64                 double dist_to = signed_distance(a, b, d, roads[remaining_roads[i]].to);
65                 if (dist_from > 0.0 && dist_to > 0.0) {
66                         ++in_right;
67                 } else if (dist_from < 0.0 && dist_to < 0.0) {
68                         ++in_left;
69                 } else {
70                         ++in_both;
71                 }
72         }
73
74         return max(in_left, in_right) + 1.1 * in_both;
75 }
76
77 BSPTreeNode* make_bsp_tree(const vector<int>& remaining_roads)
78 {
79         BSPTreeNode *node = new BSPTreeNode;
80         if (remaining_roads.size() <= KD_LEAF_SIZE) {
81                 node->is_leaf = true;
82                 node->left = node->right = NULL;
83                 node->roads_this_node = remaining_roads;
84                 return node;
85         }       
86
87         node->is_leaf = false;
88
89         // try all possible split planes (TODO: +/- epsilon)
90         double best_a = 0.0, best_b = 0.0, best_d = 0.0;
91         double best_cost = HUGE_VAL;
92         for (unsigned i = 0; i < remaining_roads.size(); ++i) {
93                 const LineSegment& ls = roads[remaining_roads[i]];
94
95                 // find the normal
96                 double a =   ls.to.y - ls.from.y;
97                 double b = -(ls.to.x - ls.from.x);
98                 double invlen = 1.0 / hypot(a, b);
99                 a *= invlen, b *= invlen;
100
101                 double d = -(a * ls.from.x + b * ls.from.y);
102                 double cost = split_cost(remaining_roads, a, b, d - 1e-6);
103                 if (cost < best_cost) {
104                         best_a = a, best_b = b, best_d = d - 1e-6;
105                         best_cost = cost;
106                 }
107                 
108                 cost = split_cost(remaining_roads, a, b, d + 1e+6);
109                 if (cost < best_cost) {
110                         best_a = a, best_b = b, best_d = d + 1e+6;
111                         best_cost = cost;
112                 }
113         }
114         node->a = best_a;
115         node->b = best_b;
116         node->d = best_d;
117
118         vector<int> left, right;
119         for (unsigned i = 0; i < remaining_roads.size(); ++i) {
120                 double dist_from = signed_distance(best_a, best_b, best_d, roads[remaining_roads[i]].from);
121                 double dist_to = signed_distance(best_a, best_b, best_d, roads[remaining_roads[i]].to);
122                 if (dist_from > 0.0 && dist_to > 0.0) {
123                         right.push_back(remaining_roads[i]);
124                 } else if (dist_from < 0.0 && dist_to < 0.0) {
125                         left.push_back(remaining_roads[i]);
126                 } else {
127                         node->roads_this_node.push_back(remaining_roads[i]);
128                 }
129         }
130
131         if (left.empty() || right.empty()) {
132                 node->is_leaf = true;
133                 node->left = node->right = NULL;
134                 node->roads_this_node = remaining_roads;
135                 return node;
136         }
137
138         if (left.size() == 0) {
139                 node->left = NULL;
140         } else {
141                 node->left = make_bsp_tree(left);
142         }
143         if (right.size() == 0) {
144                 node->right = NULL;
145         } else {
146                 node->right = make_bsp_tree(right);
147         }
148         return node;
149 }
150
151 void intersect_line_line_x(double a1, double b1, double d1, double a2, double b2, double d2, double *min_x, double *max_x)
152 {
153         // find somewhere (x,y) where:
154         //
155         //   A1x + B1y + D1 = 0  [I]
156         //   A2x + B2y + D2 = 0  [II]
157         //
158         // [I] gives: y = -((A1/B1) x + D1/B1)
159         // Insert into [II]:
160         //
161         //   A2x - B2 ((A1/B1) x + D1/B1) + D2 = 0
162         //   A2x - A1 B2 / B1 x - D1 B2 / B1 + D2 = 0
163         //   ((A2 B1 - A1 B2) / B1) x = D1 B2 / B1 - D2   [A2 B1 - A1 B2 = det]
164         //   x = D1 B2 / det - D2 B1 / det = (D1 B2 - D2 B1) / det
165         double det = a2 * b1 - a1 * b2;
166         if (fabs(det) <= 1e-6) {
167                 return;
168         }
169         double intersect_x = (d1 * b2 - d2 * b1) / det;
170
171         if (-det * (*max_x - *min_x) < 0) {
172                 *min_x = min(*min_x, intersect_x);
173                 *max_x = min(*max_x, intersect_x);
174         } else {
175                 *min_x = max(*min_x, intersect_x);
176                 *max_x = max(*max_x, intersect_x);
177         }
178 }
179
180 void intersect_line_line_y(double a1, double b1, double d1, double a2, double b2, double d2, double *min_y, double *max_y)
181 {
182         // find somewhere (x,y) where:
183         //
184         //   A1x + B1y + D1 = 0  [I]
185         //   A2x + B2y + D2 = 0  [II]
186         //
187         // [I] gives: y = -((B1/A1) x + D1/A1)
188         // Insert into [II]:
189         //
190         //   B2y - A2 ((B1/A1) x + D1/A1) + D2 = 0
191         //   B2y - B1 A2 / A1 x - D1 A2 / A1 + D2 = 0
192         //   ((A1 B2 - B1 A2) / A1) y = D1 A2 / A1 - D2   [A1 B2 - B1 A2 = det]
193         //   y = D1 A2 / det - D2 A1 / det = (D1 B2 - D2 B1) / det
194         double det = a1 * b2 - a2 * b1;
195         if (fabs(det) <= 1e-6) {
196                 return;
197         }
198         double intersect_y = (d1 * a2 - d2 * a1) / det;
199         if (det * (*max_y - *min_y) < 0) {
200                 *min_y = min(*min_y, intersect_y);
201                 *max_y = min(*max_y, intersect_y);
202         } else {
203                 *min_y = max(*min_y, intersect_y);
204                 *max_y = max(*max_y, intersect_y);
205         }
206 }
207
208 void plot_line_based_on_x(FILE *fp, double a, double b, double d, double x1, double x2)
209 {
210         // see intersect_line_line()
211         double y1 = - (a * x1 + d) / b;
212         double y2 = - (a * x2 + d) / b;
213         fprintf(fp, "%f %f %f %f\n", x1, y1, x2, y2);
214 }
215
216 void plot_line_based_on_y(FILE *fp, double a, double b, double d, double y1, double y2)
217 {
218         // see intersect_line_line()
219         double x1 = - (b * y1 + d) / a;
220         double x2 = - (b * y2 + d) / a;
221         fprintf(fp, "%f %f %f %f\n", x1, y1, x2, y2);
222 }
223
224 void plot_line(double a, double b, double d)
225 {
226         if (fabs(a) > fabs(b)) {
227                 double x1 = -2000.0, x2 = 2000.0;
228                 if (b > 0) swap(x1, x2);
229                 intersect_line_line_x(a, b, d, 0,  1.0, 2000, &x1, &x2);
230                 intersect_line_line_x(a, b, d, 0, -1.0, 2000, &x1, &x2);
231                 plot_line_based_on_x(stdout, a, b, d, x1, x2);
232         } else {
233                 double y1 = -2000.0, y2 = 2000.0;
234                 if (a < 0) swap(y1, y2);
235                 intersect_line_line_y(a, b, d,  1.0, 0.0, 2000, &y1, &y2);
236                 intersect_line_line_y(a, b, d, -1.0, 0.0, 2000, &y1, &y2);
237                 plot_line_based_on_y(stdout, a, b, d, y1, y2);
238         }
239 }
240
241 void plot_bsp_tree(FILE *fp, BSPTreeNode *node, vector<pair<BSPTreeNode*, bool> > previous_visited)
242 {
243         double a = node->a, b = node->b, d = node->d;
244
245         double x1, x2, y1, y2;
246
247         if (node->is_leaf) {
248                 return;
249         }
250
251         if (fabs(a) > fabs(b)) {
252                 x1 = -2000.0, x2 = 2000.0;
253                 if (b > 0) swap(x1, x2);
254                 intersect_line_line_x(a, b, d, 0,  1.0, 2000, &x1, &x2);
255                 intersect_line_line_x(a, b, d, 0, -1.0, 2000, &x1, &x2);
256
257                 // clip against all previous lines
258                 for (unsigned i = 0; i < previous_visited.size(); ++i) {
259                         BSPTreeNode* o = previous_visited[i].first;
260                         if (previous_visited[i].second) {
261                                 intersect_line_line_x(a, b, d, o->a, o->b, o->d, &x1, &x2);
262                         } else {
263                                 intersect_line_line_x(a, b, d, -o->a, -o->b, -o->d, &x1, &x2);
264                         }
265                 }
266
267                 if (fabs(x1 - x2) > 1e-6) {
268                         plot_line_based_on_x(fp, a, b, d, x1, x2);
269                 }
270         } else {
271                 // copy of the stuff above
272                 y1 = -2000.0, y2 = 2000.0;
273                 if (a < 0) swap(y1, y2);
274                 intersect_line_line_y(a, b, d,  1.0, 0.0, 2000, &y1, &y2);
275                 intersect_line_line_y(a, b, d, -1.0, 0.0, 2000, &y1, &y2);
276
277                 // clip against all previous lines
278                 for (unsigned i = 0; i < previous_visited.size(); ++i) {
279                         BSPTreeNode* o = previous_visited[i].first;
280                         if (previous_visited[i].second) {
281                                 intersect_line_line_y(a, b, d, o->a, o->b, o->d, &y1, &y2);
282                         } else {
283                                 intersect_line_line_y(a, b, d, -o->a, -o->b, -o->d, &y1, &y2);
284                         }
285                 }
286
287                 if (fabs(y1 - y2) > 1e-6) {
288                         plot_line_based_on_y(fp, a, b, d, y1, y2);
289                 }
290         }
291
292         previous_visited.push_back(make_pair(node, false));
293         if (node->left != NULL) {
294                 plot_bsp_tree(fp, node->left, previous_visited);
295         }
296         if (node->right != NULL) {
297                 previous_visited.back().second = true;
298                 plot_bsp_tree(fp, node->right, previous_visited);
299         }
300 }
301
302 char* write_time(time_t t)
303 {
304         static char buf[256];
305         struct tm *foo = gmtime(&t);
306         strftime(buf, 256, "%Y-%m-%dT%H:%M:%SZ", foo);
307         return buf;
308 }
309
310 class MinimizeAccelerationCostFunction {
311  public:
312         MinimizeAccelerationCostFunction() {}
313         
314         template<class T>
315         bool operator() (const T * const p0, const T * const p1, const T * const p2, T* e) const {
316                 e[0] = p0[0] - T(2.0) * p1[0] + p2[0];
317                 e[1] = p0[1] - T(2.0) * p1[1] + p2[1];
318                 return true;
319         }
320 };
321
322 double sq_distance_point_point(const Coord& a, const Coord& b)
323 {
324         //return hypot(b.x - a.x, b.y - a.y);
325         return (b.x - a.x) * (b.x - a.x) + (b.y - a.y) * (b.y - a.y);
326 }
327                         
328 double sq_distance_point_line_segment(const Coord& c, LineSegment &ls)
329 {
330         if (ls.len_sq < 1e-6) {
331                 return sq_distance_point_point(c, ls.from);
332         }
333         const double pv_x = c.x - ls.from.x;
334         const double pv_y = c.y - ls.from.y;
335         const double t = (pv_x * ls.wv_x + pv_y * ls.wv_y) * ls.inv_len_sq;
336         if (t <= 0.0) {
337                 return sq_distance_point_point(c, ls.from);
338         }
339         if (t >= 1.0) {
340                 return sq_distance_point_point(c, ls.to);
341         }
342
343         Coord r;
344         r.x = ls.from.x + t * ls.wv_x;
345         r.y = ls.from.y + t * ls.wv_y;
346         return sq_distance_point_point(c, r);
347 }
348
349 pair<int, double> find_closest_road_nonbsp(Coord c)
350 {
351         int best_idx = -1;
352         double sq_best_distance = HUGE_VAL;
353         for (unsigned i = 0; i < roads.size(); ++i) {
354                 double sq_distance = sq_distance_point_line_segment(c, roads[i]);
355                 if (sq_distance < sq_best_distance) {
356                         best_idx = i;
357                         sq_best_distance = sq_distance;
358                 }
359         }
360         return make_pair(best_idx, std::sqrt(sq_best_distance));
361 }
362
363 struct BSPTreeJob {
364         BSPTreeJob(BSPTreeNode* node, BSPTreeNode* parent) : node(node), parent(parent) {}
365         BSPTreeJob(const BSPTreeJob& other) : node(other.node), parent(other.parent) {}
366
367         BSPTreeNode* node;
368         BSPTreeNode* parent;
369 };
370 vector<BSPTreeJob> bsp_todo;
371 //vector<BSPTreeNode*> bsp_todo;
372
373 pair<int, double> find_closest_road(Coord c)
374 {
375         int best_idx = -1;
376         double sq_best_distance = HUGE_VAL;
377
378         bsp_todo.clear();
379         bsp_todo.push_back(BSPTreeJob(root, NULL));
380         int bsp_pos = 0;
381
382         while (bsp_todo.size() > bsp_pos) {
383                 BSPTreeJob job = bsp_todo[bsp_pos++];
384                 BSPTreeNode* node = job.node;
385
386                 // Re-verify versus sq_best_distance here, since it might have changed.
387                 if (job.parent != NULL) {
388                         double dist = signed_distance(job.parent->a, job.parent->b, job.parent->d, c);
389                         if (dist*dist > sq_best_distance) {
390                                 // OK, later changes to best_distance has rendered this job moot.
391                                 continue;
392                         }
393                 }
394 shortcut:
395
396                 // Check all nodes that are interior to this.
397                 for (unsigned i = 0; i < node->roads_this_node.size(); ++i) {
398                         int idx = node->roads_this_node[i];
399                         double sq_distance = sq_distance_point_line_segment(c, roads[idx]);
400                         if (sq_distance < sq_best_distance || (sq_distance == sq_best_distance && idx < best_idx)) {
401                                 best_idx = idx;
402                                 sq_best_distance = sq_distance;
403                         }
404                 }
405
406                 if (node->is_leaf) {
407                         continue;
408                 }
409
410                 double dist = signed_distance(node->a, node->b, node->d, c);
411                 if (dist * dist <= sq_best_distance) {
412                         // gah! we have to put both in there.
413                         // try at least the correct side first.
414                         if (dist > 0.0) {
415                                 if (node->left != NULL) {
416                                         bsp_todo.push_back(BSPTreeJob(node->left, node));
417                                 }
418                                 node = node->right;
419                                 if (node != NULL) {
420                                         goto shortcut;
421                                 }
422                         } else {
423                                 if (node->right != NULL) {
424                                         bsp_todo.push_back(BSPTreeJob(node->right, node));
425                                 }
426                                 node = node->left;
427                                 if (node != NULL) {
428                                         goto shortcut;
429                                 }
430                         }
431                 } else {
432                         // woo, we can do with going on only one side
433                         if (dist > 0.0) {
434                                 // go on to the right side
435                                 node = node->right;
436                                 if (node != NULL) {
437                                         goto shortcut;
438                                 }
439                                 continue;
440                         }
441                         if (dist < 0.0) {
442                                 // go on to the left side
443                                 node = node->left;
444                                 if (node != NULL) {
445                                         goto shortcut;
446                                 }
447                                 continue;
448                         }
449                 }
450         }
451
452         return make_pair(best_idx, std::sqrt(sq_best_distance));
453 }
454
455 class DistanceFromRoadCostFunction : public SizedCostFunction<1, 2, 2> {
456  public:
457          virtual bool Evaluate(double const* const* p,
458                                double* e,
459                                double** jacobians) const {
460                 (void) jacobians;  // Ignored; filled in by numeric differentiation.
461
462                 Coord c;
463                 c.x = p[0][0];
464                 c.y = p[0][1];
465
466                 Coord prev_c;
467                 prev_c.x = p[1][0];
468                 prev_c.y = p[1][1];
469
470                 pair<int, double> closest_road = find_closest_road(c);
471 #if 0
472                 // verify bsp behavior
473                 pair<int, double> closest_road_nonbsp = find_closest_road_nonbsp(c);
474                 if (closest_road.first != closest_road_nonbsp.first) {
475                         printf("oops! for <%f,%f> bsp=(%d,%.10f) and nonbsp=(%d,%.10f)\n",
476                                 c.x, c.y, closest_road.first, closest_road.second,
477                                 closest_road_nonbsp.first, closest_road_nonbsp.second);
478                         printf("bsp:\n%f %f\n%f %f\n",
479                                 roads[closest_road.first].from.x,
480                                 roads[closest_road.first].from.y,
481                                 roads[closest_road.first].to.x,
482                                 roads[closest_road.first].to.y);
483                         printf("Nd:\n%f %f\n%f %f\n",
484                                 roads[closest_road_nonbsp.first].from.x,
485                                 roads[closest_road_nonbsp.first].from.y,
486                                 roads[closest_road_nonbsp.first].to.x,
487                                 roads[closest_road_nonbsp.first].to.y);
488                         exit(1);
489                 }
490 #endif
491                 double prev_distance = std::sqrt(sq_distance_point_line_segment(prev_c, roads[closest_road.first]));
492
493                 // hack
494                 //e[0] = 2.0 - std::exp(-(best_distance * best_distance)) - std::exp(-(prev_distance * prev_distance));
495                 //e[0] = 0.2 * (best_distance + 0.5 * prev_distance);
496                 //e[0] = ceres::log(best_distance);
497                 e[0] = closest_road.second + 0.5 * prev_distance;
498                 return true;
499          }
500 };
501
502 class FootDiffCostFunction {
503  public:
504         FootDiffCostFunction(double speed) : speed_(speed) {}
505         
506         template<class T>
507         bool operator() (const T * const p0, const T * const p1, T* e) const {
508                 T ex = p1[0] - p0[0];
509                 T ey = p1[1] - p0[1];
510                 T speed = 0.5 * ceres::sqrt(ex * ex + ey * ey);
511                 e[0] = speed - speed_;
512                 return true;
513         }
514
515  private:
516         double speed_;
517 };
518
519 class GPSDiffCostFunction {
520  public:
521         GPSDiffCostFunction(double x, double y) : x_(x), y_(y) {}
522         
523         template<class T>
524         bool operator() (const T * const p, T* e) const {
525                 T x_dist = p[0] - T(x_);
526                 T y_dist = p[1] - T(y_);
527                 T sq_dist = x_dist * x_dist + y_dist * y_dist;
528                 e[0] = T(10.0) * (T(1.0) - ceres::exp(-sq_dist / T(GPS_SIGMA * GPS_SIGMA)));
529                 //e[0] = sq_dist / GPS_SIGMA;
530                 // e[0] = sq_dist;
531                 return true;
532         }
533
534  private:
535         double x_, y_;
536 };
537
538 class MyIterationCallback : public IterationCallback {
539  public:
540         MyIterationCallback(Coord *c, int num_points) : c_(c), num_points_(num_points) {}
541
542         virtual CallbackReturnType operator()(const IterationSummary& summary)
543         {
544                 char buf[256];
545                 sprintf(buf, "temp%04d.plot", summary.iteration);
546                 FILE *fp = fopen(buf, "w");
547                 for (int i = 0; i < num_points_; ++i) {
548                         fprintf(fp, "%f %f\n", c_[i].x, c_[i].y);
549                 }
550                 fclose(fp);
551                 return SOLVER_CONTINUE;
552         }
553
554  private:
555         Coord *c_;
556         int num_points_;
557 };
558
559
560 int main(int argc, char** argv) {
561         google::ParseCommandLineFlags(&argc, &argv, true);
562         google::InitGoogleLogging(argv[0]);
563
564         int max_time = INT_MIN, min_time = INT_MAX;
565
566         vector<TCXPoint> tcx_points;
567         vector<FootPoint> foot_points;
568
569         FILE *fp = fopen(argv[1], "r");
570         if (fp == NULL) {
571                 perror(argv[1]);
572                 exit(1);
573         }
574
575         while (!feof(fp)) {
576                 char buf[256];
577                 if (fgets(buf, 256, fp) == NULL) {
578                         break;
579                 }
580                 if (strncmp(buf, "tcx ", 4) == 0) {
581                         TCXPoint p;
582                         if (sscanf(buf, "tcx %d %lf %lf %lf %d", &p.time, &p.lat, &p.lon, &p.alt, &p.hr) != 5) {
583                                 fprintf(stderr, "parse error: %s\n", buf);
584                                 exit(1);
585                         }
586
587                         LLtoUTM(23, p.lat * rad2deg, p.lon * rad2deg, p.utm_north, p.utm_east, p.utm_zone);
588
589                         tcx_points.push_back(p);
590                         max_time = max(max_time, p.time);
591                         min_time = min(min_time, p.time);
592                         continue;
593                 }
594                 if (strncmp(buf, "footpod ", 8) == 0) {
595                         FootPoint p;
596                         if (sscanf(buf, "footpod %d %d %d %lf %lf", &p.time, &p.hr, &p.cadence, &p.speed, &p.distance) != 5) {
597                                 fprintf(stderr, "parse error: %s\n", buf);
598                                 exit(1);
599                         }
600                         foot_points.push_back(p);
601                         max_time = max(max_time, p.time);
602                         min_time = min(min_time, p.time);
603                         continue;
604                 }
605         }
606         fclose(fp);
607
608         // normalize the utm guys a bit
609         double utm_north_sum = 0.0, utm_east_sum = 0.0;
610         for (unsigned i = 0; i < tcx_points.size(); ++i) {
611                 utm_north_sum += tcx_points[i].utm_north;
612                 utm_east_sum += tcx_points[i].utm_east;
613         }
614         utm_north_sum /= tcx_points.size();
615         utm_east_sum /= tcx_points.size();
616         for (unsigned i = 0; i < tcx_points.size(); ++i) {
617                 tcx_points[i].utm_north -= utm_north_sum;
618                 tcx_points[i].utm_east -= utm_east_sum;
619         }
620
621         // Read the OSM file
622         fp = fopen(argv[2], "r");
623         if (fp == NULL) {
624                 perror(argv[2]);
625                 exit(1);
626         }
627
628         while (!feof(fp)) {
629                 double lat1, lon1, lat2, lon2;
630                 if (fscanf(fp, "%lf %lf %lf %lf\n", &lat1, &lon1, &lat2, &lon2) != 4) {
631                         break;
632                 }
633
634                 char utm_zone[16];
635                 LineSegment seg;
636                 LLtoUTM(23, lat1, lon1, seg.from.y, seg.from.x, utm_zone);
637                 LLtoUTM(23, lat2, lon2, seg.to.y, seg.to.x, utm_zone);
638
639                 seg.from.y -= utm_north_sum;
640                 seg.from.x -= utm_east_sum;
641                 seg.to.y -= utm_north_sum;
642                 seg.to.x -= utm_east_sum;
643
644                 seg.len_sq = (seg.to.y - seg.from.y) * (seg.to.y - seg.from.y) + (seg.to.x - seg.from.x) * (seg.to.x - seg.from.x);
645                 seg.inv_len_sq = 1.0 / seg.len_sq;
646                 seg.wv_x = seg.to.x - seg.from.x;
647                 seg.wv_y = seg.to.y - seg.from.y;
648
649                 roads.push_back(seg);
650         }
651         fclose(fp);
652
653         vector<int> all_road_indexes;
654         for (unsigned i = 0; i < roads.size(); ++i) {
655                 all_road_indexes.push_back(i);
656         }
657         root = make_bsp_tree(all_road_indexes);
658
659         fp = fopen("bsptree.plot", "w");
660         plot_bsp_tree(fp, root, vector<pair<BSPTreeNode*, bool> >());
661         fclose(fp);
662         
663         fp = fopen("map.plot", "w");
664         for (unsigned i = 0; i < roads.size(); ++i) {
665                 fprintf(fp, "%f %f %f %f\n", roads[i].from.x, roads[i].from.y, roads[i].to.x, roads[i].to.y);
666         }
667         fclose(fp);
668
669         int num_points = max_time - min_time + 1;
670         Coord c[num_points];
671
672         Problem problem;
673
674         // Seed the initial path with some guesses.
675         for (int t = min_time; t <= max_time; ++t) {
676                 // find the closest TCX point (yeah, yeah, linear search...)
677                 int best_idx = -1;
678                 int best_distance = INT_MAX;
679                 for (unsigned i = 0; i < tcx_points.size(); ++i) {
680                         int distance = abs(t - tcx_points[i].time);
681                         if (distance < best_distance) {
682                                 best_idx = i;
683                                 best_distance = distance;
684                         }
685                 }
686
687                 c[t - min_time].x = tcx_points[best_idx].utm_east + (rand() % 1000) / 1000.0;
688                 c[t - min_time].y = tcx_points[best_idx].utm_north + (rand() % 1000) / 1000.0;
689         }
690
691         // Create regularization constraints.
692         for (int t = min_time + 1; t <= max_time - 1; ++t) {
693                 problem.AddResidualBlock(
694                     new AutoDiffCostFunction<MinimizeAccelerationCostFunction, 2, 2, 2, 2>(
695                         new MinimizeAccelerationCostFunction),
696                     NULL,
697                     reinterpret_cast<double *>(&c[(t - min_time) - 1]),
698                     reinterpret_cast<double *>(&c[(t - min_time) + 0]),
699                     reinterpret_cast<double *>(&c[(t - min_time) + 1]));
700         }
701         
702         // Create close-to-road constraints.
703         for (int t = min_time + 1; t <= max_time; ++t) {
704                 problem.AddResidualBlock(
705                     new NumericDiffCostFunction<DistanceFromRoadCostFunction, FORWARD, 1, 2, 2>(
706                         new DistanceFromRoadCostFunction,
707                         ceres::TAKE_OWNERSHIP),
708                     NULL,
709                     reinterpret_cast<double *>(&c[t - min_time]),
710                     reinterpret_cast<double *>(&c[t - min_time - 1]));
711         }
712
713         // Now create one contraint per GPS point.
714         for (unsigned i = 0; i < tcx_points.size(); ++i) {
715                 int t = tcx_points[i].time;
716                 problem.AddResidualBlock(
717                     new AutoDiffCostFunction<GPSDiffCostFunction, 1, 2>(
718                         new GPSDiffCostFunction(tcx_points[i].utm_east, tcx_points[i].utm_north)),
719                     NULL,
720                     reinterpret_cast<double *>(&c[t - min_time]));
721         }
722
723         // And per foot point.
724         for (unsigned i = 0; i < foot_points.size(); ++i) {
725                 int t = foot_points[i].time;
726                 if (t - 1 < min_time || t + 1 >= max_time) {
727                         continue;
728                 }
729                 problem.AddResidualBlock(
730                     new AutoDiffCostFunction<FootDiffCostFunction, 1, 2, 2>(
731                         new FootDiffCostFunction(foot_points[i].speed)),
732                     NULL,
733                     reinterpret_cast<double *>(&c[(t - min_time) - 1]),
734                     reinterpret_cast<double *>(&c[(t - min_time) + 1]));
735         }
736
737         printf("pushed %d+%d points\n", int(tcx_points.size()), int(foot_points.size()));
738         printf("time from %d to %d\n", min_time, max_time);
739
740         // Run the solver!
741         Solver::Options options;
742         options.max_num_iterations = 1000000;
743         options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY;
744         //options.linear_solver_type = ceres::DENSE_QR;
745         options.minimizer_progress_to_stdout = true;
746
747         // callback
748         options.update_state_every_iteration = true;
749         options.callbacks.push_back(new MyIterationCallback(c, num_points));
750
751         Solver::Summary summary;
752         Solve(options, &problem, &summary);
753         // if (summary.termination_type == NUMERICAL_FAILURE) {
754         //      return 1;
755         // }
756
757         fp = fopen("out.plot", "w");
758         for (int t = min_time; t <= max_time; ++t) {
759                 fprintf(fp, "%d %f %f\n", t, c[t - min_time].x, c[t - min_time].y);
760         }
761         fclose(fp);
762
763         fp = fopen("out.tcx", "w");
764         fprintf(fp, "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n");
765         fprintf(fp, "<TrainingCenterDatabase xmlns=\"http://www.garmin.com/xmlschemas/TrainingCenterDatabase/v2\" xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\" xsi:schemaLocation=\"http://www.garmin.com/xmlschemas/TrainingCenterDatabase/v2 http://www.garmin.com/xmlschemas/TrainingCenterDatabasev2.xsd\">\n");
766         fprintf(fp, "  <Activities>\n");
767         fprintf(fp, "    <Activity Sport=\"Running\">\n");
768         fprintf(fp, "      <Id>smoothed</Id>\n");
769         fprintf(fp, "      <Lap StartTime=\"%s\">\n", write_time(min_time));
770         fprintf(fp, "        <TotalTimeSeconds>%f</TotalTimeSeconds>\n", float(max_time - min_time + 1));
771         fprintf(fp, "        <DistanceMeters>3720.0</DistanceMeters>\n");  // FIXME
772         fprintf(fp, "        <Intensity>Active</Intensity>\n");
773         fprintf(fp, "        <TriggerMethod>Manual</TriggerMethod>\n");
774         fprintf(fp, "        <Track>\n");
775
776         for (int t = min_time; t <= max_time; ++t) {
777                 double lat, lon;
778                 double north = c[t - min_time].y + utm_north_sum;
779                 double east = c[t - min_time].x + utm_east_sum;
780                 UTMtoLL(23,
781                         north,
782                         east,
783                         tcx_points[0].utm_zone,
784                         lat, lon);
785                 fprintf(fp, "          <TrackPoint>\n");
786                 fprintf(fp, "            <Time>%s</Time>\n", write_time(t));
787                 fprintf(fp, "            <Position>\n");        
788                 fprintf(fp, "              <LatitudeDegrees>%.10f</LatitudeDegrees>\n", lat);
789                 fprintf(fp, "              <LongitudeDegrees>%.10f</LongitudeDegrees>\n", lon);
790                 fprintf(fp, "            </Position>\n");
791                 fprintf(fp, "          </TrackPoint>\n");
792         }
793         fprintf(fp, "        </Track>\n");
794         fprintf(fp, "      </Lap>\n");
795         fprintf(fp, "      <Notes>Created by auto-smoothing points</Notes>\n");
796         fprintf(fp, "    </Activity>\n");
797         fprintf(fp, "  </Activities>\n");
798         fprintf(fp, "</TrainingCenterDatabase>\n");
799         fclose(fp);
800
801         std::cout << summary.BriefReport() << "\n";
802         
803         return 0;
804 }