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