lily/beam-quanting.cc

   1 /*
   2   This file is part of LilyPond, the GNU music typesetter.
   3
   4   Copyright (C) 1997--2011 Han-Wen Nienhuys <hanwen@xs4all.nl>
   5   Jan Nieuwenhuizen <janneke@gnu.org>
   6
   7   LilyPond is free software: you can redistribute it and/or modify
   8   it under the terms of the GNU General Public License as published by
   9   the Free Software Foundation, either version 3 of the License, or
  10   (at your option) any later version.
  11
  12   LilyPond is distributed in the hope that it will be useful,
  13   but WITHOUT ANY WARRANTY; without even the implied warranty of
  14   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15   GNU General Public License for more details.
  16
  17   You should have received a copy of the GNU General Public License
  18   along with LilyPond.  If not, see <http://www.gnu.org/licenses/>.
  19 */
  20
  21 #include "beam-scoring-problem.hh"
  22
  23 #include <algorithm>
  24 #include <queue>
  25 #include <set>
  26 using namespace std;
  27
  28 #include "align-interface.hh"
  29 #include "beam.hh"
  30 #include "direction.hh"
  31 #include "directional-element-interface.hh"
  32 #include "grob.hh"
  33 #include "international.hh"
  34 #include "libc-extension.hh"
  35 #include "main.hh"
  36 #include "output-def.hh"
  37 #include "pointer-group-interface.hh"
  38 #include "staff-symbol-referencer.hh"
  39 #include "stencil.hh"
  40 #include "stem.hh"
  41 #include "warn.hh"
  42
  43 Real
  44 get_detail (SCM alist, SCM sym, Real def)
  45 {
  46   SCM entry = scm_assq (sym, alist);
  47
  48   if (scm_is_pair (entry))
  49     return robust_scm2double (scm_cdr (entry), def);
  50   return def;
  51 }
  52
  53 void
  54 Beam_quant_parameters::fill (Grob *him)
  55 {
  56   SCM details = him->get_property ("details");
  57
  58   // General
  59   BEAM_EPS = get_detail (details, ly_symbol2scm ("beam-eps"), 1e-3);
  60   REGION_SIZE = get_detail (details, ly_symbol2scm ("region-size"), 2);
  61
  62   // forbidden quants
  63   SECONDARY_BEAM_DEMERIT = get_detail (details, ly_symbol2scm ("secondary-beam-demerit"), 10.0);
  64   STEM_LENGTH_DEMERIT_FACTOR = get_detail (details, ly_symbol2scm ("stem-length-demerit-factor"), 5);
  65   HORIZONTAL_INTER_QUANT_PENALTY = get_detail (details, ly_symbol2scm ("horizontal-inter-quant"), 500);
  66
  67   STEM_LENGTH_LIMIT_PENALTY = get_detail (details, ly_symbol2scm ("stem-length-limit-penalty"), 5000);
  68   DAMPING_DIRECTION_PENALTY = get_detail (details, ly_symbol2scm ("damping-direction-penalty"), 800);
  69   HINT_DIRECTION_PENALTY = get_detail (details, ly_symbol2scm ("hint-direction-penalty"), 20);
  70   MUSICAL_DIRECTION_FACTOR = get_detail (details, ly_symbol2scm ("musical-direction-factor"), 400);
  71   IDEAL_SLOPE_FACTOR = get_detail (details, ly_symbol2scm ("ideal-slope-factor"), 10);
  72   ROUND_TO_ZERO_SLOPE = get_detail (details, ly_symbol2scm ("round-to-zero-slope"), 0.02);
  73
  74   // Collisions
  75   COLLISION_PENALTY = get_detail (details, ly_symbol2scm ("collision-penalty"), 500);
  76   COLLISION_PADDING = get_detail (details, ly_symbol2scm ("collision-padding"), 0.5);
  77   STEM_COLLISION_FACTOR = get_detail (details, ly_symbol2scm ("stem-collision-factor"), 0.1);
  78 }
  79
  80 // Add x if x is positive, add |x|*fac if x is negative.
  81 static Real
  82 shrink_extra_weight (Real x, Real fac)
  83 {
  84   return fabs (x) * ((x < 0) ? fac : 1.0);
  85 }
  86
  87 /****************************************************************/
  88
  89 Beam_configuration::Beam_configuration ()
  90 {
  91   y = Interval (0.0, 0.0);
  92   demerits = 0.0;
  93   next_scorer_todo = ORIGINAL_DISTANCE;
  94 }
  95
  96 bool Beam_configuration::done () const
  97 {
  98   return next_scorer_todo >= NUM_SCORERS;
  99 }
 100
 101 void Beam_configuration::add (Real demerit, const string &reason)
 102 {
 103   demerits += demerit;
 104
 105 #if DEBUG_BEAM_SCORING
 106   if (demerit)
 107     score_card_ += to_string (" %s %.2f", reason.c_str (), demerit);
 108 #endif
 109 }
 110
 111 Beam_configuration* Beam_configuration::new_config (Interval start,
 112                                                     Interval offset)
 113 {
 114   Beam_configuration* qs = new Beam_configuration;
 115   qs->y = Interval (int (start[LEFT]) + offset[LEFT],
 116                     int (start[RIGHT]) + offset[RIGHT]);
 117
 118   // This orders the sequence so we try combinations closest to the
 119   // the ideal offset first.
 120   Real start_score = abs (offset[RIGHT]) + abs (offset[LEFT]);
 121   qs->demerits = start_score / 1000.0;
 122   qs->next_scorer_todo = ORIGINAL_DISTANCE + 1;
 123
 124   return qs;
 125 }
 126
 127 Real
 128 Beam_scoring_problem::y_at (Real x, Beam_configuration const* p) const {
 129   return p->y[LEFT] + (x - x_span[LEFT]) * p->y.delta() / x_span.delta();
 130 }
 131
 132 /****************************************************************/
 133
 134 /*
 135   TODO:
 136
 137   - Make all demerits customisable
 138
 139   - Add demerits for quants per se, as to forbid a specific quant
 140   entirely
 141 */
 142
 143 // This is a temporary hack to see how much we can gain by using a
 144 // priority queue on the beams to score.
 145 static int score_count = 0;
 146 LY_DEFINE (ly_beam_score_count, "ly:beam-score-count", 0, 0, 0,
 147            (),
 148            "count number of beam scores.") {
 149   return scm_from_int (score_count);
 150 }
 151
 152 void Beam_scoring_problem::add_collision (Real x, Interval y,
 153                                           Real score_factor)
 154 {
 155   if (edge_dirs[LEFT] == edge_dirs[RIGHT]) {
 156     Direction d = edge_dirs[LEFT];
 157
 158     Real quant_range_y = quant_range[LEFT][-d] +
 159       (x - x_span[LEFT]) * (quant_range[RIGHT][-d] - quant_range[LEFT][-d]) / x_span.delta();
 160
 161     if (d*(quant_range_y - minmax(d, y[UP], y[DOWN])) > 0) {
 162       return;
 163     }
 164   }
 165
 166   Beam_collision c;
 167   c.beam_y_.set_empty ();
 168
 169   for (vsize j = 0; j < segments_.size (); j++)
 170     {
 171       if (segments_[j].horizontal_.contains(x))
 172         c.beam_y_.add_point (segments_[j].vertical_count_ * beam_translation);
 173       if (segments_[j].horizontal_[LEFT] > x)
 174         break;
 175     }
 176   c.beam_y_.widen (0.5 * beam_thickness);
 177
 178   c.x_ = x;
 179   c.y_ = y;
 180   c.base_penalty_ = score_factor;
 181   collisions_.push_back (c);
 182 }
 183
 184 void Beam_scoring_problem::init_collisions (vector<Grob*> grobs)
 185 {
 186   Grob* common_x = NULL;
 187   segments_ = Beam::get_beam_segments (beam, &common_x);
 188   vector_sort (segments_, beam_segment_less);
 189   if (common[X_AXIS] != common_x)
 190     {
 191       programming_error ("Disagree on common x. Skipping collisions in beam scoring.");
 192       return;
 193     }
 194
 195   set<Grob*> stems;
 196   for (vsize i = 0; i < grobs.size (); i++) {
 197     Box b;
 198     for (Axis a = X_AXIS; a < NO_AXES; incr (a))
 199       b[a] = grobs[i]->extent(common[a], a);
 200
 201     Real width = b[X_AXIS].length ();
 202     Real width_factor = sqrt (width / staff_space);
 203
 204     Direction d = LEFT;
 205     do
 206       add_collision (b[X_AXIS][d], b[Y_AXIS], width_factor);
 207     while (flip (&d) != LEFT);
 208
 209     Grob* stem = unsmob_grob (grobs[i]->get_object ("stem"));
 210     if (stem && Stem::has_interface (stem) && Stem::is_normal_stem (stem))
 211       {
 212         stems.insert (stem);
 213       }
 214   }
 215
 216   for (set<Grob*>::const_iterator it(stems.begin ()); it != stems.end (); it++)
 217     {
 218       Grob *s = *it;
 219       Real x = s->extent (common[X_AXIS], X_AXIS).center();
 220
 221       Direction stem_dir = get_grob_direction (*it);
 222       Interval y;
 223       y.set_full ();
 224       y[-stem_dir] = Stem::chord_start_y (*it) + (*it)->relative_coordinate (common[Y_AXIS], Y_AXIS)
 225         - beam->relative_coordinate (common[Y_AXIS], Y_AXIS);
 226
 227       Real factor = parameters.STEM_COLLISION_FACTOR;
 228       if (!unsmob_grob (s->get_object ("beam"))
 229           && !Stem::flag (s).is_empty ())
 230         factor = 1.0;
 231       add_collision (x, y, factor);
 232     }
 233 }
 234
 235 void Beam_scoring_problem::init_stems ()
 236 {
 237   extract_grob_set (beam, "covered-grobs", collisions);
 238   extract_grob_set (beam, "stems", stems);
 239   for (int a = 2; a--;)
 240     {
 241       common[a] = common_refpoint_of_array (stems, beam, Axis (a));
 242       common[a] = common_refpoint_of_array (collisions, common[a], Axis (a));
 243     }
 244
 245   Drul_array<Grob *> edge_stems(Beam::first_normal_stem (beam),
 246                                 Beam::last_normal_stem (beam));
 247   Direction d = LEFT;
 248   do
 249     x_span[d] = edge_stems[d] ? edge_stems[d]->relative_coordinate (common[X_AXIS], X_AXIS) : 0.0;
 250   while (flip (&d) != LEFT);
 251
 252   Drul_array<bool> dirs_found (0, 0);
 253   for (vsize i = 0; i < stems.size (); i++)
 254     {
 255       Grob *s = stems[i];
 256       if (!Stem::is_normal_stem (s))
 257         continue;
 258
 259       Stem_info si (Stem::get_stem_info (s));
 260       si.scale (1 / staff_space);
 261       stem_infos.push_back (si);
 262       dirs_found[si.dir_] = true;
 263
 264       bool f = to_boolean (s->get_property ("french-beaming"))
 265         && s != edge_stems[LEFT] && s != edge_stems[RIGHT];
 266
 267       Real y = Beam::calc_stem_y (beam, s, common, x_span[LEFT], x_span[RIGHT], CENTER,
 268                                   Interval (0, 0), f);
 269       base_lengths.push_back (y / staff_space);
 270       stem_xpositions.push_back (s->relative_coordinate (common[X_AXIS], X_AXIS));
 271     }
 272
 273   edge_dirs = Drul_array<Direction> (CENTER, CENTER);
 274   if (stem_infos.size ())
 275     {
 276       edge_dirs = Drul_array<Direction> (stem_infos[0].dir_,
 277                                          stem_infos.back().dir_);
 278     }
 279
 280   is_xstaff = Align_interface::has_interface (common[Y_AXIS]);
 281   is_knee = dirs_found[LEFT] && dirs_found[RIGHT];
 282
 283   staff_radius = Staff_symbol_referencer::staff_radius (beam);
 284   edge_beam_counts =  Drul_array<int>
 285     (Stem::beam_multiplicity (stems[0]).length () + 1,
 286      Stem::beam_multiplicity (stems.back ()).length () + 1);
 287
 288   // TODO - why are we dividing by staff_space?
 289   beam_translation = Beam::get_beam_translation (beam) / staff_space;
 290
 291   d = LEFT;
 292   do
 293     {
 294       quant_range[d].set_full ();
 295       if (!edge_stems[d])
 296         continue;
 297
 298       Real stem_offset = edge_stems[d]->relative_coordinate (common[Y_AXIS], Y_AXIS)
 299         - beam->relative_coordinate (common[Y_AXIS], Y_AXIS);
 300       Interval heads = Stem::head_positions(edge_stems[d]) * 0.5 * staff_space;
 301
 302       Direction ed = edge_dirs[d];
 303       heads.widen(0.5 * staff_space
 304                   + (edge_beam_counts[d] - 1) * beam_translation + beam_thickness * .5);
 305       quant_range[d][-ed] = heads[ed] + stem_offset;
 306     }
 307   while (flip (&d) != LEFT);
 308
 309   init_collisions (collisions);
 310 }
 311
 312 Beam_scoring_problem::Beam_scoring_problem (Grob *me, Drul_array<Real> ys)
 313 {
 314   beam = me;
 315   unquanted_y = ys;
 316
 317   /*
 318     Calculations are relative to a unit-scaled staff, i.e. the quants are
 319     divided by the current staff_space.
 320   */
 321   staff_space = Staff_symbol_referencer::staff_space (me);
 322   beam_thickness = Beam::get_beam_thickness (me) / staff_space;
 323   line_thickness = Staff_symbol_referencer::line_thickness (me) / staff_space;
 324
 325   // This is the least-squares DY, corrected for concave beams.
 326   musical_dy = robust_scm2double (me->get_property ("least-squares-dy"), 0);
 327
 328   parameters.fill (me);
 329   init_stems ();
 330 }
 331
 332 void
 333 Beam_scoring_problem::generate_quants (vector<Beam_configuration*> *scores) const
 334 {
 335   int region_size = (int) parameters.REGION_SIZE;
 336
 337   // Knees and collisions are harder, lets try some more possibilities
 338   if (is_knee)
 339     region_size += 2;
 340   if (collisions_.size ())
 341     region_size += 2;
 342
 343   Real straddle = 0.0;
 344   Real sit = (beam_thickness - line_thickness) / 2;
 345   Real inter = 0.5;
 346   Real hang = 1.0 - (beam_thickness - line_thickness) / 2;
 347   Real base_quants [] = {straddle, sit, inter, hang};
 348   int num_base_quants = int (sizeof (base_quants) / sizeof (Real));
 349
 350   /*
 351     Asymetry ? should run to <= region_size ?
 352   */
 353   vector<Real> unshifted_quants;
 354   for (int i = -region_size; i < region_size; i++)
 355     for (int j = 0; j < num_base_quants; j++)
 356       {
 357         unshifted_quants.push_back (i + base_quants[j]);
 358       }
 359
 360   for (vsize i = 0; i < unshifted_quants.size (); i++)
 361     for (vsize j = 0; j < unshifted_quants.size (); j++)
 362       {
 363         Beam_configuration *c =
 364           Beam_configuration::new_config (unquanted_y,
 365                                           Interval (unshifted_quants[i],
 366                                                     unshifted_quants[j]));
 367
 368         Direction d = LEFT;
 369         do
 370           {
 371             if (!quant_range[d].contains (c->y[d]))
 372               {
 373                 delete c;
 374                 c = NULL;
 375                 break;
 376               }
 377           }
 378         while (flip (&d) != LEFT);
 379         if (c)
 380           scores->push_back (c);
 381       }
 382
 383 }
 384
 385
 386 void Beam_scoring_problem::one_scorer (Beam_configuration* config) const
 387 {
 388   score_count ++;
 389   switch (config->next_scorer_todo) {
 390   case SLOPE_IDEAL:
 391     score_slope_ideal (config);
 392     break;
 393   case SLOPE_DIRECTION:
 394     score_slope_direction (config);
 395     break;
 396   case SLOPE_MUSICAL:
 397     score_slope_musical (config);
 398     break;
 399   case FORBIDDEN:
 400     score_forbidden_quants (config);
 401     break;
 402   case STEM_LENGTHS:
 403     score_stem_lengths (config);
 404     break;
 405   case COLLISIONS:
 406     score_collisions (config);
 407     break;
 408   case HORIZONTAL_INTER:
 409     score_horizontal_inter_quants (config);
 410     break;
 411
 412   case NUM_SCORERS:
 413   case ORIGINAL_DISTANCE:
 414   default:
 415     assert (false);
 416   }
 417   config->next_scorer_todo++;
 418 }
 419
 420
 421 Beam_configuration *
 422 Beam_scoring_problem::force_score (SCM inspect_quants, const vector<Beam_configuration*> &configs) const
 423 {
 424   Drul_array<Real> ins = ly_scm2interval (inspect_quants);
 425   Real mindist = 1e6;
 426   Beam_configuration *best = NULL;
 427   for (vsize i = 0; i < configs.size (); i++)
 428     {
 429       Real d = fabs (configs[i]->y[LEFT]- ins[LEFT]) + fabs (configs[i]->y[RIGHT] - ins[RIGHT]);
 430       if (d < mindist)
 431         {
 432           best = configs[i];
 433           mindist = d;
 434         }
 435     }
 436   if (mindist > 1e5)
 437     programming_error ("cannot find quant");
 438
 439   while (!best->done ())
 440     one_scorer (best);
 441
 442   return best;
 443 }
 444
 445 Drul_array<Real>
 446 Beam_scoring_problem::solve () const {
 447   vector<Beam_configuration*> configs;
 448   generate_quants (&configs);
 449
 450   Beam_configuration *best = NULL;
 451
 452   bool debug =
 453     to_boolean (beam->layout ()->lookup_variable (ly_symbol2scm ("debug-beam-scoring")));
 454   SCM inspect_quants = beam->get_property ("inspect-quants");
 455   if (scm_is_pair (inspect_quants))
 456     {
 457       debug = true;
 458       best = force_score (inspect_quants, configs);
 459     }
 460   else
 461     {
 462       std::priority_queue<Beam_configuration*, std::vector<Beam_configuration*>,
 463                           Beam_configuration_less> queue;
 464       for (vsize i = 0; i < configs.size(); i++)
 465         queue.push(configs[i]);
 466
 467       /*
 468         TODO
 469
 470         It would be neat if we generated new configurations on the
 471         fly, depending on the best complete score so far, eg.
 472
 473         if (best->done()) {
 474           if (best->demerits < sqrt(queue.size())
 475             break;
 476           while (best->demerits > sqrt(queue.size()) {
 477             generate and insert new configuration
 478           }
 479         }
 480
 481         that would allow us to do away with region_size altogether.
 482       */
 483       while (true) {
 484         best = queue.top ();
 485         if (best->done ())
 486           break;
 487
 488         queue.pop ();
 489         one_scorer (best);
 490         queue.push (best);
 491       }
 492     }
 493
 494   Interval final_positions = best->y;
 495
 496 #if DEBUG_BEAM_SCORING
 497   if (debug)
 498     {
 499       // debug quanting
 500       int completed = 0;
 501       for (vsize i = 0; i < configs.size (); i++)
 502         {
 503           if (configs[i]->done ())
 504             completed++;
 505         }
 506
 507       string card = best->score_card_ + to_string (" c%d/%d", completed, configs.size());
 508       beam->set_property ("annotation", ly_string2scm (card));
 509     }
 510 #endif
 511
 512   junk_pointers (configs);
 513   return final_positions;
 514 }
 515
 516 void
 517 Beam_scoring_problem::score_stem_lengths (Beam_configuration* config) const
 518 {
 519   Real limit_penalty = parameters.STEM_LENGTH_LIMIT_PENALTY;
 520   Drul_array<Real> score (0, 0);
 521   Drul_array<int> count (0, 0);
 522
 523   for (vsize i = 0; i < stem_xpositions.size (); i++)
 524     {
 525       Real x = stem_xpositions[i];
 526       Real dx = x_span.delta ();
 527       Real beam_y = dx
 528         ? config->y[RIGHT] * (x - x_span[LEFT]) / dx + config->y[LEFT] * (x_span[RIGHT] - x) / dx
 529         : (config->y[RIGHT] + config->y[LEFT]) / 2;
 530       Real current_y = beam_y + base_lengths[i];
 531       Real length_pen = parameters.STEM_LENGTH_DEMERIT_FACTOR;
 532
 533       Stem_info info = stem_infos[i];
 534       Direction d = info.dir_;
 535
 536       score[d] += limit_penalty * max (0.0, (d * (info.shortest_y_ - current_y)));
 537
 538       Real ideal_diff = d * (current_y - info.ideal_y_);
 539       Real ideal_score = shrink_extra_weight (ideal_diff, 1.5);
 540
 541       /* We introduce a power, to make the scoring strictly
 542          convex. Otherwise a symmetric knee beam (up/down/up/down)
 543          does not have an optimum in the middle. */
 544       if (is_knee)
 545         ideal_score = pow (ideal_score, 1.1);
 546
 547       score[d] += length_pen * ideal_score;
 548       count[d]++;
 549     }
 550
 551   /* Divide by number of stems, to make the measure scale-free. */
 552   Direction d = DOWN;
 553   do
 554     score[d] /= max (count[d], 1);
 555   while (flip (&d) != DOWN);
 556
 557   config->add (score[LEFT] + score[RIGHT], "L");
 558 }
 559
 560 void
 561 Beam_scoring_problem::score_slope_direction (Beam_configuration *config) const
 562 {
 563   Real dy = config->y.delta ();
 564   Real damped_dy = unquanted_y.delta();
 565   Real dem = 0.0;
 566   /*
 567     DAMPING_DIRECTION_PENALTY is a very harsh measure, while for
 568     complex beaming patterns, horizontal is often a good choice.
 569
 570     TODO: find a way to incorporate the complexity of the beam in this
 571     penalty.
 572   */
 573   if (sign (damped_dy) != sign (dy))
 574     {
 575       if (!dy)
 576         {
 577           if (fabs (damped_dy / x_span.delta ()) > parameters.ROUND_TO_ZERO_SLOPE)
 578             dem += parameters.DAMPING_DIRECTION_PENALTY;
 579           else
 580             dem += parameters.HINT_DIRECTION_PENALTY;
 581         }
 582       else
 583         dem += parameters.DAMPING_DIRECTION_PENALTY;
 584     }
 585
 586   config->add (dem, "Sd");
 587 }
 588
 589 // Score for going against the direction of the musical pattern
 590 void
 591 Beam_scoring_problem::score_slope_musical (Beam_configuration *config) const
 592 {
 593   Real dy = config->y.delta ();
 594   Real dem = parameters.MUSICAL_DIRECTION_FACTOR
 595     * max (0.0, (fabs (dy) - fabs (musical_dy)));
 596   config->add (dem, "Sm");
 597 }
 598
 599 // Score deviation from calculated ideal slope.
 600 void
 601 Beam_scoring_problem::score_slope_ideal (Beam_configuration *config) const
 602 {
 603   Real dy = config->y.delta ();
 604   Real damped_dy = unquanted_y.delta();
 605   Real dem = 0.0;
 606
 607   Real slope_penalty = parameters.IDEAL_SLOPE_FACTOR;
 608
 609   /* Xstaff beams tend to use extreme slopes to get short stems. We
 610      put in a penalty here. */
 611   if (is_xstaff)
 612     slope_penalty *= 10;
 613
 614   /* Huh, why would a too steep beam be better than a too flat one ? */
 615   dem += shrink_extra_weight (fabs (damped_dy) - fabs (dy), 1.5)
 616     * slope_penalty;
 617
 618   config->add (dem, "Si");
 619 }
 620
 621 static Real
 622 my_modf (Real x)
 623 {
 624   return x - floor (x);
 625 }
 626
 627 // TODO - there is some overlap with forbidden quants, but for
 628 // horizontal beams, it is much more serious to have stafflines
 629 // appearing in the wrong place, so we have a separate scorer.
 630 void
 631 Beam_scoring_problem::score_horizontal_inter_quants (Beam_configuration *config) const
 632 {
 633   if (config->y.delta () == 0.0
 634       && abs (config->y[LEFT]) < staff_radius * staff_space)
 635     {
 636       Real yshift = config->y[LEFT] - 0.5 * staff_space;
 637       if (fabs (my_round (yshift) - yshift) < 0.01 * staff_space)
 638         config->add (parameters.HORIZONTAL_INTER_QUANT_PENALTY, "H");
 639     }
 640 }
 641
 642 /*
 643   TODO: The fixed value SECONDARY_BEAM_DEMERIT is probably flawed:
 644   because for 32nd and 64th beams the forbidden quants are relatively
 645   more important than stem lengths.
 646 */
 647 void
 648 Beam_scoring_problem::score_forbidden_quants (Beam_configuration *config) const
 649 {
 650   Real dy = config->y.delta ();
 651
 652   Real extra_demerit = parameters.SECONDARY_BEAM_DEMERIT /
 653     max (edge_beam_counts[LEFT], edge_beam_counts[RIGHT]);
 654
 655   Direction d = LEFT;
 656   Real dem = 0.0;
 657   Real eps = parameters.BEAM_EPS;
 658
 659   do
 660     {
 661       for (int j = 1; j <= edge_beam_counts[d]; j++)
 662         {
 663           Direction stem_dir = edge_dirs[d];
 664
 665           /*
 666             The 2.2 factor is to provide a little leniency for
 667             borderline cases. If we do 2.0, then the upper outer line
 668             will be in the gap of the (2, sit) quant, leading to a
 669             false demerit.
 670           */
 671           Real gap1 = config->y[d] - stem_dir * ((j - 1) * beam_translation + beam_thickness / 2 - line_thickness / 2.2);
 672           Real gap2 = config->y[d] - stem_dir * (j * beam_translation - beam_thickness / 2 + line_thickness / 2.2);
 673
 674           Interval gap;
 675           gap.add_point (gap1);
 676           gap.add_point (gap2);
 677
 678           for (Real k = -staff_radius;
 679                k <= staff_radius + eps; k += 1.0)
 680             if (gap.contains (k))
 681               {
 682                 Real dist = min (fabs (gap[UP] - k), fabs (gap[DOWN] - k));
 683
 684                 /*
 685                   this parameter is tuned to grace-stem-length.ly
 686                 */
 687                 Real fixed_demerit = 0.4;
 688
 689                 dem += extra_demerit
 690                   * (fixed_demerit
 691                      + (1 - fixed_demerit) * (dist / gap.length ()) * 2);
 692               }
 693         }
 694     }
 695   while ((flip (&d)) != LEFT);
 696
 697   if (max (edge_beam_counts[LEFT], edge_beam_counts[RIGHT]) >= 2)
 698     {
 699       Real straddle = 0.0;
 700       Real sit = (beam_thickness - line_thickness) / 2;
 701       Real inter = 0.5;
 702       Real hang = 1.0 - (beam_thickness - line_thickness) / 2;
 703
 704       Direction d = LEFT;
 705       do
 706         {
 707           if (edge_beam_counts[d] >= 2
 708               && fabs (config->y[d] - edge_dirs[d] * beam_translation) < staff_radius + inter)
 709             {
 710               // TODO up/down symmetry.
 711               if (edge_dirs[d] == UP && dy <= eps
 712                   && fabs (my_modf (config->y[d]) - sit) < eps)
 713                 dem += extra_demerit;
 714
 715               if (edge_dirs[d] == DOWN && dy >= eps
 716                   && fabs (my_modf (config->y[d]) - hang) < eps)
 717                 dem += extra_demerit;
 718             }
 719
 720           if (edge_beam_counts[d] >= 3
 721               && fabs (config->y[d] - 2 * edge_dirs[d] * beam_translation) < staff_radius + inter)
 722             {
 723               // TODO up/down symmetry.
 724               if (edge_dirs[d] == UP && dy <= eps
 725                   && fabs (my_modf (config->y[d]) - straddle) < eps)
 726                 dem += extra_demerit;
 727
 728               if (edge_dirs[d] == DOWN && dy >= eps
 729                   && fabs (my_modf (config->y[d]) - straddle) < eps)
 730                 dem += extra_demerit;
 731             }
 732         }
 733       while (flip (&d) != LEFT);
 734     }
 735
 736   config->add (dem, "F");
 737 }
 738
 739 void
 740 Beam_scoring_problem::score_collisions (Beam_configuration *config) const
 741 {
 742   Real demerits = 0.0;
 743   for (vsize i = 0; i < collisions_.size (); i++)
 744     {
 745       Interval collision_y = collisions_[i].y_;
 746       Real x = collisions_[i].x_;
 747
 748       Real center_beam_y = y_at (x, config);
 749       Interval beam_y = center_beam_y + collisions_[i].beam_y_;
 750
 751       Real dist = infinity_f;
 752       if (!intersection (beam_y, collision_y).is_empty ())
 753         dist = 0.0;
 754       else
 755         dist = min (beam_y.distance (collision_y[DOWN]),
 756                     beam_y.distance (collision_y[UP]));
 757
 758       Real scale_free =
 759         max (parameters.COLLISION_PADDING - dist, 0.0)/
 760         parameters.COLLISION_PADDING;
 761       demerits +=
 762         collisions_[i].base_penalty_ *
 763         pow (scale_free, 3) * parameters.COLLISION_PENALTY;
 764     }
 765
 766   config->add (demerits, "C");
 767 }