lily/slur-scoring.cc

   1 /*
   2   slur-quanting.cc -- Score based slur formatting
   3
   4   source file of the GNU LilyPond music typesetter
   5
   6   (c) 1996--2004 Han-Wen Nienhuys <hanwen@cs.uu.nl>
   7   Jan Nieuwenhuizen <janneke@gnu.org>
   8 */
   9
  10 #include <math.h>
  11
  12 #include "accidental-interface.hh"
  13 #include "beam.hh"
  14 #include "directional-element-interface.hh"
  15 #include "group-interface.hh"
  16 #include "libc-extension.hh"
  17 #include "lily-guile.hh"
  18 #include "slur.hh"
  19 #include "note-column.hh"
  20 #include "output-def.hh"
  21 #include "pitch.hh"
  22 #include "bezier.hh"
  23 #include "spanner.hh"
  24 #include "staff-symbol-referencer.hh"
  25 #include "staff-symbol.hh"
  26 #include "stem.hh"
  27 #include "warn.hh"
  28 #include "paper-column.hh"
  29
  30 /*
  31   TODO:
  32
  33   - curve around flag for y coordinate
  34
  35   - this file is a big mess, clean it up
  36
  37
  38   - short-cut: try a smaller region first.
  39
  40   - handle non-visible stems better.
  41
  42   - try to prune number of scoring criteria
  43
  44   - take encompass-objects more into account when determining
  45   slur shape
  46
  47   - calculate encompass scoring directly after determining slur shape.
  48
  49   - optimize.
  50
  51 */
  52
  53 struct Slur_score
  54 {
  55   Drul_array<Offset> attachment_;
  56   Real score_;
  57   Bezier curve_;
  58
  59 #if DEBUG_SLUR_QUANTING
  60   String score_card_;
  61 #endif
  62
  63   Slur_score()
  64   {
  65     score_ = 0.0;
  66   }
  67 };
  68
  69 struct Slur_score_parameters
  70 {
  71   int region_size_;
  72   Real head_encompass_penalty_;
  73   Real stem_encompass_penalty_;
  74   Real closeness_factor_;
  75   Real edge_attraction_factor_;
  76   Real same_slope_penalty_;
  77   Real steeper_slope_factor_;
  78   Real non_horizontal_penalty_;
  79   Real max_slope_;
  80   Real max_slope_factor_;
  81   Real extra_object_collision_;
  82   Real accidental_collision_;
  83   Real free_slur_distance_;
  84   Real free_head_distance_;
  85   Real extra_encompass_free_distance_;
  86
  87   Real head_slur_distance_max_ratio_;
  88   Real head_slur_distance_factor_;
  89
  90
  91
  92   Slur_score_parameters (Grob*);
  93 };
  94
  95
  96 struct Encompass_info
  97 {
  98   Real x_;
  99   Real stem_;
 100   Real head_;
 101   Encompass_info ()
 102   {
 103     x_ = 0.0;
 104     stem_ = 0.0;
 105     head_ = 0.0;
 106   }
 107   Real get_point (Direction dir)
 108   {
 109     Interval y;
 110     y.add_point (stem_);
 111     y.add_point (head_);
 112     return y[dir];
 113   }
 114 };
 115
 116 struct Bound_info
 117 {
 118   Box stem_extent_;
 119   Direction stem_dir_;
 120   Item *bound_;
 121   Grob *note_column_;
 122   Grob *slur_head_;
 123   Grob *staff_;
 124   Grob *stem_;
 125   Interval slur_head_extent_;
 126   Real neighbor_y_;
 127   Real staff_space_;
 128
 129   Bound_info ()
 130   {
 131     stem_ = 0;
 132     neighbor_y_ = 0;
 133     staff_ = 0;
 134     slur_head_ = 0;
 135     stem_dir_ = CENTER;
 136     note_column_ = 0;
 137   }
 138 };
 139
 140 /*
 141   TODO: create one object for passing all parameters.
 142  */
 143
 144
 145 static void
 146 score_extra_encompass (Grob *me, Grob *common[],
 147                        Slur_score_parameters *score_param,
 148                        Drul_array<Bound_info> ,
 149                        Drul_array<Offset> ,
 150                        Array<Slur_score> * scores);
 151 static void score_slopes (Grob *me, Grob *common[],
 152                           Slur_score_parameters *score_param,
 153                           Drul_array<Bound_info>,
 154                           Drul_array<Offset> base_attach,
 155                           Array<Slur_score> *scores);
 156
 157 static void score_edges (Grob *me, Grob *common[],
 158                          Slur_score_parameters *score_param,
 159                          Drul_array<Bound_info> extremes,
 160                          Drul_array<Offset> base_attach,
 161                          Array<Slur_score> *scores);
 162 static void score_encompass (Grob *me, Grob *common[],
 163                              Slur_score_parameters*,
 164                              Drul_array<Bound_info>,
 165                              Drul_array<Offset>, Array<Slur_score> *scores);
 166 static Bezier avoid_staff_line (Grob *me, Grob **common,
 167                                 Drul_array<Bound_info> extremes,
 168                                 Bezier bez);
 169
 170 static Encompass_info get_encompass_info (Grob *me,
 171                                           Grob *col,
 172                                           Grob **common);
 173 static Bezier get_bezier (Grob *me,
 174                           Grob **common,
 175                           Slur_score_parameters*,
 176                           Drul_array<Bound_info> extremes,
 177                           Drul_array<Offset> attachments,
 178                           Real r_0, Real h_inf);
 179 static Direction get_default_dir (Grob *me);
 180
 181 static void set_end_points (Grob *);
 182 static Real broken_trend_y (Grob *me, Grob **, Direction dir);
 183 static Drul_array<Bound_info> get_bound_info (Spanner *me, Grob **common);
 184
 185 static void generate_curves (Grob *me,
 186                              Grob *common[],Slur_score_parameters*,
 187                              Drul_array<Bound_info> extremes,
 188                              Drul_array<Offset> base_attach,
 189                              Array<Slur_score> *scores);
 190 static Array<Slur_score> enumerate_attachments
 191 (Grob *me, Grob *common[], Slur_score_parameters*,
 192  Drul_array<Bound_info> extremes,
 193  Drul_array<Offset> base_attachment, Drul_array<Real> end_ys);
 194 static Drul_array<Offset> get_base_attachments
 195 (Spanner *sp, Grob **common, Drul_array<Bound_info> extremes);
 196 static Drul_array<Real> get_y_attachment_range
 197 (Spanner *sp, Grob **common,
 198  Slur_score_parameters*,
 199  Drul_array<Bound_info> extremes,
 200  Drul_array<Offset> base_attachment);
 201
 202
 203 Real
 204 get_detail (SCM alist, SCM sym)
 205 {
 206   SCM entry = scm_assq (sym, alist);
 207   return robust_scm2double (ly_c_pair_p (entry)
 208                             ? ly_cdr (entry)
 209                             : SCM_EOL,
 210                             0.0);
 211 }
 212
 213 void
 214 init_score_param (Grob *me,
 215                   Slur_score_parameters *score_param)
 216 {
 217   SCM details = me->get_property ("slur-details");
 218
 219   score_param->region_size_
 220     = (int) get_detail (details, ly_symbol2scm ("region-size"));
 221   score_param->head_encompass_penalty_
 222     = get_detail (details, ly_symbol2scm ("head-encompass-penalty"));
 223   score_param->stem_encompass_penalty_
 224     = get_detail (details, ly_symbol2scm ("stem-encompass-penalty"));
 225   score_param->closeness_factor_
 226     = get_detail (details, ly_symbol2scm ("closeness-factor"));
 227   score_param->edge_attraction_factor_
 228     = get_detail (details, ly_symbol2scm ("edge-attraction-factor"));
 229   score_param->same_slope_penalty_
 230     = get_detail (details, ly_symbol2scm ("same-slope-penalty"));
 231   score_param->steeper_slope_factor_
 232     = get_detail (details, ly_symbol2scm ("steeper-slope-factor"));
 233   score_param->non_horizontal_penalty_
 234     = get_detail (details, ly_symbol2scm ("non-horizontal-penalty"));
 235   score_param->max_slope_
 236     = get_detail (details, ly_symbol2scm ("max-slope"));
 237   score_param->max_slope_factor_
 238     = get_detail (details, ly_symbol2scm ("max-slope-factor"));
 239   score_param->free_head_distance_
 240     = get_detail (details, ly_symbol2scm ("free-head-distance"));
 241   score_param->extra_object_collision_
 242     = get_detail (details, ly_symbol2scm ("extra-object-collision"));
 243   score_param->accidental_collision_
 244     = get_detail (details, ly_symbol2scm ("accidental-collision"));
 245   score_param->extra_encompass_free_distance_
 246     = get_detail (details, ly_symbol2scm ("extra-encompass-free-distance"));
 247   score_param->head_slur_distance_factor_
 248     = get_detail (details, ly_symbol2scm ("head-slur-distance-factor"));
 249   score_param->head_slur_distance_max_ratio_
 250     = get_detail (details, ly_symbol2scm ("head-slur-distance-max-ratio"));
 251   score_param->free_slur_distance_
 252     = get_detail (details, ly_symbol2scm ("free-slur-distance"));
 253 }
 254
 255
 256 Slur_score_parameters::Slur_score_parameters(Grob *me)
 257 {
 258   init_score_param (me, this);
 259 }
 260
 261 /* HDIR indicates which side (left or right) we are processing here.  */
 262 Real
 263 broken_trend_y (Grob *me, Grob **common, Direction hdir)
 264 {
 265   /* A broken slur should maintain the same vertical trend
 266      the unbroken slur would have had.  */
 267   Real by = 0.0;
 268   if (Spanner *mother = dynamic_cast<Spanner*> (me->original_))
 269     {
 270       int k = broken_spanner_index (dynamic_cast<Spanner*> (me));
 271       int j = k + hdir;
 272       if (j < 0 || j >= mother->broken_intos_.size ())
 273         return by;
 274
 275       Grob *neighbor = mother->broken_intos_[j];
 276       if (hdir == RIGHT)
 277         neighbor->set_property ("direction",
 278                                 me->get_property ("direction"));
 279
 280       Spanner *common_mother
 281         = dynamic_cast<Spanner*> (common[Y_AXIS]->original_);
 282       int common_k
 283         = broken_spanner_index (dynamic_cast<Spanner*> (common[Y_AXIS]));
 284       int common_j = common_k + hdir;
 285
 286       if (common_j < 0 || common_j >= common_mother->broken_intos_.size())
 287         return by;
 288
 289       Grob *common_next_system = common_mother->broken_intos_[common_j];
 290       Link_array<Grob> neighbor_cols
 291         = Pointer_group_interface__extract_grobs (neighbor, (Grob *)0,
 292                                                   "note-columns");
 293
 294       Grob *neighbor_col
 295         = (hdir == RIGHT) ? neighbor_cols[0] : neighbor_cols.top ();
 296       Grob *neighbor_common
 297         = common_next_system->common_refpoint (neighbor_col, Y_AXIS);
 298
 299       Direction vdir = get_grob_direction (me);
 300       Real neighbor_y
 301         = neighbor_col->extent (neighbor_common, Y_AXIS)
 302         .linear_combination (int(vdir))
 303         - common_next_system->relative_coordinate (neighbor_common, Y_AXIS);
 304
 305       Link_array<Grob> my_cols
 306         = Pointer_group_interface__extract_grobs (me, (Grob *)0,
 307                                                   "note-columns");
 308
 309       Grob *extreme_col = (hdir == RIGHT) ? my_cols.top() : my_cols[0];
 310       Real y = extreme_col->extent (common[Y_AXIS], Y_AXIS)
 311         .linear_combination (int ((my_cols.size() == 1) ? CENTER : vdir));
 312       by = (y*neighbor_cols.size() + neighbor_y*my_cols.size()) /
 313         (my_cols.size() + neighbor_cols.size());
 314     }
 315   return by;
 316 }
 317
 318 Encompass_info
 319 get_encompass_info (Grob *me,
 320                     Grob *col,
 321                     Grob **common)
 322 {
 323   Grob *stem = unsmob_grob (col->get_property ("stem"));
 324   Encompass_info ei;
 325   Direction dir = get_grob_direction (me);
 326
 327   if (!stem)
 328     {
 329       programming_error ("No stem for note column?");
 330       ei.x_ = col->relative_coordinate (common[X_AXIS], X_AXIS);
 331       ei.head_ = ei.stem_ = col->extent (common[Y_AXIS],
 332                                          Y_AXIS)[get_grob_direction (me)];
 333       return ei;
 334     }
 335   Direction stem_dir = get_grob_direction (stem);
 336
 337   if (Grob *head = Note_column::first_head (col))
 338     ei.x_ = head->extent (common[X_AXIS], X_AXIS).center ();
 339   else
 340     ei.x_ = col->extent (common[X_AXIS], X_AXIS).center ();
 341
 342   Grob *h = Stem::extremal_heads (stem)[Direction (dir)];
 343   if (!h)
 344     {
 345       ei.head_ = ei.stem_ = col->extent (common[Y_AXIS], Y_AXIS)[dir];
 346       return ei;
 347     }
 348
 349   ei.head_ = h->extent (common[Y_AXIS], Y_AXIS)[dir];
 350
 351   if ((stem_dir == dir)
 352       && !stem->extent (stem, Y_AXIS).is_empty ())
 353     {
 354       ei.stem_ = stem->extent (common[Y_AXIS], Y_AXIS)[dir];
 355       if (Grob *b = Stem::get_beam (stem))
 356         ei.stem_ += stem_dir * 0.5 * Beam::get_thickness (b);
 357
 358       Interval x = stem->extent (common[X_AXIS], X_AXIS);
 359       ei.x_ = x.is_empty ()
 360         ? stem->relative_coordinate (common[X_AXIS], X_AXIS)
 361         : x.center ();
 362     }
 363   else
 364     ei.stem_ = ei.head_;
 365
 366   return ei;
 367 }
 368
 369
 370 Direction
 371 get_default_dir (Grob*me)
 372 {
 373   Link_array<Grob> encompasses
 374     = Pointer_group_interface__extract_grobs (me, (Grob*) 0, "note-columns");
 375
 376   Direction d = DOWN;
 377   for (int i= 0; i < encompasses.size (); i ++)
 378     {
 379       if (Note_column::dir (encompasses[i]) < 0)
 380         {
 381           d = UP;
 382           break;
 383         }
 384     }
 385   return d;
 386 }
 387
 388
 389
 390 MAKE_SCHEME_CALLBACK (Slur, after_line_breaking,1);
 391 SCM
 392 Slur::after_line_breaking (SCM smob)
 393 {
 394   Spanner *me = dynamic_cast<Spanner*> (unsmob_grob (smob));
 395   if (!scm_ilength (me->get_property ("note-columns")))
 396     {
 397       me->suicide ();
 398       return SCM_UNSPECIFIED;
 399     }
 400
 401   if (!get_grob_direction (me))
 402     set_grob_direction (me, get_default_dir (me));
 403
 404   if (scm_ilength (me->get_property ("control-points")) < 4)
 405     set_end_points (me);
 406
 407   return SCM_UNSPECIFIED;
 408 }
 409
 410 Drul_array<Bound_info>
 411 get_bound_info (Spanner* me, Grob **common)
 412 {
 413   Drul_array<Bound_info> extremes;
 414   Direction d = LEFT;
 415   Direction dir = get_grob_direction (me);
 416
 417   do
 418     {
 419       extremes[d].bound_ = me->get_bound (d);
 420       if (Note_column::has_interface (extremes[d].bound_))
 421         {
 422           extremes[d].note_column_ = extremes[d].bound_;
 423           extremes[d].stem_ = Note_column::get_stem (extremes[d].note_column_);
 424           extremes[d].stem_dir_ = get_grob_direction (extremes[d].stem_);
 425           extremes[d].stem_extent_[X_AXIS]
 426             = extremes[d].stem_->extent (common[X_AXIS], X_AXIS);
 427           extremes[d].stem_extent_[Y_AXIS]
 428             = extremes[d].stem_->extent (common[Y_AXIS], Y_AXIS);
 429           extremes[d].slur_head_
 430             = Stem::extremal_heads (extremes[d].stem_)[dir];
 431           if (!extremes[d].slur_head_
 432               && Note_column::has_rests (extremes[d].bound_))
 433             {
 434               extremes[d].slur_head_ = Note_column::get_rest (extremes[d].bound_);
 435             }
 436
 437           if (extremes[d].slur_head_)
 438             extremes[d].slur_head_extent_
 439               = extremes[d].slur_head_->extent (common[X_AXIS], X_AXIS);
 440
 441           extremes[d].staff_ = Staff_symbol_referencer
 442             ::get_staff_symbol (extremes[d].stem_);
 443           extremes[d].staff_space_ = Staff_symbol_referencer
 444             ::staff_space (extremes[d].stem_);
 445         }
 446       else
 447         extremes[d].neighbor_y_ = broken_trend_y (me, common, d);
 448     }
 449   while (flip (&d) != LEFT);
 450   return extremes;
 451 }
 452
 453 void
 454 set_end_points (Grob *me)
 455 {
 456   Link_array<Grob> columns
 457     = Pointer_group_interface__extract_grobs (me, (Grob *) 0, "note-columns");
 458
 459   if (columns.is_empty ())
 460     {
 461       me->suicide ();
 462       return;
 463     }
 464
 465   SCM eltlist = me->get_property ("note-columns");
 466   SCM extra_list = me->get_property ("encompass-objects");
 467   Spanner *sp = dynamic_cast<Spanner*> (me);
 468
 469   Grob *common[] = {0, 0};
 470   for (int i = X_AXIS; i < NO_AXES; i++)
 471     {
 472       Axis a = (Axis)i;
 473       common[a] = common_refpoint_of_list (eltlist, me, a);
 474       common[a] = common_refpoint_of_list (extra_list, common[a], a);
 475     }
 476
 477   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (RIGHT),
 478                                                     X_AXIS);
 479   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (LEFT),
 480                                                     X_AXIS);
 481
 482   Drul_array<Bound_info> extremes = get_bound_info (sp, common);
 483   Drul_array<Offset> base_attachment
 484     = get_base_attachments (sp, common, extremes);
 485   Slur_score_parameters params (me);
 486   Drul_array<Real> end_ys
 487     = get_y_attachment_range (sp, common, &params, extremes, base_attachment);
 488   Array<Slur_score> scores = enumerate_attachments (me, common, &params,
 489                                                     extremes, base_attachment,
 490                                                     end_ys);
 491
 492   generate_curves (me, common, &params, extremes, base_attachment, &scores);
 493   score_edges (me, common, &params,extremes, base_attachment, &scores);
 494   score_slopes (me, common, &params,extremes, base_attachment, &scores);
 495   score_encompass (me, common, &params,extremes, base_attachment, &scores);
 496   score_extra_encompass (me, common, &params,extremes, base_attachment,
 497                          &scores);
 498
 499   Real opt = 1e6;
 500   int opt_idx = 0;
 501   // why backwards?
 502   for (int i = scores.size (); i--;)
 503     {
 504       if (scores[i].score_ < opt)
 505         {
 506           opt = scores[i].score_;
 507           opt_idx = i;
 508         }
 509     }
 510
 511 #if DEBUG_SLUR_QUANTING
 512   SCM inspect_quants = me->get_property ("inspect-quants");
 513   if (to_boolean (me->get_paper ()
 514                   ->lookup_variable (ly_symbol2scm ("debug-slur-scoring")))
 515       && ly_c_pair_p (inspect_quants))
 516     {
 517       Drul_array<Real> ins = ly_scm2interval (inspect_quants);
 518       Real mindist = 1e6;
 519       for (int i = 0; i < scores.size (); i ++)
 520         {
 521           Real d =fabs (scores[i].attachment_[LEFT][Y_AXIS] - ins[LEFT])
 522             + fabs (scores[i].attachment_[RIGHT][Y_AXIS] - ins[RIGHT]);
 523           if (d < mindist)
 524             {
 525               opt_idx = i;
 526               mindist= d;
 527             }
 528         }
 529       if (mindist > 1e5)
 530         programming_error ("Could not find quant.");
 531     }
 532   scores[opt_idx].score_card_ += to_string ("i%d", opt_idx);
 533
 534   // debug quanting
 535   me->set_property ("quant-score",
 536                     scm_makfrom0str (scores[opt_idx].score_card_.to_str0 ()));
 537 #endif
 538
 539   Bezier b = scores[opt_idx].curve_;
 540   SCM controls = SCM_EOL;
 541   for (int i = 4; i--;)
 542     {
 543       Offset o = b.control_[i]
 544         - Offset (me->relative_coordinate (common[X_AXIS], X_AXIS),
 545                   me->relative_coordinate (common[Y_AXIS], Y_AXIS));
 546       controls = scm_cons (ly_offset2scm (o), controls);
 547     }
 548   me->set_property ("control-points", controls);
 549 }
 550
 551 /*
 552   TODO: should analyse encompasses to determine sensible region, and
 553   should limit slopes available.
 554  */
 555
 556 Drul_array<Real>
 557 get_y_attachment_range (Spanner*me,
 558                         Grob **common, Slur_score_parameters *score_param,
 559                         Drul_array<Bound_info> extremes,
 560                         Drul_array<Offset> base_attachment)
 561 {
 562   Drul_array<Real> end_ys;
 563   Direction dir = get_grob_direction (me);
 564   Direction d = LEFT;
 565   do
 566     {
 567       if (extremes[d].note_column_)
 568         {
 569           end_ys[d] = dir
 570             * ((dir * (base_attachment[d][Y_AXIS] +  score_param->region_size_* dir))
 571                >? (dir * (dir + extremes[d].note_column_->extent(common[Y_AXIS],
 572                                                                  Y_AXIS)[dir]))
 573                >? (dir * base_attachment[-d][Y_AXIS]));
 574         }
 575       else
 576         end_ys[d] = extremes[d].neighbor_y_ + score_param->region_size_ * dir;
 577     }
 578   while (flip (&d) != LEFT);
 579
 580   return end_ys;
 581 }
 582
 583 bool
 584 spanner_less (Spanner *s1, Spanner* s2)
 585 {
 586   Slice b1, b2;
 587   Direction d  = LEFT;
 588   do
 589     {
 590       b1[d] = s1->get_bound (d)->get_column ()->rank_;
 591       b2[d] = s2->get_bound (d)->get_column ()->rank_;
 592     } while (flip (&d) != LEFT);
 593
 594   return b2[LEFT] <= b1[LEFT] && b2[RIGHT] >= b1[RIGHT]
 595     && (b2[LEFT] != b1[LEFT] || b2[RIGHT] != b1[RIGHT]);
 596 }
 597
 598
 599 Drul_array<Offset>
 600 get_base_attachments (Spanner *me,
 601                       Grob **common, Drul_array<Bound_info> extremes)
 602 {
 603   Link_array<Grob> columns
 604     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 605   Drul_array<Offset> base_attachment;
 606   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 607   Direction dir = get_grob_direction (me);
 608   Direction d = LEFT;
 609   do
 610     {
 611       Grob *stem = extremes[d].stem_;
 612       Grob *head = extremes[d].slur_head_;
 613
 614       Real x, y;
 615       if (!extremes[d].note_column_)
 616         {
 617           y = extremes[d].neighbor_y_;
 618           if (d== RIGHT)
 619             x = extremes[d].bound_->extent (common[X_AXIS], X_AXIS)[d];
 620           else
 621             x = me->get_broken_left_end_align ();
 622         }
 623       else
 624         {
 625           bool same_beam =
 626             (extremes[d].stem_ && extremes[-d].stem_
 627              && Stem::get_beam (extremes[d].stem_) == Stem::get_beam (extremes[-d].stem_));
 628
 629           /*
 630             fixme: X coord should also be set in this case.
 631            */
 632           if (stem
 633               && extremes[d].stem_dir_ == dir
 634               && Stem::get_beaming (stem, -d)
 635               && (!spanner_less (me, Stem::get_beam (stem))
 636                   || same_beam))
 637             y = extremes[d].stem_extent_[Y_AXIS][dir];
 638           else if (head)
 639             y = head->extent (common[Y_AXIS], Y_AXIS)[dir];
 640           y += dir * 0.5 * staff_space;
 641
 642           Real pos
 643             = (y - extremes[d].staff_->relative_coordinate (common[Y_AXIS],
 644                                                             Y_AXIS))
 645             * 2.0 / Staff_symbol::staff_space (extremes[d].staff_);
 646
 647           /* start off staffline. */
 648           if (fabs (pos - my_round (pos)) < 0.2
 649               && Staff_symbol_referencer::on_staffline (head, (int) rint (pos))
 650               && Staff_symbol_referencer::line_count (head) - 1 >= rint (pos)
 651               )
 652             // TODO: calc from slur thick & line thick, parameter.
 653             y += 1.5 * staff_space * dir / 10;
 654
 655           Grob * fh = Note_column::first_head (extremes[d].note_column_);
 656           x =
 657             (fh ? fh->extent (common[X_AXIS], X_AXIS)
 658              : extremes[d].bound_->extent (common[X_AXIS], X_AXIS))
 659             .linear_combination (CENTER);
 660         }
 661       base_attachment[d] = Offset (x, y);
 662
 663     } while (flip (&d) != LEFT);
 664
 665   return base_attachment;
 666 }
 667
 668 void
 669 generate_curves (Grob *me, Grob **common,
 670                  Slur_score_parameters *score_param,
 671                  Drul_array<Bound_info> extremes,
 672                  Drul_array<Offset>,
 673                  Array<Slur_score> *scores)
 674 {
 675   (void) common;
 676   (void) extremes;
 677   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 678   Real r_0 = robust_scm2double (me->get_property ("ratio"), 0.33);
 679   Real h_inf = staff_space * scm_to_double (me->get_property ("height-limit"));
 680   for (int i = 0; i < scores->size(); i++)
 681     {
 682       Bezier bez = get_bezier (me,
 683                               common,
 684                               score_param,
 685                               extremes,
 686                               (*scores)[i].attachment_, r_0, h_inf);
 687
 688       bez = avoid_staff_line (me, common, extremes, bez);
 689       (*scores)[i].attachment_[LEFT] = bez.control_[0];
 690       (*scores)[i].attachment_[RIGHT] = bez.control_[3];
 691       (*scores)[i].curve_ = bez;
 692     }
 693 }
 694
 695 Bezier
 696 avoid_staff_line (Grob *me, Grob **common,
 697                   Drul_array<Bound_info> extremes,
 698                   Bezier bez)
 699 {
 700   Offset horiz (1,0);
 701   Array<Real> ts = bez.solve_derivative (horiz);
 702   Real lt = me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
 703   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) *  lt;
 704
 705   /* TODO: handle case of broken slur.  */
 706   if (!ts.is_empty ()
 707       && (extremes[LEFT].staff_ == extremes[RIGHT].staff_)
 708       && extremes[LEFT].staff_ && extremes[RIGHT].staff_)
 709     {
 710       Real y = bez.curve_point (ts[0])[Y_AXIS];
 711
 712       Grob *staff = extremes[LEFT].staff_;
 713
 714       Real staff_space = extremes[LEFT].staff_space_;
 715       Real p = 2 * (y - staff->relative_coordinate (common[Y_AXIS], Y_AXIS))
 716         / staff_space;
 717
 718       Real distance = fabs (my_round (p) - p);  //  in halfspaces
 719       if (distance < 4 * thick
 720           && (int) fabs (my_round (p))
 721           <= 2 * Staff_symbol_referencer::staff_radius (staff) + 0.1
 722           && (int (fabs (my_round (p))) % 2
 723               != Staff_symbol_referencer::line_count (staff) % 2))
 724         {
 725           Direction resolution_dir =
 726             (distance ?  get_grob_direction (me) : Direction (sign (p - my_round(p))));
 727
 728           // TODO: parameter
 729           Real newp = my_round (p) + resolution_dir
 730             * 5 * thick;
 731
 732           Real dy = (newp - p) * staff_space / 2.0;
 733
 734           bez.control_[1][Y_AXIS] += dy;
 735           bez.control_[2][Y_AXIS] += dy;
 736         }
 737     }
 738   return bez;
 739 }
 740
 741 Array<Slur_score>
 742 enumerate_attachments (Grob *me, Grob *common[],
 743                        Slur_score_parameters *score_param,
 744                        Drul_array<Bound_info> extremes,
 745                        Drul_array<Offset> base_attachment,
 746                        Drul_array<Real> end_ys)
 747 {
 748   (void) common;
 749   /*ugh.   */
 750   Array<Slur_score> scores;
 751
 752   Direction dir = get_grob_direction (me);
 753   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 754
 755   Drul_array<Offset> os;
 756   os[LEFT] = base_attachment[LEFT];
 757   Real minimum_length = staff_space
 758     * robust_scm2double (me->get_property ("minimum-length"), 2.0);
 759
 760   for (int i = 0; dir * os[LEFT][Y_AXIS] <= dir * end_ys[LEFT]; i++)
 761     {
 762       os[RIGHT] = base_attachment[RIGHT];
 763       for (int j = 0; dir * os[RIGHT][Y_AXIS] <= dir * end_ys[RIGHT]; j++)
 764         {
 765           Slur_score s;
 766           Direction d = LEFT;
 767           Drul_array<bool> attach_to_stem (false, false);
 768           do
 769             {
 770               os[d][X_AXIS] = base_attachment[d][X_AXIS];
 771               if (extremes[d].stem_
 772                   && !Stem::is_invisible (extremes[d].stem_)
 773                   && extremes[d].stem_dir_ == dir)
 774                 {
 775                   if (dir == -d
 776                       && extremes[d].stem_extent_[Y_AXIS].contains (os[d][Y_AXIS]))
 777                     {
 778                       os[d][X_AXIS] =  extremes[d].slur_head_extent_[-d]
 779                         - d * 0.3;
 780                       attach_to_stem[d] = true;
 781                     }
 782                   else if (dir *extremes[d].stem_extent_[Y_AXIS][dir]
 783                              < dir * os[d][Y_AXIS]
 784                            && !extremes[d].stem_extent_[X_AXIS].is_empty()
 785                            )
 786
 787                     os[d][X_AXIS] = extremes[d].stem_extent_[X_AXIS].center();
 788                 }
 789             }
 790           while (flip (&d) != LEFT);
 791
 792           Offset dz;
 793           dz = os[RIGHT] - os[LEFT];
 794           if (dz[X_AXIS] < minimum_length
 795               || fabs (dz[Y_AXIS] / dz[X_AXIS]) > score_param->max_slope_
 796               )
 797             {
 798               do
 799                 {
 800                   if (extremes[d].slur_head_)
 801                     {
 802                       os[d][X_AXIS] = extremes[d].slur_head_extent_.center ();
 803                       attach_to_stem[d] = false;
 804                     }
 805                 }
 806               while (flip (&d) != LEFT);
 807             }
 808
 809           dz = os[RIGHT] - os[LEFT];
 810           do
 811             {
 812               if (extremes[d].slur_head_
 813                   && !attach_to_stem[d])
 814                 {
 815                   /* Horizontally move tilted slurs a little.  Move
 816                      more for bigger tilts.
 817
 818                      TODO: parameter */
 819                   os[d][X_AXIS]
 820                     -= dir * extremes[d].slur_head_extent_.length ()
 821                     * sin (dz.arg  ()) / 3;
 822                 }
 823             }
 824           while (flip (&d) != LEFT);
 825
 826           s.attachment_ = os;
 827           scores.push (s);
 828
 829           os[RIGHT][Y_AXIS] += dir * staff_space / 2;
 830         }
 831
 832       os[LEFT][Y_AXIS] += dir * staff_space / 2;
 833     }
 834   return scores;
 835 }
 836
 837 inline Real
 838 linear_interpolate (Real x, Real x1, Real x2,  Real y1, Real  y2)
 839 {
 840   return (x2 - x) / (x2 - x1) * y1 +
 841     (x - x1) / (x2 - x1) * y2 ;
 842 }
 843
 844
 845 void
 846 score_encompass (Grob *me, Grob *common[],
 847                  Slur_score_parameters *score_param,
 848                  Drul_array<Bound_info> extremes,
 849                  Drul_array<Offset> base_attach,
 850                  Array<Slur_score> *scores)
 851 {
 852   (void) extremes;
 853   (void) base_attach;
 854
 855   Link_array<Grob> encompasses
 856     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 857   Direction dir = get_grob_direction (me);
 858
 859   Array<Encompass_info> infos;
 860
 861   for (int i = 0; i < encompasses.size(); i++)
 862     infos.push (get_encompass_info (me, encompasses[i], common));
 863
 864   for (int i = 0; i < scores->size (); i++)
 865     {
 866       Slur_score &configuration = scores->elem_ref (i);
 867       Bezier const &bez (configuration.curve_);
 868       Real demerit = 0.0;
 869
 870       /*
 871         Distances for heads that are between slur and line between
 872         attachment points.
 873        */
 874       Array<Real> convex_head_distances;
 875       Array<Real> edge_distances;
 876       for (int j = 0; j < infos.size(); j++)
 877         {
 878           Real x = infos[j].x_;
 879
 880           bool l_edge = j==0;
 881           bool r_edge = j==infos.size()-1;
 882           bool edge =  l_edge || r_edge;
 883
 884
 885           if (edge)
 886           {
 887             edge_distances.push (fabs (configuration.attachment_[l_edge ? LEFT : RIGHT][Y_AXIS]
 888                                        - infos[j].get_point (dir)));
 889           }
 890
 891
 892           if (!(x < configuration.attachment_[RIGHT][X_AXIS]
 893                 && x > configuration.attachment_[LEFT][X_AXIS]))
 894             continue;
 895
 896           Real y = bez.get_other_coordinate (X_AXIS, x);
 897           if (!edge)
 898             {
 899               Real head_dy = (y - infos[j].head_);
 900               if (dir * head_dy < 0)
 901                 {
 902                   demerit += score_param->head_encompass_penalty_;
 903                   convex_head_distances.push (0.0);
 904                 }
 905               else
 906                 {
 907                   Real hd = (head_dy)
 908                     ? (1 / fabs (head_dy) - 1 / score_param->free_head_distance_)
 909                     : score_param->head_encompass_penalty_;
 910                   hd = (hd >? 0)<? score_param->head_encompass_penalty_;
 911
 912                   demerit += hd;
 913                 }
 914
 915               Real line_y = linear_interpolate (x,
 916                                                 configuration.attachment_[RIGHT][X_AXIS],
 917                                                 configuration.attachment_[LEFT][X_AXIS],
 918                                                 configuration.attachment_[RIGHT][Y_AXIS],
 919                                                 configuration.attachment_[LEFT][Y_AXIS]);
 920
 921               if (dir * (infos[j].get_point (dir) - line_y) > 0)
 922                 {
 923                   Real d = fabs (infos[j].get_point (dir) - y);
 924                   convex_head_distances.push (d);
 925                 }
 926             }
 927
 928
 929
 930
 931           if (dir * (y - infos[j].stem_) < 0)
 932             {
 933               Real stem_dem =score_param->stem_encompass_penalty_ ;
 934               if ((l_edge && dir == UP)
 935                   || (r_edge && dir == DOWN))
 936                 stem_dem /= 5;
 937
 938               demerit +=  stem_dem;
 939             }
 940           else if (!edge)
 941             {
 942               Interval ext;
 943               ext.add_point (infos[j].stem_);
 944               ext.add_point (infos[j].head_);
 945
 946               // ?
 947               demerit += -score_param->closeness_factor_
 948                 * (dir
 949                    * (y - (ext[dir] + dir * score_param->free_head_distance_))
 950                    <? 0)
 951                 / infos.size ();
 952             }
 953         }
 954
 955       Real variance_penalty = 0.0;
 956
 957       if (convex_head_distances.size())
 958         {
 959           Real avg_distance = 0.0;
 960           Real min_dist = infinity_f;
 961           for (int j = 0; j < convex_head_distances.size(); j++)
 962             {
 963               min_dist = min_dist <? convex_head_distances[j];
 964               avg_distance += convex_head_distances[j];
 965             }
 966
 967           /*
 968             For slurs over 3 or 4 heads, the average distance is not a
 969             good normalizer.
 970            */
 971           int n =  convex_head_distances.size();
 972           if (convex_head_distances.size() <= 2)
 973             {
 974               for (int j = 0; j < edge_distances.size(); j++)
 975                 {
 976                   avg_distance += edge_distances[j];
 977                   n++;
 978                 }
 979             }
 980
 981           /*
 982             TODO: maybe it's better to use (avgdist - mindist)*factor
 983             as penalty.
 984            */
 985           avg_distance /= n;
 986           variance_penalty = score_param->head_slur_distance_max_ratio_;
 987           if (min_dist > 0.0)
 988             variance_penalty = ((avg_distance / (min_dist  +score_param->free_head_distance_)) - 1.0)
 989               <? variance_penalty;
 990
 991           variance_penalty *= score_param->head_slur_distance_factor_;
 992         }
 993 #if DEBUG_SLUR_QUANTING
 994       (*scores)[i].score_card_ += to_string ("C%.2f", demerit);
 995       (*scores)[i].score_card_ += to_string ("D%.2f", variance_penalty);
 996 #endif
 997
 998       (*scores)[i].score_ += demerit + variance_penalty;
 999     }
1000 }
1001
1002 struct Extra_collision_info
1003 {
1004   Real idx_;
1005   Box extents_;
1006   Real penalty_;
1007
1008   Extra_collision_info (Real idx, Interval x, Interval y, Real p)
1009   {
1010     idx_ = idx;
1011     extents_[X_AXIS] = x;
1012     extents_[Y_AXIS] = y;
1013     penalty_ = p;
1014   }
1015   Extra_collision_info ()
1016   {
1017     idx_ = 0.0;
1018     penalty_ = 0.;
1019   }
1020 };
1021
1022 void
1023 score_extra_encompass (Grob *me, Grob *common[],
1024                        Slur_score_parameters *score_param,
1025                        Drul_array<Bound_info> extremes,
1026                        Drul_array<Offset> base_attach,
1027                        Array<Slur_score> *scores)
1028 {
1029   (void) base_attach;
1030   (void) extremes;
1031
1032   Spanner *me_spanner = dynamic_cast<Spanner*> (me);
1033
1034   Link_array<Grob> encompasses
1035     = Pointer_group_interface__extract_grobs (me, (Grob *)0,
1036                                               "encompass-objects");
1037   Direction dir = get_grob_direction (me);
1038   Real lt =  me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
1039   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) * lt;
1040
1041   Array<Extra_collision_info> collision_infos;
1042   for (int i = encompasses.size (); i--; )
1043     {
1044       if (Slur::has_interface (encompasses[i]))
1045         {
1046           Spanner * small_slur = dynamic_cast<Spanner*> (encompasses[i]);
1047           Bezier b = Slur::get_curve (small_slur);
1048
1049           Offset relative (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1050                            small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1051
1052           for (int k = 0; k < 3; k++)
1053           {
1054             Direction hdir =  Direction (k /2 - 1);
1055
1056             /*
1057               Only take bound into account if small slur starts
1058               together with big slur.
1059              */
1060             if (hdir && small_slur->get_bound (hdir) != me_spanner->get_bound (hdir))
1061               continue;
1062
1063
1064             Offset z = b.curve_point ( k / 2.0);
1065             z += relative;
1066
1067             Interval yext;
1068             yext.set_full();
1069             yext[dir] = z[Y_AXIS] + dir * thick * 1.0;
1070
1071             Interval xext(-1, 1);
1072             xext = xext *(thick*2) + z[X_AXIS];
1073             Extra_collision_info info (k - 1.0,
1074                                        xext,
1075                                        yext,
1076                                        score_param->extra_object_collision_);
1077             collision_infos.push (info);
1078           }
1079         }
1080       else
1081         {
1082           Grob *g = encompasses [i];
1083           Interval xe = g->extent (common[X_AXIS], X_AXIS);
1084           Interval ye = g->extent (common[Y_AXIS], Y_AXIS);
1085
1086           Real xp = 0.0;
1087           Real penalty = score_param->extra_object_collision_;
1088           if (Accidental_interface::has_interface (g))
1089             {
1090               penalty = score_param->accidental_collision_;
1091               /* Begin copy accidental.cc */
1092               bool parens = false;
1093               if (to_boolean (g->get_property ("cautionary")))
1094                 {
1095                   SCM cstyle = g->get_property ("cautionary-style");
1096                   parens = ly_c_equal_p (cstyle, ly_symbol2scm ("parentheses"));
1097                 }
1098
1099               SCM accs = g->get_property ("accidentals");
1100               SCM scm_style = g->get_property ("style");
1101               if (!scm_is_symbol (scm_style)
1102                   && !parens
1103                   && scm_ilength (accs) == 1)
1104                 {
1105                   /* End copy accidental.cc */
1106                   switch (scm_to_int (ly_car (accs)))
1107                     {
1108                     case FLAT:
1109                     case DOUBLE_FLAT:
1110                       xp = LEFT;
1111                       break ;
1112                     case SHARP:
1113                       xp = 0.5 * dir;
1114                       break ;
1115                     case NATURAL:
1116                       xp = -dir;
1117                       break;
1118                     }
1119                 }
1120             }
1121
1122           ye.widen (thick * 0.5);
1123           Extra_collision_info info (xp, xe, ye,  penalty);
1124           collision_infos.push (info);
1125         }
1126     }
1127   for (int i = 0; i < scores->size (); i++)
1128     {
1129       Real demerit = 0.0;
1130       for (int j = 0; j < collision_infos.size(); j++)
1131         {
1132           Drul_array<Offset> at = scores->elem (i).attachment_;
1133           Interval slur_wid (at[LEFT][X_AXIS], at[RIGHT][X_AXIS]);
1134
1135           /*
1136             to prevent numerical inaccuracies in
1137             Bezier::get_other_coordinate().
1138            */
1139           slur_wid.widen (- 0.5 * thick);
1140           Real x = collision_infos[j].extents_[X_AXIS]
1141             .linear_combination (collision_infos[j].idx_);
1142           Real y = 0.0;
1143
1144           if (!slur_wid.contains (x))
1145             {
1146               Direction contains_dir = CENTER;
1147               Direction d = LEFT;
1148               do
1149                 {
1150                   if (collision_infos[j].extents_[X_AXIS].contains (at[d][X_AXIS]))
1151                     contains_dir = d;
1152                 }
1153               while (flip (&d) != LEFT);
1154
1155               if (!contains_dir)
1156                 continue;
1157               else
1158                 y = at[contains_dir][Y_AXIS];
1159             }
1160           else
1161             {
1162               y = scores->elem (i).curve_.get_other_coordinate (X_AXIS, x);
1163             }
1164
1165           Real dist = collision_infos[j].extents_[Y_AXIS].distance (y);
1166           demerit +=
1167             fabs (0 >? (score_param->extra_encompass_free_distance_ - dist)) /
1168             score_param->extra_encompass_free_distance_
1169             * collision_infos[j].penalty_;
1170         }
1171 #if DEBUG_SLUR_QUANTING
1172       (*scores)[i].score_card_ += to_string ("X%.2f", demerit);
1173 #endif
1174       (*scores)[i].score_ += demerit;
1175     }
1176 }
1177
1178 void
1179 score_edges (Grob *me, Grob *common[],
1180              Slur_score_parameters * score_param,
1181              Drul_array<Bound_info> extremes,
1182              Drul_array<Offset> base_attach,
1183              Array<Slur_score> *scores)
1184 {
1185   (void) common;
1186   Direction dir = get_grob_direction (me);
1187
1188   for (int i = 0; i < scores->size (); i++)
1189     {
1190       Direction d = LEFT;
1191       do
1192         {
1193           Real y = scores->elem (i).attachment_[d][Y_AXIS];
1194           Real dy = fabs (y - base_attach[d][Y_AXIS]);
1195
1196           Real factor = score_param->edge_attraction_factor_;
1197           Real demerit = factor * dy;
1198           if (extremes[d].stem_
1199               && extremes[d].stem_dir_ == dir
1200               && !Stem::get_beaming (extremes[d].stem_, -d)
1201               )
1202             demerit /= 5;
1203
1204           (*scores)[i].score_ += demerit;
1205 #if DEBUG_SLUR_QUANTING
1206           (*scores)[i].score_card_ += to_string ("E%.2f", demerit);
1207 #endif
1208         }
1209       while (flip (&d) != LEFT);
1210     }
1211 }
1212
1213 void
1214 score_slopes (Grob *me, Grob *common[],
1215               Slur_score_parameters *score_param,
1216               Drul_array<Bound_info> extremes,
1217               Drul_array<Offset> base_attach,
1218               Array<Slur_score> * scores)
1219 {
1220   (void) me;
1221   (void) base_attach;
1222
1223   Drul_array<Real> ys;
1224   Direction d = LEFT;
1225   do
1226     {
1227       if (extremes[d].slur_head_)
1228         ys[d] = extremes[d].slur_head_->relative_coordinate (common[Y_AXIS],
1229                                                               Y_AXIS);
1230       else
1231         ys[d] = extremes[d].neighbor_y_;
1232     }
1233   while (flip (&d) != LEFT);
1234
1235   bool has_beams
1236     = (extremes[LEFT].stem_ && Stem::get_beam (extremes[LEFT].stem_))
1237     || (extremes[RIGHT].stem_ && Stem::get_beam (extremes[RIGHT].stem_));
1238
1239   Real dy = ys[RIGHT] - ys[LEFT];
1240   for (int i = 0; i < scores->size (); i++)
1241     {
1242       Offset slur_dz = (*scores)[i].attachment_[RIGHT]
1243         - (*scores)[i].attachment_[LEFT];
1244       Real slur_dy = slur_dz[Y_AXIS];
1245       Real demerit = 0.0;
1246
1247       demerit += ((fabs (slur_dy / slur_dz[X_AXIS])
1248                    - score_param->max_slope_) >? 0)
1249         * score_param->max_slope_factor_;
1250
1251       /* 0.2: account for staffline offset. */
1252       Real max_dy = (fabs (dy) + 0.2);
1253       if (has_beams)
1254         max_dy += 1.0;
1255
1256       demerit += score_param->steeper_slope_factor_
1257         * ((fabs (slur_dy) -max_dy) >? 0);
1258
1259       demerit += ((fabs (slur_dy/slur_dz[X_AXIS])
1260                    - score_param->max_slope_) >? 0)
1261         * score_param->max_slope_factor_;
1262
1263       if (sign (dy) == 0
1264           && sign (slur_dy) != 0)
1265         demerit += score_param->non_horizontal_penalty_;
1266
1267       if (sign (dy)
1268           && sign (slur_dy)
1269           && sign (slur_dy) != sign (dy))
1270         demerit += has_beams
1271           ? score_param->same_slope_penalty_ / 10
1272           : score_param->same_slope_penalty_;
1273
1274 #if DEBUG_SLUR_QUANTING
1275       (*scores)[i].score_card_ += to_string ("S%.2f", d);
1276 #endif
1277       (*scores)[i].score_ += demerit;
1278     }
1279
1280
1281
1282 }
1283
1284
1285 Real
1286 fit_factor (Offset dz_unit, Offset dz_perp,
1287             Bezier curve, Direction d,  Array<Offset> const &avoid)
1288 {
1289   Real fit_factor = 0.0;
1290   Offset x0 = curve.control_[0];
1291   curve.translate (-x0);
1292   curve.rotate (-dz_unit.arg ());
1293   curve.scale (1, d);
1294
1295   Interval curve_xext;
1296   curve_xext.add_point (curve.control_[0][X_AXIS]);
1297   curve_xext.add_point (curve.control_[3][X_AXIS]);
1298
1299   for (int i = 0; i < avoid.size (); i++)
1300     {
1301       Offset z = (avoid[i] - x0) ;
1302       Offset p (dot_product (z, dz_unit),
1303                 d* dot_product (z, dz_perp));
1304       if (!curve_xext.contains (p[X_AXIS]))
1305         continue;
1306
1307       Real y = curve.get_other_coordinate (X_AXIS, p[X_AXIS]);
1308       if (y)
1309         {
1310           fit_factor = fit_factor >? (p[Y_AXIS] / y);
1311         }
1312     }
1313   return fit_factor;
1314 }
1315
1316
1317 Bezier
1318 get_bezier (Grob *me,
1319             Grob **common,
1320             Slur_score_parameters *score_param,
1321             Drul_array<Bound_info> extremes,
1322             Drul_array<Offset> attachments,
1323             Real r_0, Real h_inf
1324             )
1325 {
1326   Link_array<Grob> encompasses
1327     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
1328   Direction dir = get_grob_direction (me);
1329
1330   Array<Offset> avoid;
1331   for (int i = 0; i < encompasses.size(); i++)
1332     {
1333       if (extremes[LEFT].note_column_ == encompasses[i]
1334           ||extremes[RIGHT].note_column_ == encompasses[i])
1335         continue;
1336
1337       Encompass_info inf (get_encompass_info (me, encompasses[i], common));
1338
1339       Real y = dir*((dir * inf.head_) >? (dir *inf.stem_));
1340
1341       avoid.push (Offset (inf.x_,  y + dir * score_param->free_head_distance_));
1342     }
1343
1344   Link_array<Grob> extra_encompasses
1345     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "encompass-objects");
1346   for (int i = 0;  i < extra_encompasses.size (); i++)
1347     if (Slur::has_interface (extra_encompasses[i]))
1348       {
1349         Grob * small_slur = extra_encompasses[i];
1350         Bezier b = Slur::get_curve (small_slur);
1351
1352         Offset z = b.curve_point (0.5);
1353         z += Offset (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1354                      small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1355
1356         z[Y_AXIS] += dir * score_param->free_slur_distance_;
1357         avoid.push (z);
1358       }
1359
1360   Offset dz = attachments[RIGHT]- attachments[LEFT];;
1361   Offset dz_unit = dz;
1362   dz_unit *= 1 / dz.length();
1363   Offset dz_perp = dz_unit * Offset(0,1);
1364
1365   Real indent, height;
1366   get_slur_indent_height (&indent, &height, dz.length (), h_inf, r_0);
1367
1368   Real excentricity = robust_scm2double (me->get_property ("excentricity"), 0.0);
1369   Bezier curve;
1370
1371   Real x1 = (excentricity + indent);
1372   Real x2 = (excentricity - indent);
1373   curve.control_[0] = attachments[LEFT];
1374   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1375   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1376   curve.control_[3] = attachments[RIGHT];
1377
1378
1379   Real ff = fit_factor (dz_unit, dz_perp, curve, dir, avoid);
1380   Real l = dz.length ();
1381
1382   /*
1383     This condition,
1384
1385     l^2 > 4h^2 +  3(i  1/3l)^2  - 1/3 l^2
1386
1387     is equivalent to:
1388
1389     |bez'(0)| < | bez'(.5)|
1390
1391     when (control2-control1) has the same direction as (control3 -
1392     control0).
1393
1394    */
1395   Real max_h = sqrt (sqr (l)/3 - .75 * sqr (indent + l / 3));
1396   height = height >? ((height * ff) <? max_h);
1397
1398   curve.control_[0] = attachments[LEFT];
1399   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1400   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1401   curve.control_[3] = attachments[RIGHT];
1402
1403   return curve;
1404 }