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 if (d == RIGHT)
 447         /*
 448           right side anticipates on the next note.
 449         */
 450         extremes[d].neighbor_y_ = broken_trend_y (me, common, d);
 451
 452       else
 453         {
 454           Link_array<Grob> columns
 455             = Pointer_group_interface__extract_grobs (me, (Grob *) 0, "note-columns");
 456           extremes[d].neighbor_y_ = columns[0]->extent (common[Y_AXIS], Y_AXIS)[dir];
 457         }
 458     }
 459   while (flip (&d) != LEFT);
 460   return extremes;
 461 }
 462
 463 void
 464 set_end_points (Grob *me)
 465 {
 466   Link_array<Grob> columns
 467     = Pointer_group_interface__extract_grobs (me, (Grob *) 0, "note-columns");
 468
 469   if (columns.is_empty ())
 470     {
 471       me->suicide ();
 472       return;
 473     }
 474
 475   SCM eltlist = me->get_property ("note-columns");
 476   SCM extra_list = me->get_property ("encompass-objects");
 477   Spanner *sp = dynamic_cast<Spanner*> (me);
 478
 479   Grob *common[] = {0, 0};
 480   for (int i = X_AXIS; i < NO_AXES; i++)
 481     {
 482       Axis a = (Axis)i;
 483       common[a] = common_refpoint_of_list (eltlist, me, a);
 484       common[a] = common_refpoint_of_list (extra_list, common[a], a);
 485     }
 486
 487   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (RIGHT),
 488                                                     X_AXIS);
 489   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (LEFT),
 490                                                     X_AXIS);
 491
 492   Drul_array<Bound_info> extremes = get_bound_info (sp, common);
 493   Drul_array<Offset> base_attachment
 494     = get_base_attachments (sp, common, extremes);
 495   Slur_score_parameters params (me);
 496   Drul_array<Real> end_ys
 497     = get_y_attachment_range (sp, common, &params, extremes, base_attachment);
 498   Array<Slur_score> scores = enumerate_attachments (me, common, &params,
 499                                                     extremes, base_attachment,
 500                                                     end_ys);
 501
 502   generate_curves (me, common, &params, extremes, base_attachment, &scores);
 503   score_edges (me, common, &params,extremes, base_attachment, &scores);
 504   score_slopes (me, common, &params,extremes, base_attachment, &scores);
 505   score_encompass (me, common, &params,extremes, base_attachment, &scores);
 506   score_extra_encompass (me, common, &params,extremes, base_attachment,
 507                          &scores);
 508
 509   Real opt = 1e6;
 510   int opt_idx = 0;
 511   // why backwards?
 512   for (int i = scores.size (); i--;)
 513     {
 514       if (scores[i].score_ < opt)
 515         {
 516           opt = scores[i].score_;
 517           opt_idx = i;
 518         }
 519     }
 520
 521 #if DEBUG_SLUR_QUANTING
 522   SCM inspect_quants = me->get_property ("inspect-quants");
 523   if (to_boolean (me->get_paper ()
 524                   ->lookup_variable (ly_symbol2scm ("debug-slur-scoring")))
 525       && ly_c_pair_p (inspect_quants))
 526     {
 527       Drul_array<Real> ins = ly_scm2interval (inspect_quants);
 528       Real mindist = 1e6;
 529       for (int i = 0; i < scores.size (); i ++)
 530         {
 531           Real d =fabs (scores[i].attachment_[LEFT][Y_AXIS] - ins[LEFT])
 532             + fabs (scores[i].attachment_[RIGHT][Y_AXIS] - ins[RIGHT]);
 533           if (d < mindist)
 534             {
 535               opt_idx = i;
 536               mindist= d;
 537             }
 538         }
 539       if (mindist > 1e5)
 540         programming_error ("Could not find quant.");
 541     }
 542   scores[opt_idx].score_card_ += to_string ("i%d", opt_idx);
 543
 544   // debug quanting
 545   me->set_property ("quant-score",
 546                     scm_makfrom0str (scores[opt_idx].score_card_.to_str0 ()));
 547 #endif
 548
 549   Bezier b = scores[opt_idx].curve_;
 550   SCM controls = SCM_EOL;
 551   for (int i = 4; i--;)
 552     {
 553       Offset o = b.control_[i]
 554         - Offset (me->relative_coordinate (common[X_AXIS], X_AXIS),
 555                   me->relative_coordinate (common[Y_AXIS], Y_AXIS));
 556       controls = scm_cons (ly_offset2scm (o), controls);
 557     }
 558   me->set_property ("control-points", controls);
 559 }
 560
 561 /*
 562   TODO: should analyse encompasses to determine sensible region, and
 563   should limit slopes available.
 564  */
 565
 566 Drul_array<Real>
 567 get_y_attachment_range (Spanner*me,
 568                         Grob **common, Slur_score_parameters *score_param,
 569                         Drul_array<Bound_info> extremes,
 570                         Drul_array<Offset> base_attachment)
 571 {
 572   Drul_array<Real> end_ys;
 573   Direction dir = get_grob_direction (me);
 574   Direction d = LEFT;
 575   do
 576     {
 577       if (extremes[d].note_column_)
 578         {
 579           end_ys[d] = dir
 580             * ((dir * (base_attachment[d][Y_AXIS] +  score_param->region_size_* dir))
 581                >? (dir * (dir + extremes[d].note_column_->extent(common[Y_AXIS],
 582                                                                  Y_AXIS)[dir]))
 583                >? (dir * base_attachment[-d][Y_AXIS]));
 584         }
 585       else
 586         end_ys[d] = extremes[d].neighbor_y_ + score_param->region_size_ * dir;
 587     }
 588   while (flip (&d) != LEFT);
 589
 590   return end_ys;
 591 }
 592
 593 bool
 594 spanner_less (Spanner *s1, Spanner* s2)
 595 {
 596   Slice b1, b2;
 597   Direction d  = LEFT;
 598   do
 599     {
 600       b1[d] = s1->get_bound (d)->get_column ()->rank_;
 601       b2[d] = s2->get_bound (d)->get_column ()->rank_;
 602     } while (flip (&d) != LEFT);
 603
 604   return b2[LEFT] <= b1[LEFT] && b2[RIGHT] >= b1[RIGHT]
 605     && (b2[LEFT] != b1[LEFT] || b2[RIGHT] != b1[RIGHT]);
 606 }
 607
 608
 609 Drul_array<Offset>
 610 get_base_attachments (Spanner *me,
 611                       Grob **common, Drul_array<Bound_info> extremes)
 612 {
 613   Link_array<Grob> columns
 614     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 615   Drul_array<Offset> base_attachment;
 616   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 617   Direction dir = get_grob_direction (me);
 618   Direction d = LEFT;
 619   do
 620     {
 621       Grob *stem = extremes[d].stem_;
 622       Grob *head = extremes[d].slur_head_;
 623
 624       Real x, y;
 625       if (!extremes[d].note_column_)
 626         {
 627           y = extremes[d].neighbor_y_;
 628           if (d== RIGHT)
 629             x = extremes[d].bound_->extent (common[X_AXIS], X_AXIS)[d];
 630           else
 631             x = me->get_broken_left_end_align ();
 632         }
 633       else
 634         {
 635           bool same_beam =
 636             (extremes[d].stem_ && extremes[-d].stem_
 637              && Stem::get_beam (extremes[d].stem_) == Stem::get_beam (extremes[-d].stem_));
 638
 639           /*
 640             fixme: X coord should also be set in this case.
 641            */
 642           if (stem
 643               && extremes[d].stem_dir_ == dir
 644               && Stem::get_beaming (stem, -d)
 645               && (!spanner_less (me, Stem::get_beam (stem))
 646                   || same_beam))
 647             y = extremes[d].stem_extent_[Y_AXIS][dir];
 648           else if (head)
 649             y = head->extent (common[Y_AXIS], Y_AXIS)[dir];
 650           y += dir * 0.5 * staff_space;
 651
 652           Real pos
 653             = (y - extremes[d].staff_->relative_coordinate (common[Y_AXIS],
 654                                                             Y_AXIS))
 655             * 2.0 / Staff_symbol::staff_space (extremes[d].staff_);
 656
 657           /* start off staffline. */
 658           if (fabs (pos - my_round (pos)) < 0.2
 659               && Staff_symbol_referencer::on_staffline (head, (int) rint (pos))
 660               && Staff_symbol_referencer::line_count (head) - 1 >= rint (pos)
 661               )
 662             // TODO: calc from slur thick & line thick, parameter.
 663             y += 1.5 * staff_space * dir / 10;
 664
 665           Grob * fh = Note_column::first_head (extremes[d].note_column_);
 666           x =
 667             (fh ? fh->extent (common[X_AXIS], X_AXIS)
 668              : extremes[d].bound_->extent (common[X_AXIS], X_AXIS))
 669             .linear_combination (CENTER);
 670         }
 671       base_attachment[d] = Offset (x, y);
 672
 673     } while (flip (&d) != LEFT);
 674
 675   return base_attachment;
 676 }
 677
 678 void
 679 generate_curves (Grob *me, Grob **common,
 680                  Slur_score_parameters *score_param,
 681                  Drul_array<Bound_info> extremes,
 682                  Drul_array<Offset>,
 683                  Array<Slur_score> *scores)
 684 {
 685   (void) common;
 686   (void) extremes;
 687   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 688   Real r_0 = robust_scm2double (me->get_property ("ratio"), 0.33);
 689   Real h_inf = staff_space * scm_to_double (me->get_property ("height-limit"));
 690   for (int i = 0; i < scores->size(); i++)
 691     {
 692       Bezier bez = get_bezier (me,
 693                               common,
 694                               score_param,
 695                               extremes,
 696                               (*scores)[i].attachment_, r_0, h_inf);
 697
 698       bez = avoid_staff_line (me, common, extremes, bez);
 699       (*scores)[i].attachment_[LEFT] = bez.control_[0];
 700       (*scores)[i].attachment_[RIGHT] = bez.control_[3];
 701       (*scores)[i].curve_ = bez;
 702     }
 703 }
 704
 705 Bezier
 706 avoid_staff_line (Grob *me, Grob **common,
 707                   Drul_array<Bound_info> extremes,
 708                   Bezier bez)
 709 {
 710   Offset horiz (1,0);
 711   Array<Real> ts = bez.solve_derivative (horiz);
 712   Real lt = me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
 713   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) *  lt;
 714
 715   /* TODO: handle case of broken slur.  */
 716   if (!ts.is_empty ()
 717       && (extremes[LEFT].staff_ == extremes[RIGHT].staff_)
 718       && extremes[LEFT].staff_ && extremes[RIGHT].staff_)
 719     {
 720       Real y = bez.curve_point (ts[0])[Y_AXIS];
 721
 722       Grob *staff = extremes[LEFT].staff_;
 723
 724       Real staff_space = extremes[LEFT].staff_space_;
 725       Real p = 2 * (y - staff->relative_coordinate (common[Y_AXIS], Y_AXIS))
 726         / staff_space;
 727
 728       Real distance = fabs (my_round (p) - p);  //  in halfspaces
 729       if (distance < 4 * thick
 730           && (int) fabs (my_round (p))
 731           <= 2 * Staff_symbol_referencer::staff_radius (staff) + 0.1
 732           && (int (fabs (my_round (p))) % 2
 733               != Staff_symbol_referencer::line_count (staff) % 2))
 734         {
 735           Direction resolution_dir =
 736             (distance ?  get_grob_direction (me) : Direction (sign (p - my_round(p))));
 737
 738           // TODO: parameter
 739           Real newp = my_round (p) + resolution_dir
 740             * 5 * thick;
 741
 742           Real dy = (newp - p) * staff_space / 2.0;
 743
 744           bez.control_[1][Y_AXIS] += dy;
 745           bez.control_[2][Y_AXIS] += dy;
 746         }
 747     }
 748   return bez;
 749 }
 750
 751 Array<Slur_score>
 752 enumerate_attachments (Grob *me, Grob *common[],
 753                        Slur_score_parameters *score_param,
 754                        Drul_array<Bound_info> extremes,
 755                        Drul_array<Offset> base_attachment,
 756                        Drul_array<Real> end_ys)
 757 {
 758   (void) common;
 759   /*ugh.   */
 760   Array<Slur_score> scores;
 761
 762   Direction dir = get_grob_direction (me);
 763   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 764
 765   Drul_array<Offset> os;
 766   os[LEFT] = base_attachment[LEFT];
 767   Real minimum_length = staff_space
 768     * robust_scm2double (me->get_property ("minimum-length"), 2.0);
 769
 770   for (int i = 0; dir * os[LEFT][Y_AXIS] <= dir * end_ys[LEFT]; i++)
 771     {
 772       os[RIGHT] = base_attachment[RIGHT];
 773       for (int j = 0; dir * os[RIGHT][Y_AXIS] <= dir * end_ys[RIGHT]; j++)
 774         {
 775           Slur_score s;
 776           Direction d = LEFT;
 777           Drul_array<bool> attach_to_stem (false, false);
 778           do
 779             {
 780               os[d][X_AXIS] = base_attachment[d][X_AXIS];
 781               if (extremes[d].stem_
 782                   && !Stem::is_invisible (extremes[d].stem_)
 783                   && extremes[d].stem_dir_ == dir)
 784                 {
 785                   if (dir == -d
 786                       && extremes[d].stem_extent_[Y_AXIS].contains (os[d][Y_AXIS]))
 787                     {
 788                       os[d][X_AXIS] =  extremes[d].slur_head_extent_[-d]
 789                         - d * 0.3;
 790                       attach_to_stem[d] = true;
 791                     }
 792                   else if (dir *extremes[d].stem_extent_[Y_AXIS][dir]
 793                              < dir * os[d][Y_AXIS]
 794                            && !extremes[d].stem_extent_[X_AXIS].is_empty()
 795                            )
 796
 797                     os[d][X_AXIS] = extremes[d].stem_extent_[X_AXIS].center();
 798                 }
 799             }
 800           while (flip (&d) != LEFT);
 801
 802           Offset dz;
 803           dz = os[RIGHT] - os[LEFT];
 804           if (dz[X_AXIS] < minimum_length
 805               || fabs (dz[Y_AXIS] / dz[X_AXIS]) > score_param->max_slope_
 806               )
 807             {
 808               do
 809                 {
 810                   if (extremes[d].slur_head_)
 811                     {
 812                       os[d][X_AXIS] = extremes[d].slur_head_extent_.center ();
 813                       attach_to_stem[d] = false;
 814                     }
 815                 }
 816               while (flip (&d) != LEFT);
 817             }
 818
 819           dz = os[RIGHT] - os[LEFT];
 820           do
 821             {
 822               if (extremes[d].slur_head_
 823                   && !attach_to_stem[d])
 824                 {
 825                   /* Horizontally move tilted slurs a little.  Move
 826                      more for bigger tilts.
 827
 828                      TODO: parameter */
 829                   os[d][X_AXIS]
 830                     -= dir * extremes[d].slur_head_extent_.length ()
 831                     * sin (dz.arg  ()) / 3;
 832                 }
 833             }
 834           while (flip (&d) != LEFT);
 835
 836           s.attachment_ = os;
 837           scores.push (s);
 838
 839           os[RIGHT][Y_AXIS] += dir * staff_space / 2;
 840         }
 841
 842       os[LEFT][Y_AXIS] += dir * staff_space / 2;
 843     }
 844   return scores;
 845 }
 846
 847 inline Real
 848 linear_interpolate (Real x, Real x1, Real x2,  Real y1, Real  y2)
 849 {
 850   return (x2 - x) / (x2 - x1) * y1 +
 851     (x - x1) / (x2 - x1) * y2 ;
 852 }
 853
 854
 855 void
 856 score_encompass (Grob *me, Grob *common[],
 857                  Slur_score_parameters *score_param,
 858                  Drul_array<Bound_info> extremes,
 859                  Drul_array<Offset> base_attach,
 860                  Array<Slur_score> *scores)
 861 {
 862   (void) extremes;
 863   (void) base_attach;
 864
 865   Link_array<Grob> encompasses
 866     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 867   Direction dir = get_grob_direction (me);
 868
 869   Array<Encompass_info> infos;
 870
 871   for (int i = 0; i < encompasses.size(); i++)
 872     infos.push (get_encompass_info (me, encompasses[i], common));
 873
 874   for (int i = 0; i < scores->size (); i++)
 875     {
 876       Slur_score &configuration = scores->elem_ref (i);
 877       Bezier const &bez (configuration.curve_);
 878       Real demerit = 0.0;
 879
 880       /*
 881         Distances for heads that are between slur and line between
 882         attachment points.
 883        */
 884       Array<Real> convex_head_distances;
 885       Array<Real> edge_distances;
 886       for (int j = 0; j < infos.size(); j++)
 887         {
 888           Real x = infos[j].x_;
 889
 890           bool l_edge = j==0;
 891           bool r_edge = j==infos.size()-1;
 892           bool edge =  l_edge || r_edge;
 893
 894
 895           if (edge)
 896           {
 897             edge_distances.push (fabs (configuration.attachment_[l_edge ? LEFT : RIGHT][Y_AXIS]
 898                                        - infos[j].get_point (dir)));
 899           }
 900
 901
 902           if (!(x < configuration.attachment_[RIGHT][X_AXIS]
 903                 && x > configuration.attachment_[LEFT][X_AXIS]))
 904             continue;
 905
 906           Real y = bez.get_other_coordinate (X_AXIS, x);
 907           if (!edge)
 908             {
 909               Real head_dy = (y - infos[j].head_);
 910               if (dir * head_dy < 0)
 911                 {
 912                   demerit += score_param->head_encompass_penalty_;
 913                   convex_head_distances.push (0.0);
 914                 }
 915               else
 916                 {
 917                   Real hd = (head_dy)
 918                     ? (1 / fabs (head_dy) - 1 / score_param->free_head_distance_)
 919                     : score_param->head_encompass_penalty_;
 920                   hd = (hd >? 0)<? score_param->head_encompass_penalty_;
 921
 922                   demerit += hd;
 923                 }
 924
 925               Real line_y = linear_interpolate (x,
 926                                                 configuration.attachment_[RIGHT][X_AXIS],
 927                                                 configuration.attachment_[LEFT][X_AXIS],
 928                                                 configuration.attachment_[RIGHT][Y_AXIS],
 929                                                 configuration.attachment_[LEFT][Y_AXIS]);
 930
 931               if (dir * (infos[j].get_point (dir) - line_y) > 0)
 932                 {
 933                   Real d = fabs (infos[j].get_point (dir) - y);
 934                   convex_head_distances.push (d);
 935                 }
 936             }
 937
 938
 939
 940
 941           if (dir * (y - infos[j].stem_) < 0)
 942             {
 943               Real stem_dem =score_param->stem_encompass_penalty_ ;
 944               if ((l_edge && dir == UP)
 945                   || (r_edge && dir == DOWN))
 946                 stem_dem /= 5;
 947
 948               demerit +=  stem_dem;
 949             }
 950           else if (!edge)
 951             {
 952               Interval ext;
 953               ext.add_point (infos[j].stem_);
 954               ext.add_point (infos[j].head_);
 955
 956               // ?
 957               demerit += -score_param->closeness_factor_
 958                 * (dir
 959                    * (y - (ext[dir] + dir * score_param->free_head_distance_))
 960                    <? 0)
 961                 / infos.size ();
 962             }
 963         }
 964
 965       Real variance_penalty = 0.0;
 966
 967       if (convex_head_distances.size())
 968         {
 969           Real avg_distance = 0.0;
 970           Real min_dist = infinity_f;
 971           for (int j = 0; j < convex_head_distances.size(); j++)
 972             {
 973               min_dist = min_dist <? convex_head_distances[j];
 974               avg_distance += convex_head_distances[j];
 975             }
 976
 977           /*
 978             For slurs over 3 or 4 heads, the average distance is not a
 979             good normalizer.
 980            */
 981           int n =  convex_head_distances.size();
 982           if (convex_head_distances.size() <= 2)
 983             {
 984               for (int j = 0; j < edge_distances.size(); j++)
 985                 {
 986                   avg_distance += edge_distances[j];
 987                   n++;
 988                 }
 989             }
 990
 991           /*
 992             TODO: maybe it's better to use (avgdist - mindist)*factor
 993             as penalty.
 994            */
 995           avg_distance /= n;
 996           variance_penalty = score_param->head_slur_distance_max_ratio_;
 997           if (min_dist > 0.0)
 998             variance_penalty = ((avg_distance / (min_dist  +score_param->free_head_distance_)) - 1.0)
 999               <? variance_penalty;
1000
1001           variance_penalty *= score_param->head_slur_distance_factor_;
1002         }
1003 #if DEBUG_SLUR_QUANTING
1004       (*scores)[i].score_card_ += to_string ("C%.2f", demerit);
1005       (*scores)[i].score_card_ += to_string ("D%.2f", variance_penalty);
1006 #endif
1007
1008       (*scores)[i].score_ += demerit + variance_penalty;
1009     }
1010 }
1011
1012 struct Extra_collision_info
1013 {
1014   Real idx_;
1015   Box extents_;
1016   Real penalty_;
1017
1018   Extra_collision_info (Real idx, Interval x, Interval y, Real p)
1019   {
1020     idx_ = idx;
1021     extents_[X_AXIS] = x;
1022     extents_[Y_AXIS] = y;
1023     penalty_ = p;
1024   }
1025   Extra_collision_info ()
1026   {
1027     idx_ = 0.0;
1028     penalty_ = 0.;
1029   }
1030 };
1031
1032 void
1033 score_extra_encompass (Grob *me, Grob *common[],
1034                        Slur_score_parameters *score_param,
1035                        Drul_array<Bound_info> extremes,
1036                        Drul_array<Offset> base_attach,
1037                        Array<Slur_score> *scores)
1038 {
1039   (void) base_attach;
1040   (void) extremes;
1041
1042   Spanner *me_spanner = dynamic_cast<Spanner*> (me);
1043
1044   Link_array<Grob> encompasses
1045     = Pointer_group_interface__extract_grobs (me, (Grob *)0,
1046                                               "encompass-objects");
1047   Direction dir = get_grob_direction (me);
1048   Real lt =  me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
1049   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) * lt;
1050
1051   Array<Extra_collision_info> collision_infos;
1052   for (int i = encompasses.size (); i--; )
1053     {
1054       if (Slur::has_interface (encompasses[i]))
1055         {
1056           Spanner * small_slur = dynamic_cast<Spanner*> (encompasses[i]);
1057           Bezier b = Slur::get_curve (small_slur);
1058
1059           Offset relative (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1060                            small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1061
1062           for (int k = 0; k < 3; k++)
1063           {
1064             Direction hdir =  Direction (k /2 - 1);
1065
1066             /*
1067               Only take bound into account if small slur starts
1068               together with big slur.
1069              */
1070             if (hdir && small_slur->get_bound (hdir) != me_spanner->get_bound (hdir))
1071               continue;
1072
1073
1074             Offset z = b.curve_point ( k / 2.0);
1075             z += relative;
1076
1077             Interval yext;
1078             yext.set_full();
1079             yext[dir] = z[Y_AXIS] + dir * thick * 1.0;
1080
1081             Interval xext(-1, 1);
1082             xext = xext *(thick*2) + z[X_AXIS];
1083             Extra_collision_info info (k - 1.0,
1084                                        xext,
1085                                        yext,
1086                                        score_param->extra_object_collision_);
1087             collision_infos.push (info);
1088           }
1089         }
1090       else
1091         {
1092           Grob *g = encompasses [i];
1093           Interval xe = g->extent (common[X_AXIS], X_AXIS);
1094           Interval ye = g->extent (common[Y_AXIS], Y_AXIS);
1095
1096           Real xp = 0.0;
1097           Real penalty = score_param->extra_object_collision_;
1098           if (Accidental_interface::has_interface (g))
1099             {
1100               penalty = score_param->accidental_collision_;
1101               /* Begin copy accidental.cc */
1102               bool parens = false;
1103               if (to_boolean (g->get_property ("cautionary")))
1104                 {
1105                   SCM cstyle = g->get_property ("cautionary-style");
1106                   parens = ly_c_equal_p (cstyle, ly_symbol2scm ("parentheses"));
1107                 }
1108
1109               SCM accs = g->get_property ("accidentals");
1110               SCM scm_style = g->get_property ("style");
1111               if (!scm_is_symbol (scm_style)
1112                   && !parens
1113                   && scm_ilength (accs) == 1)
1114                 {
1115                   /* End copy accidental.cc */
1116                   switch (scm_to_int (ly_car (accs)))
1117                     {
1118                     case FLAT:
1119                     case DOUBLE_FLAT:
1120                       xp = LEFT;
1121                       break ;
1122                     case SHARP:
1123                       xp = 0.5 * dir;
1124                       break ;
1125                     case NATURAL:
1126                       xp = -dir;
1127                       break;
1128                     }
1129                 }
1130             }
1131
1132           ye.widen (thick * 0.5);
1133           Extra_collision_info info (xp, xe, ye,  penalty);
1134           collision_infos.push (info);
1135         }
1136     }
1137   for (int i = 0; i < scores->size (); i++)
1138     {
1139       Real demerit = 0.0;
1140       for (int j = 0; j < collision_infos.size(); j++)
1141         {
1142           Drul_array<Offset> at = scores->elem (i).attachment_;
1143           Interval slur_wid (at[LEFT][X_AXIS], at[RIGHT][X_AXIS]);
1144
1145           /*
1146             to prevent numerical inaccuracies in
1147             Bezier::get_other_coordinate().
1148            */
1149           slur_wid.widen (- 0.5 * thick);
1150           Real x = collision_infos[j].extents_[X_AXIS]
1151             .linear_combination (collision_infos[j].idx_);
1152           Real y = 0.0;
1153
1154           if (!slur_wid.contains (x))
1155             {
1156               Direction contains_dir = CENTER;
1157               Direction d = LEFT;
1158               do
1159                 {
1160                   if (collision_infos[j].extents_[X_AXIS].contains (at[d][X_AXIS]))
1161                     contains_dir = d;
1162                 }
1163               while (flip (&d) != LEFT);
1164
1165               if (!contains_dir)
1166                 continue;
1167               else
1168                 y = at[contains_dir][Y_AXIS];
1169             }
1170           else
1171             {
1172               y = scores->elem (i).curve_.get_other_coordinate (X_AXIS, x);
1173             }
1174
1175           Real dist = collision_infos[j].extents_[Y_AXIS].distance (y);
1176           demerit +=
1177             fabs (0 >? (score_param->extra_encompass_free_distance_ - dist)) /
1178             score_param->extra_encompass_free_distance_
1179             * collision_infos[j].penalty_;
1180         }
1181 #if DEBUG_SLUR_QUANTING
1182       (*scores)[i].score_card_ += to_string ("X%.2f", demerit);
1183 #endif
1184       (*scores)[i].score_ += demerit;
1185     }
1186 }
1187
1188 void
1189 score_edges (Grob *me, Grob *common[],
1190              Slur_score_parameters * score_param,
1191              Drul_array<Bound_info> extremes,
1192              Drul_array<Offset> base_attach,
1193              Array<Slur_score> *scores)
1194 {
1195   (void) common;
1196   Direction dir = get_grob_direction (me);
1197
1198   for (int i = 0; i < scores->size (); i++)
1199     {
1200       Direction d = LEFT;
1201       do
1202         {
1203           Real y = scores->elem (i).attachment_[d][Y_AXIS];
1204           Real dy = fabs (y - base_attach[d][Y_AXIS]);
1205
1206           Real factor = score_param->edge_attraction_factor_;
1207           Real demerit = factor * dy;
1208           if (extremes[d].stem_
1209               && extremes[d].stem_dir_ == dir
1210               && !Stem::get_beaming (extremes[d].stem_, -d)
1211               )
1212             demerit /= 5;
1213
1214           (*scores)[i].score_ += demerit;
1215 #if DEBUG_SLUR_QUANTING
1216           (*scores)[i].score_card_ += to_string ("E%.2f", demerit);
1217 #endif
1218         }
1219       while (flip (&d) != LEFT);
1220     }
1221 }
1222
1223 void
1224 score_slopes (Grob *me, Grob *common[],
1225               Slur_score_parameters *score_param,
1226               Drul_array<Bound_info> extremes,
1227               Drul_array<Offset> base_attach,
1228               Array<Slur_score> * scores)
1229 {
1230   (void) me;
1231   (void) base_attach;
1232
1233   Drul_array<Real> ys;
1234   Direction d = LEFT;
1235   do
1236     {
1237       if (extremes[d].slur_head_)
1238         ys[d] = extremes[d].slur_head_->relative_coordinate (common[Y_AXIS],
1239                                                               Y_AXIS);
1240       else
1241         ys[d] = extremes[d].neighbor_y_;
1242     }
1243   while (flip (&d) != LEFT);
1244
1245   bool has_beams
1246     = (extremes[LEFT].stem_ && Stem::get_beam (extremes[LEFT].stem_))
1247     || (extremes[RIGHT].stem_ && Stem::get_beam (extremes[RIGHT].stem_));
1248
1249   Real dy = ys[RIGHT] - ys[LEFT];
1250   for (int i = 0; i < scores->size (); i++)
1251     {
1252       Offset slur_dz = (*scores)[i].attachment_[RIGHT]
1253         - (*scores)[i].attachment_[LEFT];
1254       Real slur_dy = slur_dz[Y_AXIS];
1255       Real demerit = 0.0;
1256
1257       demerit += ((fabs (slur_dy / slur_dz[X_AXIS])
1258                    - score_param->max_slope_) >? 0)
1259         * score_param->max_slope_factor_;
1260
1261       /* 0.2: account for staffline offset. */
1262       Real max_dy = (fabs (dy) + 0.2);
1263       if (has_beams)
1264         max_dy += 1.0;
1265
1266       demerit += score_param->steeper_slope_factor_
1267         * ((fabs (slur_dy) -max_dy) >? 0);
1268
1269       demerit += ((fabs (slur_dy/slur_dz[X_AXIS])
1270                    - score_param->max_slope_) >? 0)
1271         * score_param->max_slope_factor_;
1272
1273       if (sign (dy) == 0
1274           && sign (slur_dy) != 0)
1275         demerit += score_param->non_horizontal_penalty_;
1276
1277       if (sign (dy)
1278           && sign (slur_dy)
1279           && sign (slur_dy) != sign (dy))
1280         demerit += has_beams
1281           ? score_param->same_slope_penalty_ / 10
1282           : score_param->same_slope_penalty_;
1283
1284 #if DEBUG_SLUR_QUANTING
1285       (*scores)[i].score_card_ += to_string ("S%.2f", d);
1286 #endif
1287       (*scores)[i].score_ += demerit;
1288     }
1289
1290
1291
1292 }
1293
1294
1295 Real
1296 fit_factor (Offset dz_unit, Offset dz_perp,
1297             Bezier curve, Direction d,  Array<Offset> const &avoid)
1298 {
1299   Real fit_factor = 0.0;
1300   Offset x0 = curve.control_[0];
1301   curve.translate (-x0);
1302   curve.rotate (-dz_unit.arg ());
1303   curve.scale (1, d);
1304
1305   Interval curve_xext;
1306   curve_xext.add_point (curve.control_[0][X_AXIS]);
1307   curve_xext.add_point (curve.control_[3][X_AXIS]);
1308
1309   for (int i = 0; i < avoid.size (); i++)
1310     {
1311       Offset z = (avoid[i] - x0) ;
1312       Offset p (dot_product (z, dz_unit),
1313                 d* dot_product (z, dz_perp));
1314       if (!curve_xext.contains (p[X_AXIS]))
1315         continue;
1316
1317       Real y = curve.get_other_coordinate (X_AXIS, p[X_AXIS]);
1318       if (y)
1319         {
1320           fit_factor = fit_factor >? (p[Y_AXIS] / y);
1321         }
1322     }
1323   return fit_factor;
1324 }
1325
1326
1327 Bezier
1328 get_bezier (Grob *me,
1329             Grob **common,
1330             Slur_score_parameters *score_param,
1331             Drul_array<Bound_info> extremes,
1332             Drul_array<Offset> attachments,
1333             Real r_0, Real h_inf
1334             )
1335 {
1336   Link_array<Grob> encompasses
1337     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
1338   Direction dir = get_grob_direction (me);
1339
1340   Array<Offset> avoid;
1341   for (int i = 0; i < encompasses.size(); i++)
1342     {
1343       if (extremes[LEFT].note_column_ == encompasses[i]
1344           ||extremes[RIGHT].note_column_ == encompasses[i])
1345         continue;
1346
1347       Encompass_info inf (get_encompass_info (me, encompasses[i], common));
1348
1349       Real y = dir*((dir * inf.head_) >? (dir *inf.stem_));
1350
1351       avoid.push (Offset (inf.x_,  y + dir * score_param->free_head_distance_));
1352     }
1353
1354   Link_array<Grob> extra_encompasses
1355     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "encompass-objects");
1356   for (int i = 0;  i < extra_encompasses.size (); i++)
1357     if (Slur::has_interface (extra_encompasses[i]))
1358       {
1359         Grob * small_slur = extra_encompasses[i];
1360         Bezier b = Slur::get_curve (small_slur);
1361
1362         Offset z = b.curve_point (0.5);
1363         z += Offset (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1364                      small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1365
1366         z[Y_AXIS] += dir * score_param->free_slur_distance_;
1367         avoid.push (z);
1368       }
1369
1370   Offset dz = attachments[RIGHT]- attachments[LEFT];;
1371   Offset dz_unit = dz;
1372   dz_unit *= 1 / dz.length();
1373   Offset dz_perp = dz_unit * Offset(0,1);
1374
1375   Real indent, height;
1376   get_slur_indent_height (&indent, &height, dz.length (), h_inf, r_0);
1377
1378   Real excentricity = robust_scm2double (me->get_property ("excentricity"), 0.0);
1379   Bezier curve;
1380
1381   Real x1 = (excentricity + indent);
1382   Real x2 = (excentricity - indent);
1383   curve.control_[0] = attachments[LEFT];
1384   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1385   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1386   curve.control_[3] = attachments[RIGHT];
1387
1388
1389   Real ff = fit_factor (dz_unit, dz_perp, curve, dir, avoid);
1390   Real l = dz.length ();
1391
1392   /*
1393     This condition,
1394
1395     l^2 > 4h^2 +  3(i  1/3l)^2  - 1/3 l^2
1396
1397     is equivalent to:
1398
1399     |bez'(0)| < | bez'(.5)|
1400
1401     when (control2-control1) has the same direction as (control3 -
1402     control0).
1403
1404    */
1405   Real max_h = sqrt (sqr (l)/3 - .75 * sqr (indent + l / 3));
1406   height = height >? ((height * ff) <? max_h);
1407
1408   curve.control_[0] = attachments[LEFT];
1409   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1410   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1411   curve.control_[3] = attachments[RIGHT];
1412
1413   return curve;
1414 }