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   Real edge_slope_exponent_;
  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   score_param->edge_slope_exponent_
 254     = get_detail (details, ly_symbol2scm ("edge-slope-exponent"));
 255 }
 256
 257
 258 Slur_score_parameters::Slur_score_parameters(Grob *me)
 259 {
 260   init_score_param (me, this);
 261 }
 262
 263 /* HDIR indicates which side (left or right) we are processing here.  */
 264 Real
 265 broken_trend_y (Grob *me, Grob **common, Direction hdir)
 266 {
 267   /* A broken slur should maintain the same vertical trend
 268      the unbroken slur would have had.  */
 269   Real by = 0.0;
 270   if (Spanner *mother = dynamic_cast<Spanner*> (me->original_))
 271     {
 272       int k = broken_spanner_index (dynamic_cast<Spanner*> (me));
 273       int j = k + hdir;
 274       if (j < 0 || j >= mother->broken_intos_.size ())
 275         return by;
 276
 277       Grob *neighbor = mother->broken_intos_[j];
 278       if (hdir == RIGHT)
 279         neighbor->set_property ("direction",
 280                                 me->get_property ("direction"));
 281
 282       Spanner *common_mother
 283         = dynamic_cast<Spanner*> (common[Y_AXIS]->original_);
 284       int common_k
 285         = broken_spanner_index (dynamic_cast<Spanner*> (common[Y_AXIS]));
 286       int common_j = common_k + hdir;
 287
 288       if (common_j < 0 || common_j >= common_mother->broken_intos_.size())
 289         return by;
 290
 291       Grob *common_next_system = common_mother->broken_intos_[common_j];
 292       Link_array<Grob> neighbor_cols
 293         = Pointer_group_interface__extract_grobs (neighbor, (Grob *)0,
 294                                                   "note-columns");
 295
 296       Grob *neighbor_col
 297         = (hdir == RIGHT) ? neighbor_cols[0] : neighbor_cols.top ();
 298       Grob *neighbor_common
 299         = common_next_system->common_refpoint (neighbor_col, Y_AXIS);
 300
 301       Direction vdir = get_grob_direction (me);
 302       Real neighbor_y
 303         = neighbor_col->extent (neighbor_common, Y_AXIS)
 304         .linear_combination (int(vdir))
 305         - common_next_system->relative_coordinate (neighbor_common, Y_AXIS);
 306
 307       Link_array<Grob> my_cols
 308         = Pointer_group_interface__extract_grobs (me, (Grob *)0,
 309                                                   "note-columns");
 310
 311       Grob *extreme_col = (hdir == RIGHT) ? my_cols.top() : my_cols[0];
 312       Real y = extreme_col->extent (common[Y_AXIS], Y_AXIS)
 313         .linear_combination (int ((my_cols.size() == 1) ? CENTER : vdir));
 314       by = (y*neighbor_cols.size() + neighbor_y*my_cols.size()) /
 315         (my_cols.size() + neighbor_cols.size());
 316     }
 317   return by;
 318 }
 319
 320 Encompass_info
 321 get_encompass_info (Grob *me,
 322                     Grob *col,
 323                     Grob **common)
 324 {
 325   Grob *stem = unsmob_grob (col->get_property ("stem"));
 326   Encompass_info ei;
 327   Direction dir = get_grob_direction (me);
 328
 329   if (!stem)
 330     {
 331       programming_error ("No stem for note column?");
 332       ei.x_ = col->relative_coordinate (common[X_AXIS], X_AXIS);
 333       ei.head_ = ei.stem_ = col->extent (common[Y_AXIS],
 334                                          Y_AXIS)[get_grob_direction (me)];
 335       return ei;
 336     }
 337   Direction stem_dir = get_grob_direction (stem);
 338
 339   if (Grob *head = Note_column::first_head (col))
 340     ei.x_ = head->extent (common[X_AXIS], X_AXIS).center ();
 341   else
 342     ei.x_ = col->extent (common[X_AXIS], X_AXIS).center ();
 343
 344   Grob *h = Stem::extremal_heads (stem)[Direction (dir)];
 345   if (!h)
 346     {
 347       ei.head_ = ei.stem_ = col->extent (common[Y_AXIS], Y_AXIS)[dir];
 348       return ei;
 349     }
 350
 351   ei.head_ = h->extent (common[Y_AXIS], Y_AXIS)[dir];
 352
 353   if ((stem_dir == dir)
 354       && !stem->extent (stem, Y_AXIS).is_empty ())
 355     {
 356       ei.stem_ = stem->extent (common[Y_AXIS], Y_AXIS)[dir];
 357       if (Grob *b = Stem::get_beam (stem))
 358         ei.stem_ += stem_dir * 0.5 * Beam::get_thickness (b);
 359
 360       Interval x = stem->extent (common[X_AXIS], X_AXIS);
 361       ei.x_ = x.is_empty ()
 362         ? stem->relative_coordinate (common[X_AXIS], X_AXIS)
 363         : x.center ();
 364     }
 365   else
 366     ei.stem_ = ei.head_;
 367
 368   return ei;
 369 }
 370
 371
 372 Direction
 373 get_default_dir (Grob*me)
 374 {
 375   Link_array<Grob> encompasses
 376     = Pointer_group_interface__extract_grobs (me, (Grob*) 0, "note-columns");
 377
 378   Direction d = DOWN;
 379   for (int i= 0; i < encompasses.size (); i ++)
 380     {
 381       if (Note_column::dir (encompasses[i]) < 0)
 382         {
 383           d = UP;
 384           break;
 385         }
 386     }
 387   return d;
 388 }
 389
 390
 391
 392 MAKE_SCHEME_CALLBACK (Slur, after_line_breaking,1);
 393 SCM
 394 Slur::after_line_breaking (SCM smob)
 395 {
 396   Spanner *me = dynamic_cast<Spanner*> (unsmob_grob (smob));
 397   if (!scm_ilength (me->get_property ("note-columns")))
 398     {
 399       me->suicide ();
 400       return SCM_UNSPECIFIED;
 401     }
 402
 403   if (!get_grob_direction (me))
 404     set_grob_direction (me, get_default_dir (me));
 405
 406   if (scm_ilength (me->get_property ("control-points")) < 4)
 407     set_end_points (me);
 408
 409   return SCM_UNSPECIFIED;
 410 }
 411
 412 Drul_array<Bound_info>
 413 get_bound_info (Spanner* me, Grob **common)
 414 {
 415   Drul_array<Bound_info> extremes;
 416   Direction d = LEFT;
 417   Direction dir = get_grob_direction (me);
 418
 419   do
 420     {
 421       extremes[d].bound_ = me->get_bound (d);
 422       if (Note_column::has_interface (extremes[d].bound_))
 423         {
 424           extremes[d].note_column_ = extremes[d].bound_;
 425           extremes[d].stem_ = Note_column::get_stem (extremes[d].note_column_);
 426           extremes[d].stem_dir_ = get_grob_direction (extremes[d].stem_);
 427           extremes[d].stem_extent_[X_AXIS]
 428             = extremes[d].stem_->extent (common[X_AXIS], X_AXIS);
 429           extremes[d].stem_extent_[Y_AXIS]
 430             = extremes[d].stem_->extent (common[Y_AXIS], Y_AXIS);
 431           extremes[d].slur_head_
 432             = Stem::extremal_heads (extremes[d].stem_)[dir];
 433           if (!extremes[d].slur_head_
 434               && Note_column::has_rests (extremes[d].bound_))
 435             {
 436               extremes[d].slur_head_ = Note_column::get_rest (extremes[d].bound_);
 437             }
 438
 439           if (extremes[d].slur_head_)
 440             extremes[d].slur_head_extent_
 441               = extremes[d].slur_head_->extent (common[X_AXIS], X_AXIS);
 442
 443           extremes[d].staff_ = Staff_symbol_referencer
 444             ::get_staff_symbol (extremes[d].stem_);
 445           extremes[d].staff_space_ = Staff_symbol_referencer
 446             ::staff_space (extremes[d].stem_);
 447         }
 448       else if (d == RIGHT)
 449         /*
 450           right side anticipates on the next note.
 451         */
 452         extremes[d].neighbor_y_ = broken_trend_y (me, common, d);
 453
 454       else
 455         {
 456           Link_array<Grob> columns
 457             = Pointer_group_interface__extract_grobs (me, (Grob *) 0, "note-columns");
 458           extremes[d].neighbor_y_ = columns[0]->extent (common[Y_AXIS], Y_AXIS)[dir];
 459         }
 460     }
 461   while (flip (&d) != LEFT);
 462   return extremes;
 463 }
 464
 465 void
 466 set_end_points (Grob *me)
 467 {
 468   Link_array<Grob> columns
 469     = Pointer_group_interface__extract_grobs (me, (Grob *) 0, "note-columns");
 470
 471   if (columns.is_empty ())
 472     {
 473       me->suicide ();
 474       return;
 475     }
 476
 477   SCM eltlist = me->get_property ("note-columns");
 478   SCM extra_list = me->get_property ("encompass-objects");
 479   Spanner *sp = dynamic_cast<Spanner*> (me);
 480
 481   Grob *common[] = {0, 0};
 482   for (int i = X_AXIS; i < NO_AXES; i++)
 483     {
 484       Axis a = (Axis)i;
 485       common[a] = common_refpoint_of_list (eltlist, me, a);
 486       common[a] = common_refpoint_of_list (extra_list, common[a], a);
 487     }
 488
 489   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (RIGHT),
 490                                                     X_AXIS);
 491   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (LEFT),
 492                                                     X_AXIS);
 493
 494   Drul_array<Bound_info> extremes = get_bound_info (sp, common);
 495   Drul_array<Offset> base_attachment
 496     = get_base_attachments (sp, common, extremes);
 497   Slur_score_parameters params (me);
 498   Drul_array<Real> end_ys
 499     = get_y_attachment_range (sp, common, &params, extremes, base_attachment);
 500   Array<Slur_score> scores = enumerate_attachments (me, common, &params,
 501                                                     extremes, base_attachment,
 502                                                     end_ys);
 503
 504   generate_curves (me, common, &params, extremes, base_attachment, &scores);
 505   score_edges (me, common, &params,extremes, base_attachment, &scores);
 506   score_slopes (me, common, &params,extremes, base_attachment, &scores);
 507   score_encompass (me, common, &params,extremes, base_attachment, &scores);
 508   score_extra_encompass (me, common, &params,extremes, base_attachment,
 509                          &scores);
 510
 511   Real opt = 1e6;
 512   int opt_idx = 0;
 513   // why backwards?
 514   for (int i = scores.size (); i--;)
 515     {
 516       if (scores[i].score_ < opt)
 517         {
 518           opt = scores[i].score_;
 519           opt_idx = i;
 520         }
 521     }
 522
 523 #if DEBUG_SLUR_QUANTING
 524   SCM inspect_quants = me->get_property ("inspect-quants");
 525   if (to_boolean (me->get_paper ()
 526                   ->lookup_variable (ly_symbol2scm ("debug-slur-scoring")))
 527       && ly_c_pair_p (inspect_quants))
 528     {
 529       Drul_array<Real> ins = ly_scm2interval (inspect_quants);
 530       Real mindist = 1e6;
 531       for (int i = 0; i < scores.size (); i ++)
 532         {
 533           Real d =fabs (scores[i].attachment_[LEFT][Y_AXIS] - ins[LEFT])
 534             + fabs (scores[i].attachment_[RIGHT][Y_AXIS] - ins[RIGHT]);
 535           if (d < mindist)
 536             {
 537               opt_idx = i;
 538               mindist= d;
 539             }
 540         }
 541       if (mindist > 1e5)
 542         programming_error ("Could not find quant.");
 543     }
 544   scores[opt_idx].score_card_ += to_string ("i%d", opt_idx);
 545
 546   // debug quanting
 547   me->set_property ("quant-score",
 548                     scm_makfrom0str (scores[opt_idx].score_card_.to_str0 ()));
 549 #endif
 550
 551   Bezier b = scores[opt_idx].curve_;
 552   SCM controls = SCM_EOL;
 553   for (int i = 4; i--;)
 554     {
 555       Offset o = b.control_[i]
 556         - Offset (me->relative_coordinate (common[X_AXIS], X_AXIS),
 557                   me->relative_coordinate (common[Y_AXIS], Y_AXIS));
 558       controls = scm_cons (ly_offset2scm (o), controls);
 559     }
 560   me->set_property ("control-points", controls);
 561 }
 562
 563 /*
 564   TODO: should analyse encompasses to determine sensible region, and
 565   should limit slopes available.
 566  */
 567
 568 Drul_array<Real>
 569 get_y_attachment_range (Spanner*me,
 570                         Grob **common, Slur_score_parameters *score_param,
 571                         Drul_array<Bound_info> extremes,
 572                         Drul_array<Offset> base_attachment)
 573 {
 574   Drul_array<Real> end_ys;
 575   Direction dir = get_grob_direction (me);
 576   Direction d = LEFT;
 577   do
 578     {
 579       if (extremes[d].note_column_)
 580         {
 581           end_ys[d] = dir
 582             * ((dir * (base_attachment[d][Y_AXIS] +  score_param->region_size_* dir))
 583                >? (dir * (dir + extremes[d].note_column_->extent(common[Y_AXIS],
 584                                                                  Y_AXIS)[dir]))
 585                >? (dir * base_attachment[-d][Y_AXIS]));
 586         }
 587       else
 588         end_ys[d] = extremes[d].neighbor_y_ + score_param->region_size_ * dir;
 589     }
 590   while (flip (&d) != LEFT);
 591
 592   return end_ys;
 593 }
 594
 595 bool
 596 spanner_less (Spanner *s1, Spanner* s2)
 597 {
 598   Slice b1, b2;
 599   Direction d  = LEFT;
 600   do
 601     {
 602       b1[d] = s1->get_bound (d)->get_column ()->rank_;
 603       b2[d] = s2->get_bound (d)->get_column ()->rank_;
 604     } while (flip (&d) != LEFT);
 605
 606   return b2[LEFT] <= b1[LEFT] && b2[RIGHT] >= b1[RIGHT]
 607     && (b2[LEFT] != b1[LEFT] || b2[RIGHT] != b1[RIGHT]);
 608 }
 609
 610
 611 Drul_array<Offset>
 612 get_base_attachments (Spanner *me,
 613                       Grob **common, Drul_array<Bound_info> extremes)
 614 {
 615   Link_array<Grob> columns
 616     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 617   Drul_array<Offset> base_attachment;
 618   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 619   Direction dir = get_grob_direction (me);
 620   Direction d = LEFT;
 621   do
 622     {
 623       Grob *stem = extremes[d].stem_;
 624       Grob *head = extremes[d].slur_head_;
 625
 626       Real x, y;
 627       if (!extremes[d].note_column_)
 628         {
 629           y = extremes[d].neighbor_y_;
 630           if (d== RIGHT)
 631             x = extremes[d].bound_->extent (common[X_AXIS], X_AXIS)[d];
 632           else
 633             x = me->get_broken_left_end_align ();
 634         }
 635       else
 636         {
 637           bool same_beam =
 638             (extremes[d].stem_ && extremes[-d].stem_
 639              && Stem::get_beam (extremes[d].stem_) == Stem::get_beam (extremes[-d].stem_));
 640
 641           /*
 642             fixme: X coord should also be set in this case.
 643            */
 644           if (stem
 645               && extremes[d].stem_dir_ == dir
 646               && Stem::get_beaming (stem, -d)
 647               && (!spanner_less (me, Stem::get_beam (stem))
 648                   || same_beam))
 649             y = extremes[d].stem_extent_[Y_AXIS][dir];
 650           else if (head)
 651             y = head->extent (common[Y_AXIS], Y_AXIS)[dir];
 652           y += dir * 0.5 * staff_space;
 653
 654           Real pos
 655             = (y - extremes[d].staff_->relative_coordinate (common[Y_AXIS],
 656                                                             Y_AXIS))
 657             * 2.0 / Staff_symbol::staff_space (extremes[d].staff_);
 658
 659           /* start off staffline. */
 660           if (fabs (pos - my_round (pos)) < 0.2
 661               && Staff_symbol_referencer::on_staffline (head, (int) rint (pos))
 662               && Staff_symbol_referencer::line_count (head) - 1 >= rint (pos)
 663               )
 664             // TODO: calc from slur thick & line thick, parameter.
 665             y += 1.5 * staff_space * dir / 10;
 666
 667           Grob * fh = Note_column::first_head (extremes[d].note_column_);
 668           x =
 669             (fh ? fh->extent (common[X_AXIS], X_AXIS)
 670              : extremes[d].bound_->extent (common[X_AXIS], X_AXIS))
 671             .linear_combination (CENTER);
 672         }
 673       base_attachment[d] = Offset (x, y);
 674
 675     } while (flip (&d) != LEFT);
 676
 677   return base_attachment;
 678 }
 679
 680 void
 681 generate_curves (Grob *me, Grob **common,
 682                  Slur_score_parameters *score_param,
 683                  Drul_array<Bound_info> extremes,
 684                  Drul_array<Offset>,
 685                  Array<Slur_score> *scores)
 686 {
 687   (void) common;
 688   (void) extremes;
 689   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 690   Real r_0 = robust_scm2double (me->get_property ("ratio"), 0.33);
 691   Real h_inf = staff_space * scm_to_double (me->get_property ("height-limit"));
 692   for (int i = 0; i < scores->size(); i++)
 693     {
 694       Bezier bez = get_bezier (me,
 695                               common,
 696                               score_param,
 697                               extremes,
 698                               (*scores)[i].attachment_, r_0, h_inf);
 699
 700       bez = avoid_staff_line (me, common, extremes, bez);
 701       (*scores)[i].attachment_[LEFT] = bez.control_[0];
 702       (*scores)[i].attachment_[RIGHT] = bez.control_[3];
 703       (*scores)[i].curve_ = bez;
 704     }
 705 }
 706
 707 Bezier
 708 avoid_staff_line (Grob *me, Grob **common,
 709                   Drul_array<Bound_info> extremes,
 710                   Bezier bez)
 711 {
 712   Offset horiz (1,0);
 713   Array<Real> ts = bez.solve_derivative (horiz);
 714   Real lt = me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
 715   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) *  lt;
 716
 717   /* TODO: handle case of broken slur.  */
 718   if (!ts.is_empty ()
 719       && (extremes[LEFT].staff_ == extremes[RIGHT].staff_)
 720       && extremes[LEFT].staff_ && extremes[RIGHT].staff_)
 721     {
 722       Real y = bez.curve_point (ts[0])[Y_AXIS];
 723
 724       Grob *staff = extremes[LEFT].staff_;
 725
 726       Real staff_space = extremes[LEFT].staff_space_;
 727       Real p = 2 * (y - staff->relative_coordinate (common[Y_AXIS], Y_AXIS))
 728         / staff_space;
 729
 730       Real distance = fabs (my_round (p) - p);  //  in halfspaces
 731       if (distance < 4 * thick
 732           && (int) fabs (my_round (p))
 733           <= 2 * Staff_symbol_referencer::staff_radius (staff) + 0.1
 734           && (int (fabs (my_round (p))) % 2
 735               != Staff_symbol_referencer::line_count (staff) % 2))
 736         {
 737           Direction resolution_dir =
 738             (distance ?  get_grob_direction (me) : Direction (sign (p - my_round(p))));
 739
 740           // TODO: parameter
 741           Real newp = my_round (p) + resolution_dir
 742             * 5 * thick;
 743
 744           Real dy = (newp - p) * staff_space / 2.0;
 745
 746           bez.control_[1][Y_AXIS] += dy;
 747           bez.control_[2][Y_AXIS] += dy;
 748         }
 749     }
 750   return bez;
 751 }
 752
 753 Array<Slur_score>
 754 enumerate_attachments (Grob *me, Grob *common[],
 755                        Slur_score_parameters *score_param,
 756                        Drul_array<Bound_info> extremes,
 757                        Drul_array<Offset> base_attachment,
 758                        Drul_array<Real> end_ys)
 759 {
 760   (void) common;
 761   /*ugh.   */
 762   Array<Slur_score> scores;
 763
 764   Direction dir = get_grob_direction (me);
 765   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 766
 767   Drul_array<Offset> os;
 768   os[LEFT] = base_attachment[LEFT];
 769   Real minimum_length = staff_space
 770     * robust_scm2double (me->get_property ("minimum-length"), 2.0);
 771
 772   for (int i = 0; dir * os[LEFT][Y_AXIS] <= dir * end_ys[LEFT]; i++)
 773     {
 774       os[RIGHT] = base_attachment[RIGHT];
 775       for (int j = 0; dir * os[RIGHT][Y_AXIS] <= dir * end_ys[RIGHT]; j++)
 776         {
 777           Slur_score s;
 778           Direction d = LEFT;
 779           Drul_array<bool> attach_to_stem (false, false);
 780           do
 781             {
 782               os[d][X_AXIS] = base_attachment[d][X_AXIS];
 783               if (extremes[d].stem_
 784                   && !Stem::is_invisible (extremes[d].stem_)
 785                   && extremes[d].stem_dir_ == dir)
 786                 {
 787                   if (dir == -d
 788                       && extremes[d].stem_extent_[Y_AXIS].contains (os[d][Y_AXIS]))
 789                     {
 790                       os[d][X_AXIS] =  extremes[d].slur_head_extent_[-d]
 791                         - d * 0.3;
 792                       attach_to_stem[d] = true;
 793                     }
 794                   else if (dir *extremes[d].stem_extent_[Y_AXIS][dir]
 795                              < dir * os[d][Y_AXIS]
 796                            && !extremes[d].stem_extent_[X_AXIS].is_empty()
 797                            )
 798
 799                     os[d][X_AXIS] = extremes[d].stem_extent_[X_AXIS].center();
 800                 }
 801             }
 802           while (flip (&d) != LEFT);
 803
 804           Offset dz;
 805           dz = os[RIGHT] - os[LEFT];
 806           if (dz[X_AXIS] < minimum_length
 807               || fabs (dz[Y_AXIS] / dz[X_AXIS]) > score_param->max_slope_
 808               )
 809             {
 810               do
 811                 {
 812                   if (extremes[d].slur_head_)
 813                     {
 814                       os[d][X_AXIS] = extremes[d].slur_head_extent_.center ();
 815                       attach_to_stem[d] = false;
 816                     }
 817                 }
 818               while (flip (&d) != LEFT);
 819             }
 820
 821           dz = os[RIGHT] - os[LEFT];
 822           do
 823             {
 824               if (extremes[d].slur_head_
 825                   && !attach_to_stem[d])
 826                 {
 827                   /* Horizontally move tilted slurs a little.  Move
 828                      more for bigger tilts.
 829
 830                      TODO: parameter */
 831                   os[d][X_AXIS]
 832                     -= dir * extremes[d].slur_head_extent_.length ()
 833                     * sin (dz.arg  ()) / 3;
 834                 }
 835             }
 836           while (flip (&d) != LEFT);
 837
 838           s.attachment_ = os;
 839           scores.push (s);
 840
 841           os[RIGHT][Y_AXIS] += dir * staff_space / 2;
 842         }
 843
 844       os[LEFT][Y_AXIS] += dir * staff_space / 2;
 845     }
 846   return scores;
 847 }
 848
 849 inline Real
 850 linear_interpolate (Real x, Real x1, Real x2,  Real y1, Real  y2)
 851 {
 852   return (x2 - x) / (x2 - x1) * y1 +
 853     (x - x1) / (x2 - x1) * y2 ;
 854 }
 855
 856
 857 void
 858 score_encompass (Grob *me, Grob *common[],
 859                  Slur_score_parameters *score_param,
 860                  Drul_array<Bound_info> extremes,
 861                  Drul_array<Offset> base_attach,
 862                  Array<Slur_score> *scores)
 863 {
 864   (void) extremes;
 865   (void) base_attach;
 866
 867   Link_array<Grob> encompasses
 868     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 869   Direction dir = get_grob_direction (me);
 870
 871   Array<Encompass_info> infos;
 872
 873   for (int i = 0; i < encompasses.size(); i++)
 874     infos.push (get_encompass_info (me, encompasses[i], common));
 875
 876   for (int i = 0; i < scores->size (); i++)
 877     {
 878       Slur_score &configuration = scores->elem_ref (i);
 879       Bezier const &bez (configuration.curve_);
 880       Real demerit = 0.0;
 881
 882       /*
 883         Distances for heads that are between slur and line between
 884         attachment points.
 885        */
 886       Array<Real> convex_head_distances;
 887       Array<Real> edge_distances;
 888       for (int j = 0; j < infos.size(); j++)
 889         {
 890           Real x = infos[j].x_;
 891
 892           bool l_edge = j==0;
 893           bool r_edge = j==infos.size()-1;
 894           bool edge =  l_edge || r_edge;
 895
 896
 897           if (edge)
 898           {
 899             edge_distances.push (fabs (configuration.attachment_[l_edge ? LEFT : RIGHT][Y_AXIS]
 900                                        - infos[j].get_point (dir)));
 901           }
 902
 903
 904           if (!(x < configuration.attachment_[RIGHT][X_AXIS]
 905                 && x > configuration.attachment_[LEFT][X_AXIS]))
 906             continue;
 907
 908           Real y = bez.get_other_coordinate (X_AXIS, x);
 909           if (!edge)
 910             {
 911               Real head_dy = (y - infos[j].head_);
 912               if (dir * head_dy < 0)
 913                 {
 914                   demerit += score_param->head_encompass_penalty_;
 915                   convex_head_distances.push (0.0);
 916                 }
 917               else
 918                 {
 919                   Real hd = (head_dy)
 920                     ? (1 / fabs (head_dy) - 1 / score_param->free_head_distance_)
 921                     : score_param->head_encompass_penalty_;
 922                   hd = (hd >? 0)<? score_param->head_encompass_penalty_;
 923
 924                   demerit += hd;
 925                 }
 926
 927               Real line_y = linear_interpolate (x,
 928                                                 configuration.attachment_[RIGHT][X_AXIS],
 929                                                 configuration.attachment_[LEFT][X_AXIS],
 930                                                 configuration.attachment_[RIGHT][Y_AXIS],
 931                                                 configuration.attachment_[LEFT][Y_AXIS]);
 932
 933               if ( 1 ) // dir * infos[j].get_point (dir) > dir *line_y )
 934                 {
 935
 936                   Real closest =
 937                     dir * (dir * infos[j].get_point (dir)
 938                            >? dir *line_y
 939                            );
 940                   Real d = fabs(closest - y);
 941
 942                   convex_head_distances.push (d);
 943                 }
 944             }
 945
 946
 947
 948           if (dir * (y - infos[j].stem_) < 0)
 949             {
 950               Real stem_dem =score_param->stem_encompass_penalty_ ;
 951               if ((l_edge && dir == UP)
 952                   || (r_edge && dir == DOWN))
 953                 stem_dem /= 5;
 954
 955               demerit +=  stem_dem;
 956             }
 957           else if (!edge)
 958             {
 959               Interval ext;
 960               ext.add_point (infos[j].stem_);
 961               ext.add_point (infos[j].head_);
 962
 963               // ?
 964               demerit += -score_param->closeness_factor_
 965                 * (dir
 966                    * (y - (ext[dir] + dir * score_param->free_head_distance_))
 967                    <? 0)
 968                 / infos.size ();
 969             }
 970         }
 971
 972       Real variance_penalty = 0.0;
 973
 974       if (convex_head_distances.size())
 975         {
 976           Real avg_distance = 0.0;
 977           Real min_dist = infinity_f;
 978           for (int j = 0; j < convex_head_distances.size(); j++)
 979             {
 980               min_dist = min_dist <? convex_head_distances[j];
 981               avg_distance += convex_head_distances[j];
 982             }
 983
 984           /*
 985             For slurs over 3 or 4 heads, the average distance is not a
 986             good normalizer.
 987            */
 988           int n =  convex_head_distances.size();
 989           if (convex_head_distances.size() <= 2)
 990             {
 991               //              Real min_edge_dist = 1e6;
 992               for (int j = 0; j < edge_distances.size(); j++)
 993                 {
 994                   avg_distance += edge_distances[j];
 995                   n++;
 996                 }
 997
 998             }
 999
1000           /*
1001             TODO: maybe it's better to use (avgdist - mindist)*factor
1002             as penalty.
1003            */
1004           avg_distance /= n;
1005           variance_penalty = score_param->head_slur_distance_max_ratio_;
1006           if (min_dist > 0.0)
1007             variance_penalty = ((avg_distance / (min_dist  +score_param->free_head_distance_)) - 1.0)
1008               <? variance_penalty;
1009
1010           variance_penalty *= score_param->head_slur_distance_factor_;
1011         }
1012 #if DEBUG_SLUR_QUANTING
1013       (*scores)[i].score_card_ += to_string ("C%.2f", demerit);
1014       (*scores)[i].score_card_ += to_string ("D%.2f", variance_penalty);
1015 #endif
1016
1017       (*scores)[i].score_ += demerit + variance_penalty;
1018     }
1019 }
1020
1021 struct Extra_collision_info
1022 {
1023   Real idx_;
1024   Box extents_;
1025   Real penalty_;
1026
1027   Extra_collision_info (Real idx, Interval x, Interval y, Real p)
1028   {
1029     idx_ = idx;
1030     extents_[X_AXIS] = x;
1031     extents_[Y_AXIS] = y;
1032     penalty_ = p;
1033   }
1034   Extra_collision_info ()
1035   {
1036     idx_ = 0.0;
1037     penalty_ = 0.;
1038   }
1039 };
1040
1041 void
1042 score_extra_encompass (Grob *me, Grob *common[],
1043                        Slur_score_parameters *score_param,
1044                        Drul_array<Bound_info> extremes,
1045                        Drul_array<Offset> base_attach,
1046                        Array<Slur_score> *scores)
1047 {
1048   (void) base_attach;
1049   (void) extremes;
1050
1051   Spanner *me_spanner = dynamic_cast<Spanner*> (me);
1052
1053   Link_array<Grob> encompasses
1054     = Pointer_group_interface__extract_grobs (me, (Grob *)0,
1055                                               "encompass-objects");
1056   Direction dir = get_grob_direction (me);
1057   Real lt =  me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
1058   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) * lt;
1059
1060   Array<Extra_collision_info> collision_infos;
1061   for (int i = encompasses.size (); i--; )
1062     {
1063       if (Slur::has_interface (encompasses[i]))
1064         {
1065           Spanner * small_slur = dynamic_cast<Spanner*> (encompasses[i]);
1066           Bezier b = Slur::get_curve (small_slur);
1067
1068           Offset relative (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1069                            small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1070
1071           for (int k = 0; k < 3; k++)
1072           {
1073             Direction hdir =  Direction (k /2 - 1);
1074
1075             /*
1076               Only take bound into account if small slur starts
1077               together with big slur.
1078              */
1079             if (hdir && small_slur->get_bound (hdir) != me_spanner->get_bound (hdir))
1080               continue;
1081
1082
1083             Offset z = b.curve_point ( k / 2.0);
1084             z += relative;
1085
1086             Interval yext;
1087             yext.set_full();
1088             yext[dir] = z[Y_AXIS] + dir * thick * 1.0;
1089
1090             Interval xext(-1, 1);
1091             xext = xext *(thick*2) + z[X_AXIS];
1092             Extra_collision_info info (k - 1.0,
1093                                        xext,
1094                                        yext,
1095                                        score_param->extra_object_collision_);
1096             collision_infos.push (info);
1097           }
1098         }
1099       else
1100         {
1101           Grob *g = encompasses [i];
1102           Interval xe = g->extent (common[X_AXIS], X_AXIS);
1103           Interval ye = g->extent (common[Y_AXIS], Y_AXIS);
1104
1105           Real xp = 0.0;
1106           Real penalty = score_param->extra_object_collision_;
1107           if (Accidental_interface::has_interface (g))
1108             {
1109               penalty = score_param->accidental_collision_;
1110               /* Begin copy accidental.cc */
1111               bool parens = false;
1112               if (to_boolean (g->get_property ("cautionary")))
1113                 {
1114                   SCM cstyle = g->get_property ("cautionary-style");
1115                   parens = ly_c_equal_p (cstyle, ly_symbol2scm ("parentheses"));
1116                 }
1117
1118               SCM accs = g->get_property ("accidentals");
1119               SCM scm_style = g->get_property ("style");
1120               if (!scm_is_symbol (scm_style)
1121                   && !parens
1122                   && scm_ilength (accs) == 1)
1123                 {
1124                   /* End copy accidental.cc */
1125                   switch (scm_to_int (ly_car (accs)))
1126                     {
1127                     case FLAT:
1128                     case DOUBLE_FLAT:
1129                       xp = LEFT;
1130                       break ;
1131                     case SHARP:
1132                       xp = 0.5 * dir;
1133                       break ;
1134                     case NATURAL:
1135                       xp = -dir;
1136                       break;
1137                     }
1138                 }
1139             }
1140
1141           ye.widen (thick * 0.5);
1142           Extra_collision_info info (xp, xe, ye,  penalty);
1143           collision_infos.push (info);
1144         }
1145     }
1146   for (int i = 0; i < scores->size (); i++)
1147     {
1148       Real demerit = 0.0;
1149       for (int j = 0; j < collision_infos.size(); j++)
1150         {
1151           Drul_array<Offset> at = scores->elem (i).attachment_;
1152           Interval slur_wid (at[LEFT][X_AXIS], at[RIGHT][X_AXIS]);
1153
1154           /*
1155             to prevent numerical inaccuracies in
1156             Bezier::get_other_coordinate().
1157            */
1158           slur_wid.widen (- 0.5 * thick);
1159           Real x = collision_infos[j].extents_[X_AXIS]
1160             .linear_combination (collision_infos[j].idx_);
1161           Real y = 0.0;
1162
1163           if (!slur_wid.contains (x))
1164             {
1165               Direction contains_dir = CENTER;
1166               Direction d = LEFT;
1167               do
1168                 {
1169                   if (collision_infos[j].extents_[X_AXIS].contains (at[d][X_AXIS]))
1170                     contains_dir = d;
1171                 }
1172               while (flip (&d) != LEFT);
1173
1174               if (!contains_dir)
1175                 continue;
1176               else
1177                 y = at[contains_dir][Y_AXIS];
1178             }
1179           else
1180             {
1181               y = scores->elem (i).curve_.get_other_coordinate (X_AXIS, x);
1182             }
1183
1184           Real dist = collision_infos[j].extents_[Y_AXIS].distance (y);
1185           demerit +=
1186             fabs (0 >? (score_param->extra_encompass_free_distance_ - dist)) /
1187             score_param->extra_encompass_free_distance_
1188             * collision_infos[j].penalty_;
1189         }
1190 #if DEBUG_SLUR_QUANTING
1191       (*scores)[i].score_card_ += to_string ("X%.2f", demerit);
1192 #endif
1193       (*scores)[i].score_ += demerit;
1194     }
1195 }
1196
1197 /*
1198   TODO: should make edge penalties dependent on the direction that the
1199   slur-end is pointing.
1200  */
1201 void
1202 score_edges (Grob *me, Grob *common[],
1203              Slur_score_parameters * score_param,
1204              Drul_array<Bound_info> extremes,
1205              Drul_array<Offset> base_attach,
1206              Array<Slur_score> *scores)
1207 {
1208   (void) common;
1209   Direction dir = get_grob_direction (me);
1210
1211   for (int i = 0; i < scores->size (); i++)
1212     {
1213       Direction d = LEFT;
1214       Slur_score &config = scores->elem_ref (i);
1215       Offset dz = config.attachment_[RIGHT] - config.attachment_[LEFT];
1216       Real slope = dz[Y_AXIS] / dz[X_AXIS];
1217       do
1218         {
1219           Real y = config.attachment_[d][Y_AXIS];
1220           Real dy = fabs (y - base_attach[d][Y_AXIS]);
1221
1222           Real factor = score_param->edge_attraction_factor_;
1223           Real demerit = factor * dy;
1224           if (extremes[d].stem_
1225               && extremes[d].stem_dir_ == dir
1226               && !Stem::get_beaming (extremes[d].stem_, -d)
1227               )
1228             demerit /= 5;
1229
1230           demerit *= exp (dir * d * slope
1231                           * score_param->edge_slope_exponent_ );
1232
1233           (*scores)[i].score_ += demerit;
1234 #if DEBUG_SLUR_QUANTING
1235           (*scores)[i].score_card_ += to_string ("E%.2f", demerit);
1236 #endif
1237         }
1238       while (flip (&d) != LEFT);
1239     }
1240 }
1241
1242 void
1243 score_slopes (Grob *me, Grob *common[],
1244               Slur_score_parameters *score_param,
1245               Drul_array<Bound_info> extremes,
1246               Drul_array<Offset> base_attach,
1247               Array<Slur_score> * scores)
1248 {
1249   (void) me;
1250   (void) base_attach;
1251
1252   Drul_array<Real> ys;
1253   Direction d = LEFT;
1254   do
1255     {
1256       if (extremes[d].slur_head_)
1257         ys[d] = extremes[d].slur_head_->relative_coordinate (common[Y_AXIS],
1258                                                               Y_AXIS);
1259       else
1260         ys[d] = extremes[d].neighbor_y_;
1261     }
1262   while (flip (&d) != LEFT);
1263
1264   bool has_beams
1265     = (extremes[LEFT].stem_ && Stem::get_beam (extremes[LEFT].stem_))
1266     || (extremes[RIGHT].stem_ && Stem::get_beam (extremes[RIGHT].stem_));
1267
1268   Real dy = ys[RIGHT] - ys[LEFT];
1269   for (int i = 0; i < scores->size (); i++)
1270     {
1271       Offset slur_dz = (*scores)[i].attachment_[RIGHT]
1272         - (*scores)[i].attachment_[LEFT];
1273       Real slur_dy = slur_dz[Y_AXIS];
1274       Real demerit = 0.0;
1275
1276       demerit += ((fabs (slur_dy / slur_dz[X_AXIS])
1277                    - score_param->max_slope_) >? 0)
1278         * score_param->max_slope_factor_;
1279
1280       /* 0.2: account for staffline offset. */
1281       Real max_dy = (fabs (dy) + 0.2);
1282       if (has_beams)
1283         max_dy += 1.0;
1284
1285       demerit += score_param->steeper_slope_factor_
1286         * ((fabs (slur_dy) -max_dy) >? 0);
1287
1288       demerit += ((fabs (slur_dy/slur_dz[X_AXIS])
1289                    - score_param->max_slope_) >? 0)
1290         * score_param->max_slope_factor_;
1291
1292       if (sign (dy) == 0
1293           && sign (slur_dy) != 0)
1294         demerit += score_param->non_horizontal_penalty_;
1295
1296       if (sign (dy)
1297           && sign (slur_dy)
1298           && sign (slur_dy) != sign (dy))
1299         demerit += has_beams
1300           ? score_param->same_slope_penalty_ / 10
1301           : score_param->same_slope_penalty_;
1302
1303 #if DEBUG_SLUR_QUANTING
1304       (*scores)[i].score_card_ += to_string ("S%.2f", d);
1305 #endif
1306       (*scores)[i].score_ += demerit;
1307     }
1308
1309
1310
1311 }
1312
1313
1314 Real
1315 fit_factor (Offset dz_unit, Offset dz_perp,
1316             Bezier curve, Direction d,  Array<Offset> const &avoid)
1317 {
1318   Real fit_factor = 0.0;
1319   Offset x0 = curve.control_[0];
1320   curve.translate (-x0);
1321   curve.rotate (-dz_unit.arg ());
1322   curve.scale (1, d);
1323
1324   Interval curve_xext;
1325   curve_xext.add_point (curve.control_[0][X_AXIS]);
1326   curve_xext.add_point (curve.control_[3][X_AXIS]);
1327
1328   for (int i = 0; i < avoid.size (); i++)
1329     {
1330       Offset z = (avoid[i] - x0) ;
1331       Offset p (dot_product (z, dz_unit),
1332                 d* dot_product (z, dz_perp));
1333       if (!curve_xext.contains (p[X_AXIS]))
1334         continue;
1335
1336       Real y = curve.get_other_coordinate (X_AXIS, p[X_AXIS]);
1337       if (y)
1338         {
1339           fit_factor = fit_factor >? (p[Y_AXIS] / y);
1340         }
1341     }
1342   return fit_factor;
1343 }
1344
1345
1346 Bezier
1347 get_bezier (Grob *me,
1348             Grob **common,
1349             Slur_score_parameters *score_param,
1350             Drul_array<Bound_info> extremes,
1351             Drul_array<Offset> attachments,
1352             Real r_0, Real h_inf
1353             )
1354 {
1355   Link_array<Grob> encompasses
1356     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
1357   Direction dir = get_grob_direction (me);
1358
1359   Array<Offset> avoid;
1360   for (int i = 0; i < encompasses.size(); i++)
1361     {
1362       if (extremes[LEFT].note_column_ == encompasses[i]
1363           ||extremes[RIGHT].note_column_ == encompasses[i])
1364         continue;
1365
1366       Encompass_info inf (get_encompass_info (me, encompasses[i], common));
1367
1368       Real y = dir*((dir * inf.head_) >? (dir *inf.stem_));
1369
1370       avoid.push (Offset (inf.x_,  y + dir * score_param->free_head_distance_));
1371     }
1372
1373   Link_array<Grob> extra_encompasses
1374     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "encompass-objects");
1375   for (int i = 0;  i < extra_encompasses.size (); i++)
1376     if (Slur::has_interface (extra_encompasses[i]))
1377       {
1378         Grob * small_slur = extra_encompasses[i];
1379         Bezier b = Slur::get_curve (small_slur);
1380
1381         Offset z = b.curve_point (0.5);
1382         z += Offset (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1383                      small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1384
1385         z[Y_AXIS] += dir * score_param->free_slur_distance_;
1386         avoid.push (z);
1387       }
1388
1389   Offset dz = attachments[RIGHT]- attachments[LEFT];;
1390   Offset dz_unit = dz;
1391   dz_unit *= 1 / dz.length();
1392   Offset dz_perp = dz_unit * Offset(0,1);
1393
1394   Real indent, height;
1395   get_slur_indent_height (&indent, &height, dz.length (), h_inf, r_0);
1396
1397   Real excentricity = robust_scm2double (me->get_property ("excentricity"), 0.0);
1398   Bezier curve;
1399
1400   Real x1 = (excentricity + indent);
1401   Real x2 = (excentricity - indent);
1402   curve.control_[0] = attachments[LEFT];
1403   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1404   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1405   curve.control_[3] = attachments[RIGHT];
1406
1407
1408   Real ff = fit_factor (dz_unit, dz_perp, curve, dir, avoid);
1409   Real l = dz.length ();
1410
1411   /*
1412     This condition,
1413
1414     l^2 > 4h^2 +  3(i  1/3l)^2  - 1/3 l^2
1415
1416     is equivalent to:
1417
1418     |bez'(0)| < | bez'(.5)|
1419
1420     when (control2-control1) has the same direction as (control3 -
1421     control0).
1422
1423    */
1424   Real max_h = sqrt (sqr (l)/3 - .75 * sqr (indent + l / 3));
1425   height = height >? ((height * ff) <? max_h);
1426
1427   curve.control_[0] = attachments[LEFT];
1428   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1429   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1430   curve.control_[3] = attachments[RIGHT];
1431
1432   return curve;
1433 }