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
 417   Direction d = RIGHT;
 418   Direction dir = get_grob_direction (me);
 419
 420   do
 421     {
 422       extremes[d].bound_ = me->get_bound (d);
 423       if (Note_column::has_interface (extremes[d].bound_))
 424         {
 425           extremes[d].note_column_ = extremes[d].bound_;
 426           extremes[d].stem_ = Note_column::get_stem (extremes[d].note_column_);
 427           extremes[d].stem_dir_ = get_grob_direction (extremes[d].stem_);
 428           extremes[d].stem_extent_[X_AXIS]
 429             = extremes[d].stem_->extent (common[X_AXIS], X_AXIS);
 430           extremes[d].stem_extent_[Y_AXIS]
 431             = extremes[d].stem_->extent (common[Y_AXIS], Y_AXIS);
 432           extremes[d].slur_head_
 433             = Stem::extremal_heads (extremes[d].stem_)[dir];
 434           if (!extremes[d].slur_head_
 435               && Note_column::has_rests (extremes[d].bound_))
 436             {
 437               extremes[d].slur_head_ = Note_column::get_rest (extremes[d].bound_);
 438             }
 439
 440           if (extremes[d].slur_head_)
 441             extremes[d].slur_head_extent_
 442               = extremes[d].slur_head_->extent (common[X_AXIS], X_AXIS);
 443
 444           extremes[d].staff_ = Staff_symbol_referencer
 445             ::get_staff_symbol (extremes[d].stem_);
 446           extremes[d].staff_space_ = Staff_symbol_referencer
 447             ::staff_space (extremes[d].stem_);
 448         }
 449       else if (d == RIGHT)
 450         /*
 451           right side anticipates on the next note.
 452         */
 453         extremes[d].neighbor_y_ = broken_trend_y (me, common, d);
 454     }
 455   while (flip (&d) != RIGHT);
 456   return extremes;
 457 }
 458
 459 void
 460 set_end_points (Grob *me)
 461 {
 462   Link_array<Grob> columns
 463     = Pointer_group_interface__extract_grobs (me, (Grob *) 0, "note-columns");
 464
 465   if (columns.is_empty ())
 466     {
 467       me->suicide ();
 468       return;
 469     }
 470
 471   SCM eltlist = me->get_property ("note-columns");
 472   SCM extra_list = me->get_property ("encompass-objects");
 473   Spanner *sp = dynamic_cast<Spanner*> (me);
 474
 475   Grob *common[] = {0, 0};
 476   for (int i = X_AXIS; i < NO_AXES; i++)
 477     {
 478       Axis a = (Axis)i;
 479       common[a] = common_refpoint_of_list (eltlist, me, a);
 480       common[a] = common_refpoint_of_list (extra_list, common[a], a);
 481     }
 482
 483   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (RIGHT),
 484                                                     X_AXIS);
 485   common[X_AXIS] = common[X_AXIS]->common_refpoint (sp->get_bound (LEFT),
 486                                                     X_AXIS);
 487
 488   Drul_array<Bound_info> extremes = get_bound_info (sp, common);
 489   Drul_array<Offset> base_attachment
 490     = get_base_attachments (sp, common, extremes);
 491   Slur_score_parameters params (me);
 492   Drul_array<Real> end_ys
 493     = get_y_attachment_range (sp, common, &params, extremes, base_attachment);
 494   Array<Slur_score> scores = enumerate_attachments (me, common, &params,
 495                                                     extremes, base_attachment,
 496                                                     end_ys);
 497
 498   generate_curves (me, common, &params, extremes, base_attachment, &scores);
 499   score_edges (me, common, &params,extremes, base_attachment, &scores);
 500   score_slopes (me, common, &params,extremes, base_attachment, &scores);
 501   score_encompass (me, common, &params,extremes, base_attachment, &scores);
 502   score_extra_encompass (me, common, &params,extremes, base_attachment,
 503                          &scores);
 504
 505   Real opt = 1e6;
 506   int opt_idx = 0;
 507   // why backwards?
 508   for (int i = scores.size (); i--;)
 509     {
 510       if (scores[i].score_ < opt)
 511         {
 512           opt = scores[i].score_;
 513           opt_idx = i;
 514         }
 515     }
 516
 517 #if DEBUG_SLUR_QUANTING
 518   SCM inspect_quants = me->get_property ("inspect-quants");
 519   if (to_boolean (me->get_paper ()
 520                   ->lookup_variable (ly_symbol2scm ("debug-slur-scoring")))
 521       && ly_c_pair_p (inspect_quants))
 522     {
 523       Drul_array<Real> ins = ly_scm2interval (inspect_quants);
 524       Real mindist = 1e6;
 525       for (int i = 0; i < scores.size (); i ++)
 526         {
 527           Real d =fabs (scores[i].attachment_[LEFT][Y_AXIS] - ins[LEFT])
 528             + fabs (scores[i].attachment_[RIGHT][Y_AXIS] - ins[RIGHT]);
 529           if (d < mindist)
 530             {
 531               opt_idx = i;
 532               mindist= d;
 533             }
 534         }
 535       if (mindist > 1e5)
 536         programming_error ("Could not find quant.");
 537     }
 538   scores[opt_idx].score_card_ += to_string ("i%d", opt_idx);
 539
 540   // debug quanting
 541   me->set_property ("quant-score",
 542                     scm_makfrom0str (scores[opt_idx].score_card_.to_str0 ()));
 543 #endif
 544
 545   Bezier b = scores[opt_idx].curve_;
 546   SCM controls = SCM_EOL;
 547   for (int i = 4; i--;)
 548     {
 549       Offset o = b.control_[i]
 550         - Offset (me->relative_coordinate (common[X_AXIS], X_AXIS),
 551                   me->relative_coordinate (common[Y_AXIS], Y_AXIS));
 552       controls = scm_cons (ly_offset2scm (o), controls);
 553     }
 554   me->set_property ("control-points", controls);
 555 }
 556
 557 /*
 558   TODO: should analyse encompasses to determine sensible region, and
 559   should limit slopes available.
 560  */
 561
 562 Drul_array<Real>
 563 get_y_attachment_range (Spanner*me,
 564                         Grob **common, Slur_score_parameters *score_param,
 565                         Drul_array<Bound_info> extremes,
 566                         Drul_array<Offset> base_attachment)
 567 {
 568   Drul_array<Real> end_ys;
 569   Direction dir = get_grob_direction (me);
 570   Direction d = LEFT;
 571   do
 572     {
 573       if (extremes[d].note_column_)
 574         {
 575           end_ys[d] = dir
 576             * ((dir * (base_attachment[d][Y_AXIS] +  score_param->region_size_* dir))
 577                >? (dir * (dir + extremes[d].note_column_->extent(common[Y_AXIS],
 578                                                                  Y_AXIS)[dir]))
 579                >? (dir * base_attachment[-d][Y_AXIS]));
 580         }
 581       else
 582         end_ys[d] = extremes[d].neighbor_y_ + score_param->region_size_ * dir;
 583     }
 584   while (flip (&d) != LEFT);
 585
 586   return end_ys;
 587 }
 588
 589 bool
 590 spanner_less (Spanner *s1, Spanner* s2)
 591 {
 592   Slice b1, b2;
 593   Direction d  = LEFT;
 594   do
 595     {
 596       b1[d] = s1->get_bound (d)->get_column ()->rank_;
 597       b2[d] = s2->get_bound (d)->get_column ()->rank_;
 598     } while (flip (&d) != LEFT);
 599
 600   return b2[LEFT] <= b1[LEFT] && b2[RIGHT] >= b1[RIGHT]
 601     && (b2[LEFT] != b1[LEFT] || b2[RIGHT] != b1[RIGHT]);
 602 }
 603
 604
 605 Drul_array<Offset>
 606 get_base_attachments (Spanner *me,
 607                       Grob **common, Drul_array<Bound_info> extremes)
 608 {
 609   Link_array<Grob> columns
 610     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 611   Drul_array<Offset> base_attachment;
 612   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 613   Direction dir = get_grob_direction (me);
 614   Direction d = RIGHT;
 615   do
 616     {
 617       Grob *stem = extremes[d].stem_;
 618       Grob *head = extremes[d].slur_head_;
 619
 620       Real x, y;
 621       if (!extremes[d].note_column_)
 622         {
 623           if (d == RIGHT)
 624             {
 625               y = extremes[d].neighbor_y_;
 626               x = extremes[d].bound_->extent (common[X_AXIS], X_AXIS)[d];
 627             }
 628           else
 629             {
 630               x = me->get_broken_left_end_align ();
 631               if (extremes[RIGHT].bound_ == columns[0])
 632                 {
 633                   y = base_attachment[RIGHT][Y_AXIS];
 634                 }
 635               else
 636                 {
 637                   y = columns[0]->extent (common[Y_AXIS], Y_AXIS)[dir];
 638                 }
 639             }
 640         }
 641       else
 642         {
 643           bool same_beam =
 644             (extremes[d].stem_ && extremes[-d].stem_
 645              && Stem::get_beam (extremes[d].stem_) == Stem::get_beam (extremes[-d].stem_));
 646
 647           /*
 648             fixme: X coord should also be set in this case.
 649            */
 650           if (stem
 651               && extremes[d].stem_dir_ == dir
 652               && Stem::get_beaming (stem, -d)
 653               && (!spanner_less (me, Stem::get_beam (stem))
 654                   || same_beam))
 655             y = extremes[d].stem_extent_[Y_AXIS][dir];
 656           else if (head)
 657             y = head->extent (common[Y_AXIS], Y_AXIS)[dir];
 658           y += dir * 0.5 * staff_space;
 659
 660           Real pos
 661             = (y - extremes[d].staff_->relative_coordinate (common[Y_AXIS],
 662                                                             Y_AXIS))
 663             * 2.0 / Staff_symbol::staff_space (extremes[d].staff_);
 664
 665           /* start off staffline. */
 666           if (fabs (pos - my_round (pos)) < 0.2
 667               && Staff_symbol_referencer::on_staffline (head, (int) rint (pos))
 668               && Staff_symbol_referencer::line_count (head) - 1 >= rint (pos)
 669               )
 670             // TODO: calc from slur thick & line thick, parameter.
 671             y += 1.5 * staff_space * dir / 10;
 672
 673           Grob * fh = Note_column::first_head (extremes[d].note_column_);
 674           x =
 675             (fh ? fh->extent (common[X_AXIS], X_AXIS)
 676              : extremes[d].bound_->extent (common[X_AXIS], X_AXIS))
 677             .linear_combination (CENTER);
 678         }
 679       base_attachment[d] = Offset (x, y);
 680
 681     } while (flip (&d) != RIGHT);
 682
 683   return base_attachment;
 684 }
 685
 686 void
 687 generate_curves (Grob *me, Grob **common,
 688                  Slur_score_parameters *score_param,
 689                  Drul_array<Bound_info> extremes,
 690                  Drul_array<Offset>,
 691                  Array<Slur_score> *scores)
 692 {
 693   (void) common;
 694   (void) extremes;
 695   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 696   Real r_0 = robust_scm2double (me->get_property ("ratio"), 0.33);
 697   Real h_inf = staff_space * scm_to_double (me->get_property ("height-limit"));
 698   for (int i = 0; i < scores->size(); i++)
 699     {
 700       Bezier bez = get_bezier (me,
 701                               common,
 702                               score_param,
 703                               extremes,
 704                               (*scores)[i].attachment_, r_0, h_inf);
 705
 706       bez = avoid_staff_line (me, common, extremes, bez);
 707       (*scores)[i].attachment_[LEFT] = bez.control_[0];
 708       (*scores)[i].attachment_[RIGHT] = bez.control_[3];
 709       (*scores)[i].curve_ = bez;
 710     }
 711 }
 712
 713 Bezier
 714 avoid_staff_line (Grob *me, Grob **common,
 715                   Drul_array<Bound_info> extremes,
 716                   Bezier bez)
 717 {
 718   Offset horiz (1,0);
 719   Array<Real> ts = bez.solve_derivative (horiz);
 720   Real lt = me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
 721   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) *  lt;
 722
 723   /* TODO: handle case of broken slur.  */
 724   if (!ts.is_empty ()
 725       && (extremes[LEFT].staff_ == extremes[RIGHT].staff_)
 726       && extremes[LEFT].staff_ && extremes[RIGHT].staff_)
 727     {
 728       Real y = bez.curve_point (ts[0])[Y_AXIS];
 729
 730       Grob *staff = extremes[LEFT].staff_;
 731
 732       Real staff_space = extremes[LEFT].staff_space_;
 733       Real p = 2 * (y - staff->relative_coordinate (common[Y_AXIS], Y_AXIS))
 734         / staff_space;
 735
 736       Real distance = fabs (my_round (p) - p);  //  in halfspaces
 737       if (distance < 4 * thick
 738           && (int) fabs (my_round (p))
 739           <= 2 * Staff_symbol_referencer::staff_radius (staff) + 0.1
 740           && (int (fabs (my_round (p))) % 2
 741               != Staff_symbol_referencer::line_count (staff) % 2))
 742         {
 743           Direction resolution_dir =
 744             (distance ?  get_grob_direction (me) : Direction (sign (p - my_round(p))));
 745
 746           // TODO: parameter
 747           Real newp = my_round (p) + resolution_dir
 748             * 5 * thick;
 749
 750           Real dy = (newp - p) * staff_space / 2.0;
 751
 752           bez.control_[1][Y_AXIS] += dy;
 753           bez.control_[2][Y_AXIS] += dy;
 754         }
 755     }
 756   return bez;
 757 }
 758
 759 Array<Slur_score>
 760 enumerate_attachments (Grob *me, Grob *common[],
 761                        Slur_score_parameters *score_param,
 762                        Drul_array<Bound_info> extremes,
 763                        Drul_array<Offset> base_attachment,
 764                        Drul_array<Real> end_ys)
 765 {
 766   (void) common;
 767   /*ugh.   */
 768   Array<Slur_score> scores;
 769
 770   Direction dir = get_grob_direction (me);
 771   Real staff_space = Staff_symbol_referencer::staff_space ((Grob *) me);
 772
 773   Drul_array<Offset> os;
 774   os[LEFT] = base_attachment[LEFT];
 775   Real minimum_length = staff_space
 776     * robust_scm2double (me->get_property ("minimum-length"), 2.0);
 777
 778   for (int i = 0; dir * os[LEFT][Y_AXIS] <= dir * end_ys[LEFT]; i++)
 779     {
 780       os[RIGHT] = base_attachment[RIGHT];
 781       for (int j = 0; dir * os[RIGHT][Y_AXIS] <= dir * end_ys[RIGHT]; j++)
 782         {
 783           Slur_score s;
 784           Direction d = LEFT;
 785           Drul_array<bool> attach_to_stem (false, false);
 786           do
 787             {
 788               os[d][X_AXIS] = base_attachment[d][X_AXIS];
 789               if (extremes[d].stem_
 790                   && !Stem::is_invisible (extremes[d].stem_)
 791                   && extremes[d].stem_dir_ == dir)
 792                 {
 793                   if (dir == -d
 794                       && extremes[d].stem_extent_[Y_AXIS].contains (os[d][Y_AXIS]))
 795                     {
 796                       os[d][X_AXIS] =  extremes[d].slur_head_extent_[-d]
 797                         - d * 0.3;
 798                       attach_to_stem[d] = true;
 799                     }
 800                   else if (dir *extremes[d].stem_extent_[Y_AXIS][dir]
 801                              < dir * os[d][Y_AXIS]
 802                            && !extremes[d].stem_extent_[X_AXIS].is_empty()
 803                            )
 804
 805                     os[d][X_AXIS] = extremes[d].stem_extent_[X_AXIS].center();
 806                 }
 807             }
 808           while (flip (&d) != LEFT);
 809
 810           Offset dz;
 811           dz = os[RIGHT] - os[LEFT];
 812           if (dz[X_AXIS] < minimum_length
 813               || fabs (dz[Y_AXIS] / dz[X_AXIS]) > score_param->max_slope_
 814               )
 815             {
 816               do
 817                 {
 818                   if (extremes[d].slur_head_)
 819                     {
 820                       os[d][X_AXIS] = extremes[d].slur_head_extent_.center ();
 821                       attach_to_stem[d] = false;
 822                     }
 823                 }
 824               while (flip (&d) != LEFT);
 825             }
 826
 827           dz = os[RIGHT] - os[LEFT];
 828           do
 829             {
 830               if (extremes[d].slur_head_
 831                   && !attach_to_stem[d])
 832                 {
 833                   /* Horizontally move tilted slurs a little.  Move
 834                      more for bigger tilts.
 835
 836                      TODO: parameter */
 837                   os[d][X_AXIS]
 838                     -= dir * extremes[d].slur_head_extent_.length ()
 839                     * sin (dz.arg  ()) / 3;
 840                 }
 841             }
 842           while (flip (&d) != LEFT);
 843
 844           s.attachment_ = os;
 845           scores.push (s);
 846
 847           os[RIGHT][Y_AXIS] += dir * staff_space / 2;
 848         }
 849
 850       os[LEFT][Y_AXIS] += dir * staff_space / 2;
 851     }
 852   return scores;
 853 }
 854
 855 inline Real
 856 linear_interpolate (Real x, Real x1, Real x2,  Real y1, Real  y2)
 857 {
 858   return (x2 - x) / (x2 - x1) * y1 +
 859     (x - x1) / (x2 - x1) * y2 ;
 860 }
 861
 862
 863 void
 864 score_encompass (Grob *me, Grob *common[],
 865                  Slur_score_parameters *score_param,
 866                  Drul_array<Bound_info> extremes,
 867                  Drul_array<Offset> base_attach,
 868                  Array<Slur_score> *scores)
 869 {
 870   (void) extremes;
 871   (void) base_attach;
 872
 873   Link_array<Grob> encompasses
 874     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
 875   Direction dir = get_grob_direction (me);
 876
 877   Array<Encompass_info> infos;
 878
 879   for (int i = 0; i < encompasses.size(); i++)
 880     infos.push (get_encompass_info (me, encompasses[i], common));
 881
 882   for (int i = 0; i < scores->size (); i++)
 883     {
 884       Slur_score &configuration = scores->elem_ref (i);
 885       Bezier const &bez (configuration.curve_);
 886       Real demerit = 0.0;
 887
 888       /*
 889         Distances for heads that are between slur and line between
 890         attachment points.
 891        */
 892       Array<Real> convex_head_distances;
 893       Array<Real> edge_distances;
 894       for (int j = 0; j < infos.size(); j++)
 895         {
 896           Real x = infos[j].x_;
 897
 898           bool l_edge = j==0;
 899           bool r_edge = j==infos.size()-1;
 900           bool edge =  l_edge || r_edge;
 901
 902
 903           if (edge)
 904           {
 905             edge_distances.push (fabs (configuration.attachment_[l_edge ? LEFT : RIGHT][Y_AXIS]
 906                                        - infos[j].get_point (dir)));
 907           }
 908
 909
 910           if (!(x < configuration.attachment_[RIGHT][X_AXIS]
 911                 && x > configuration.attachment_[LEFT][X_AXIS]))
 912             continue;
 913
 914           Real y = bez.get_other_coordinate (X_AXIS, x);
 915           if (!edge)
 916             {
 917               Real head_dy = (y - infos[j].head_);
 918               if (dir * head_dy < 0)
 919                 {
 920                   demerit += score_param->head_encompass_penalty_;
 921                   convex_head_distances.push (0.0);
 922                 }
 923               else
 924                 {
 925                   Real hd = (head_dy)
 926                     ? (1 / fabs (head_dy) - 1 / score_param->free_head_distance_)
 927                     : score_param->head_encompass_penalty_;
 928                   hd = (hd >? 0)<? score_param->head_encompass_penalty_;
 929
 930                   demerit += hd;
 931                 }
 932
 933               Real line_y = linear_interpolate (x,
 934                                                 configuration.attachment_[RIGHT][X_AXIS],
 935                                                 configuration.attachment_[LEFT][X_AXIS],
 936                                                 configuration.attachment_[RIGHT][Y_AXIS],
 937                                                 configuration.attachment_[LEFT][Y_AXIS]);
 938
 939               if ( 1 ) // dir * infos[j].get_point (dir) > dir *line_y )
 940                 {
 941
 942                   Real closest =
 943                     dir * (dir * infos[j].get_point (dir)
 944                            >? dir *line_y
 945                            );
 946                   Real d = fabs(closest - y);
 947
 948                   convex_head_distances.push (d);
 949                 }
 950             }
 951
 952
 953
 954           if (dir * (y - infos[j].stem_) < 0)
 955             {
 956               Real stem_dem =score_param->stem_encompass_penalty_ ;
 957               if ((l_edge && dir == UP)
 958                   || (r_edge && dir == DOWN))
 959                 stem_dem /= 5;
 960
 961               demerit +=  stem_dem;
 962             }
 963           else if (!edge)
 964             {
 965               Interval ext;
 966               ext.add_point (infos[j].stem_);
 967               ext.add_point (infos[j].head_);
 968
 969               // ?
 970               demerit += -score_param->closeness_factor_
 971                 * (dir
 972                    * (y - (ext[dir] + dir * score_param->free_head_distance_))
 973                    <? 0)
 974                 / infos.size ();
 975             }
 976         }
 977
 978       Real variance_penalty = 0.0;
 979
 980       if (convex_head_distances.size())
 981         {
 982           Real avg_distance = 0.0;
 983           Real min_dist = infinity_f;
 984           for (int j = 0; j < convex_head_distances.size(); j++)
 985             {
 986               min_dist = min_dist <? convex_head_distances[j];
 987               avg_distance += convex_head_distances[j];
 988             }
 989
 990           /*
 991             For slurs over 3 or 4 heads, the average distance is not a
 992             good normalizer.
 993            */
 994           int n =  convex_head_distances.size();
 995           if (convex_head_distances.size() <= 2)
 996             {
 997               //              Real min_edge_dist = 1e6;
 998               for (int j = 0; j < edge_distances.size(); j++)
 999                 {
1000                   avg_distance += edge_distances[j];
1001                   n++;
1002                 }
1003
1004             }
1005
1006           /*
1007             TODO: maybe it's better to use (avgdist - mindist)*factor
1008             as penalty.
1009            */
1010           avg_distance /= n;
1011           variance_penalty = score_param->head_slur_distance_max_ratio_;
1012           if (min_dist > 0.0)
1013             variance_penalty = ((avg_distance / (min_dist  +score_param->free_head_distance_)) - 1.0)
1014               <? variance_penalty;
1015
1016           variance_penalty *= score_param->head_slur_distance_factor_;
1017         }
1018 #if DEBUG_SLUR_QUANTING
1019       (*scores)[i].score_card_ += to_string ("C%.2f", demerit);
1020       (*scores)[i].score_card_ += to_string ("D%.2f", variance_penalty);
1021 #endif
1022
1023       (*scores)[i].score_ += demerit + variance_penalty;
1024     }
1025 }
1026
1027 struct Extra_collision_info
1028 {
1029   Real idx_;
1030   Box extents_;
1031   Real penalty_;
1032
1033   Extra_collision_info (Real idx, Interval x, Interval y, Real p)
1034   {
1035     idx_ = idx;
1036     extents_[X_AXIS] = x;
1037     extents_[Y_AXIS] = y;
1038     penalty_ = p;
1039   }
1040   Extra_collision_info ()
1041   {
1042     idx_ = 0.0;
1043     penalty_ = 0.;
1044   }
1045 };
1046
1047 void
1048 score_extra_encompass (Grob *me, Grob *common[],
1049                        Slur_score_parameters *score_param,
1050                        Drul_array<Bound_info> extremes,
1051                        Drul_array<Offset> base_attach,
1052                        Array<Slur_score> *scores)
1053 {
1054   (void) base_attach;
1055   (void) extremes;
1056
1057   Spanner *me_spanner = dynamic_cast<Spanner*> (me);
1058
1059   Link_array<Grob> encompasses
1060     = Pointer_group_interface__extract_grobs (me, (Grob *)0,
1061                                               "encompass-objects");
1062   Direction dir = get_grob_direction (me);
1063   Real lt =  me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
1064   Real thick = robust_scm2double (me->get_property ("thickness"), 1.0) * lt;
1065
1066   Array<Extra_collision_info> collision_infos;
1067   for (int i = encompasses.size (); i--; )
1068     {
1069       if (Slur::has_interface (encompasses[i]))
1070         {
1071           Spanner * small_slur = dynamic_cast<Spanner*> (encompasses[i]);
1072           Bezier b = Slur::get_curve (small_slur);
1073
1074           Offset relative (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1075                            small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1076
1077           for (int k = 0; k < 3; k++)
1078           {
1079             Direction hdir =  Direction (k /2 - 1);
1080
1081             /*
1082               Only take bound into account if small slur starts
1083               together with big slur.
1084              */
1085             if (hdir && small_slur->get_bound (hdir) != me_spanner->get_bound (hdir))
1086               continue;
1087
1088
1089             Offset z = b.curve_point ( k / 2.0);
1090             z += relative;
1091
1092             Interval yext;
1093             yext.set_full();
1094             yext[dir] = z[Y_AXIS] + dir * thick * 1.0;
1095
1096             Interval xext(-1, 1);
1097             xext = xext *(thick*2) + z[X_AXIS];
1098             Extra_collision_info info (k - 1.0,
1099                                        xext,
1100                                        yext,
1101                                        score_param->extra_object_collision_);
1102             collision_infos.push (info);
1103           }
1104         }
1105       else
1106         {
1107           Grob *g = encompasses [i];
1108           Interval xe = g->extent (common[X_AXIS], X_AXIS);
1109           Interval ye = g->extent (common[Y_AXIS], Y_AXIS);
1110
1111           Real xp = 0.0;
1112           Real penalty = score_param->extra_object_collision_;
1113           if (Accidental_interface::has_interface (g))
1114             {
1115               penalty = score_param->accidental_collision_;
1116               /* Begin copy accidental.cc */
1117               bool parens = false;
1118               if (to_boolean (g->get_property ("cautionary")))
1119                 {
1120                   SCM cstyle = g->get_property ("cautionary-style");
1121                   parens = ly_c_equal_p (cstyle, ly_symbol2scm ("parentheses"));
1122                 }
1123
1124               SCM accs = g->get_property ("accidentals");
1125               SCM scm_style = g->get_property ("style");
1126               if (!scm_is_symbol (scm_style)
1127                   && !parens
1128                   && scm_ilength (accs) == 1)
1129                 {
1130                   /* End copy accidental.cc */
1131                   switch (scm_to_int (ly_car (accs)))
1132                     {
1133                     case FLAT:
1134                     case DOUBLE_FLAT:
1135                       xp = LEFT;
1136                       break ;
1137                     case SHARP:
1138                       xp = 0.5 * dir;
1139                       break ;
1140                     case NATURAL:
1141                       xp = -dir;
1142                       break;
1143                     }
1144                 }
1145             }
1146
1147           ye.widen (thick * 0.5);
1148           Extra_collision_info info (xp, xe, ye,  penalty);
1149           collision_infos.push (info);
1150         }
1151     }
1152   for (int i = 0; i < scores->size (); i++)
1153     {
1154       Real demerit = 0.0;
1155       for (int j = 0; j < collision_infos.size(); j++)
1156         {
1157           Drul_array<Offset> at = scores->elem (i).attachment_;
1158           Interval slur_wid (at[LEFT][X_AXIS], at[RIGHT][X_AXIS]);
1159
1160           /*
1161             to prevent numerical inaccuracies in
1162             Bezier::get_other_coordinate().
1163            */
1164           slur_wid.widen (- 0.5 * thick);
1165           Real x = collision_infos[j].extents_[X_AXIS]
1166             .linear_combination (collision_infos[j].idx_);
1167           Real y = 0.0;
1168
1169           if (!slur_wid.contains (x))
1170             {
1171               Direction contains_dir = CENTER;
1172               Direction d = LEFT;
1173               do
1174                 {
1175                   if (collision_infos[j].extents_[X_AXIS].contains (at[d][X_AXIS]))
1176                     contains_dir = d;
1177                 }
1178               while (flip (&d) != LEFT);
1179
1180               if (!contains_dir)
1181                 continue;
1182               else
1183                 y = at[contains_dir][Y_AXIS];
1184             }
1185           else
1186             {
1187               y = scores->elem (i).curve_.get_other_coordinate (X_AXIS, x);
1188             }
1189
1190           Real dist = collision_infos[j].extents_[Y_AXIS].distance (y);
1191           demerit +=
1192             fabs (0 >? (score_param->extra_encompass_free_distance_ - dist)) /
1193             score_param->extra_encompass_free_distance_
1194             * collision_infos[j].penalty_;
1195         }
1196 #if DEBUG_SLUR_QUANTING
1197       (*scores)[i].score_card_ += to_string ("X%.2f", demerit);
1198 #endif
1199       (*scores)[i].score_ += demerit;
1200     }
1201 }
1202
1203 /*
1204   TODO: should make edge penalties dependent on the direction that the
1205   slur-end is pointing.
1206  */
1207 void
1208 score_edges (Grob *me, Grob *common[],
1209              Slur_score_parameters * score_param,
1210              Drul_array<Bound_info> extremes,
1211              Drul_array<Offset> base_attach,
1212              Array<Slur_score> *scores)
1213 {
1214   (void) common;
1215   Direction dir = get_grob_direction (me);
1216
1217   for (int i = 0; i < scores->size (); i++)
1218     {
1219       Direction d = LEFT;
1220       Slur_score &config = scores->elem_ref (i);
1221       Offset dz = config.attachment_[RIGHT] - config.attachment_[LEFT];
1222       Real slope = dz[Y_AXIS] / dz[X_AXIS];
1223       do
1224         {
1225           Real y = config.attachment_[d][Y_AXIS];
1226           Real dy = fabs (y - base_attach[d][Y_AXIS]);
1227
1228           Real factor = score_param->edge_attraction_factor_;
1229           Real demerit = factor * dy;
1230           if (extremes[d].stem_
1231               && extremes[d].stem_dir_ == dir
1232               && !Stem::get_beaming (extremes[d].stem_, -d)
1233               )
1234             demerit /= 5;
1235
1236           demerit *= exp (dir * d * slope
1237                           * score_param->edge_slope_exponent_ );
1238
1239           (*scores)[i].score_ += demerit;
1240 #if DEBUG_SLUR_QUANTING
1241           (*scores)[i].score_card_ += to_string ("E%.2f", demerit);
1242 #endif
1243         }
1244       while (flip (&d) != LEFT);
1245     }
1246 }
1247
1248 void
1249 score_slopes (Grob *me, Grob *common[],
1250               Slur_score_parameters *score_param,
1251               Drul_array<Bound_info> extremes,
1252               Drul_array<Offset> base_attach,
1253               Array<Slur_score> * scores)
1254 {
1255   (void) me;
1256   (void) base_attach;
1257
1258   Drul_array<Real> ys;
1259   Direction d = LEFT;
1260   do
1261     {
1262       if (extremes[d].slur_head_)
1263         ys[d] = extremes[d].slur_head_->relative_coordinate (common[Y_AXIS],
1264                                                               Y_AXIS);
1265       else
1266         ys[d] = extremes[d].neighbor_y_;
1267     }
1268   while (flip (&d) != LEFT);
1269
1270   bool has_beams
1271     = (extremes[LEFT].stem_ && Stem::get_beam (extremes[LEFT].stem_))
1272     || (extremes[RIGHT].stem_ && Stem::get_beam (extremes[RIGHT].stem_));
1273
1274   Real dy = ys[RIGHT] - ys[LEFT];
1275   for (int i = 0; i < scores->size (); i++)
1276     {
1277       Offset slur_dz = (*scores)[i].attachment_[RIGHT]
1278         - (*scores)[i].attachment_[LEFT];
1279       Real slur_dy = slur_dz[Y_AXIS];
1280       Real demerit = 0.0;
1281
1282       demerit += ((fabs (slur_dy / slur_dz[X_AXIS])
1283                    - score_param->max_slope_) >? 0)
1284         * score_param->max_slope_factor_;
1285
1286       /* 0.2: account for staffline offset. */
1287       Real max_dy = (fabs (dy) + 0.2);
1288       if (has_beams)
1289         max_dy += 1.0;
1290
1291       demerit += score_param->steeper_slope_factor_
1292         * ((fabs (slur_dy) -max_dy) >? 0);
1293
1294       demerit += ((fabs (slur_dy/slur_dz[X_AXIS])
1295                    - score_param->max_slope_) >? 0)
1296         * score_param->max_slope_factor_;
1297
1298       if (sign (dy) == 0
1299           && sign (slur_dy) != 0)
1300         demerit += score_param->non_horizontal_penalty_;
1301
1302       if (sign (dy)
1303           && sign (slur_dy)
1304           && sign (slur_dy) != sign (dy))
1305         demerit += has_beams
1306           ? score_param->same_slope_penalty_ / 10
1307           : score_param->same_slope_penalty_;
1308
1309 #if DEBUG_SLUR_QUANTING
1310       (*scores)[i].score_card_ += to_string ("S%.2f", d);
1311 #endif
1312       (*scores)[i].score_ += demerit;
1313     }
1314
1315
1316
1317 }
1318
1319
1320 Real
1321 fit_factor (Offset dz_unit, Offset dz_perp,
1322             Bezier curve, Direction d,  Array<Offset> const &avoid)
1323 {
1324   Real fit_factor = 0.0;
1325   Offset x0 = curve.control_[0];
1326   curve.translate (-x0);
1327   curve.rotate (-dz_unit.arg ());
1328   curve.scale (1, d);
1329
1330   Interval curve_xext;
1331   curve_xext.add_point (curve.control_[0][X_AXIS]);
1332   curve_xext.add_point (curve.control_[3][X_AXIS]);
1333
1334   for (int i = 0; i < avoid.size (); i++)
1335     {
1336       Offset z = (avoid[i] - x0) ;
1337       Offset p (dot_product (z, dz_unit),
1338                 d* dot_product (z, dz_perp));
1339       if (!curve_xext.contains (p[X_AXIS]))
1340         continue;
1341
1342       Real y = curve.get_other_coordinate (X_AXIS, p[X_AXIS]);
1343       if (y)
1344         {
1345           fit_factor = fit_factor >? (p[Y_AXIS] / y);
1346         }
1347     }
1348   return fit_factor;
1349 }
1350
1351
1352 Bezier
1353 get_bezier (Grob *me,
1354             Grob **common,
1355             Slur_score_parameters *score_param,
1356             Drul_array<Bound_info> extremes,
1357             Drul_array<Offset> attachments,
1358             Real r_0, Real h_inf
1359             )
1360 {
1361   Link_array<Grob> encompasses
1362     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "note-columns");
1363   Direction dir = get_grob_direction (me);
1364
1365   Array<Offset> avoid;
1366   for (int i = 0; i < encompasses.size(); i++)
1367     {
1368       if (extremes[LEFT].note_column_ == encompasses[i]
1369           ||extremes[RIGHT].note_column_ == encompasses[i])
1370         continue;
1371
1372       Encompass_info inf (get_encompass_info (me, encompasses[i], common));
1373
1374       Real y = dir*((dir * inf.head_) >? (dir *inf.stem_));
1375
1376       avoid.push (Offset (inf.x_,  y + dir * score_param->free_head_distance_));
1377     }
1378
1379   Link_array<Grob> extra_encompasses
1380     = Pointer_group_interface__extract_grobs (me, (Grob *)0, "encompass-objects");
1381   for (int i = 0;  i < extra_encompasses.size (); i++)
1382     if (Slur::has_interface (extra_encompasses[i]))
1383       {
1384         Grob * small_slur = extra_encompasses[i];
1385         Bezier b = Slur::get_curve (small_slur);
1386
1387         Offset z = b.curve_point (0.5);
1388         z += Offset (small_slur->relative_coordinate (common[X_AXIS], X_AXIS),
1389                      small_slur->relative_coordinate (common[Y_AXIS], Y_AXIS));
1390
1391         z[Y_AXIS] += dir * score_param->free_slur_distance_;
1392         avoid.push (z);
1393       }
1394
1395   Offset dz = attachments[RIGHT]- attachments[LEFT];;
1396   Offset dz_unit = dz;
1397   dz_unit *= 1 / dz.length();
1398   Offset dz_perp = dz_unit * Offset(0,1);
1399
1400   Real indent, height;
1401   get_slur_indent_height (&indent, &height, dz.length (), h_inf, r_0);
1402
1403   Real excentricity = robust_scm2double (me->get_property ("excentricity"), 0.0);
1404   Bezier curve;
1405
1406   Real x1 = (excentricity + indent);
1407   Real x2 = (excentricity - indent);
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
1414   Real ff = fit_factor (dz_unit, dz_perp, curve, dir, avoid);
1415   Real l = dz.length ();
1416
1417   /*
1418     This condition,
1419
1420     l^2 > 4h^2 +  3(i  1/3l)^2  - 1/3 l^2
1421
1422     is equivalent to:
1423
1424     |bez'(0)| < | bez'(.5)|
1425
1426     when (control2-control1) has the same direction as (control3 -
1427     control0).
1428
1429    */
1430   Real max_h = sqrt (sqr (l)/3 - .75 * sqr (indent + l / 3));
1431   height = height >? ((height * ff) <? max_h);
1432
1433   curve.control_[0] = attachments[LEFT];
1434   curve.control_[1] = attachments[LEFT] + dz_perp * height * dir + dz_unit * x1;
1435   curve.control_[2] = attachments[RIGHT] + dz_perp * height * dir + dz_unit * x2;
1436   curve.control_[3] = attachments[RIGHT];
1437
1438   return curve;
1439 }