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