]> git.donarmstrong.com Git - lilypond.git/blobdiff - lily/tie-formatting-problem.cc
Fix some bugs in the dynamic engraver and PostScript backend
[lilypond.git] / lily / tie-formatting-problem.cc
index c0c31a31acb13fbe557efb008c1901b72d234b00..f6d9675d648c423464fad05cc1247f77434b9981 100644 (file)
@@ -9,10 +9,12 @@
 
 #include "tie-formatting-problem.hh"
 
+#include "paper-column.hh"
 #include "bezier.hh" 
 #include "directional-element-interface.hh"
 #include "item.hh"
 #include "libc-extension.hh"
+#include "misc.hh"
 #include "note-head.hh"
 #include "rhythmic-head.hh"
 #include "spanner.hh" 
 #include "tie.hh"
 #include "warn.hh"
 
-/*
-   0 at threshold,  1 at 0, with 1/x falloff.
- */
-Real peak_around (Real epsilon,  Real threshold, Real x)
+
+void
+Tie_formatting_problem::print_ties_configuration (Ties_configuration const *ties)
 {
-  if (x < 0)
-    return 1.0;
-  return max (- epsilon * (x - threshold) / ((x + epsilon)  * threshold), 0.0);
+  for (vsize i = 0; i < ties->size (); i++)
+    {
+      char const *man_pos = (specifications_[i].has_manual_position_) ? "(M)" : "";
+      char const *man_dir = (specifications_[i].has_manual_dir_) ? "(M)" : "";
+      char const *dir = (ties->at (i).dir_ == UP) ? "up" : "dn";
+      
+      printf ("(P%d%s, %s%s) ", ties->at (i).position_, man_pos, dir, man_dir);
+    }
+  printf ("\n");
 }
 
 Interval
-Tie_formatting_problem::get_attachment (Real y) const
+Tie_formatting_problem::get_attachment (Real y, Drul_array<int> columns) const
 {
-  Interval attachments;
+  Interval attachments (0,0);
   Direction d = LEFT;
   do
     {
-      attachments[d] = skyline_height (chord_outlines_[d], y, -d);
+      Tuple2<int> key (columns[d], int (d));
+      Chord_outline_map::const_iterator i (chord_outlines_.find (key));
+      if (i == chord_outlines_.end ())
+       programming_error ("Can't find chord outline");
+      else
+       attachments[d] = skyline_height ((*i).second, y, -d);
     }
   while (flip (&d) != LEFT);
   
@@ -59,20 +71,22 @@ Tie_formatting_problem::~Tie_formatting_problem ()
 }
 
 void
-Tie_formatting_problem::set_chord_outline (Link_array<Item> bounds,
-                                          Direction d)
+Tie_formatting_problem::set_column_chord_outline (vector<Item*> bounds,
+                                                 Direction dir,
+                                                 int column_rank)
 {
   Real staff_space = Staff_symbol_referencer::staff_space (bounds[0]);
 
-  Array<Box> boxes;
+  vector<Box> boxes;
+  vector<Box> head_boxes;
 
   Grob *stem = 0;
-  for (int i = 0; i < bounds.size (); i++)
+  for (vsize i = 0; i < bounds.size (); i++)
     {
       Grob *head = bounds[i];
       if (!Note_head::has_interface (head))
        continue;
-      
+         
       if (!stem)
        stem = unsmob_grob (head->get_object ("stem"));
          
@@ -81,35 +95,48 @@ Tie_formatting_problem::set_chord_outline (Link_array<Item> bounds,
                  (p+1) * 0.5 * staff_space);
 
       Interval x = head->extent (x_refpoint_, X_AXIS);
-      boxes.push (Box (x, y));
+      head_boxes.push_back (Box (x, y));
+      boxes.push_back (Box (x, y));
 
       Grob *dots = Rhythmic_head::get_dots (head);
-      if (d == LEFT && dots)
+      if (dir == LEFT && dots)
        {
          Interval x = dots->extent (x_refpoint_, X_AXIS);
-         Interval y (-0.5, 0.5);
          int p = int (Staff_symbol_referencer::get_position (dots));
-         y.translate (p);
 
          dot_positions_.insert (p);
          dot_x_.unite (x);
+
+         Interval y (dots->extent (dots, Y_AXIS));
+         y.translate (p * staff_space * 0.5);
          
-         y *= staff_space * 0.5;
-         // boxes.push (Box (x, y));
+         boxes.push_back (Box (x, y));
        }
     }
 
-  chord_outlines_[d] = empty_skyline (-d);
-
+  Tuple2<int> key (column_rank, int (dir));
+  
+  chord_outlines_[key] = empty_skyline (-dir);
+      
   if (bounds[0]->break_status_dir ())
     {
-      Real x = robust_relative_extent (bounds[0],  x_refpoint_, X_AXIS)[-d];
-      chord_outlines_[d].elem_ref (0).height_ = x; 
+      Real x = robust_relative_extent (bounds[0],  x_refpoint_, X_AXIS)[-dir];
+      chord_outlines_[key].at (0).height_ = x; 
     }
-         
-  for (int i = 0; i < boxes.size (); i++)
-    insert_extent_into_skyline (&chord_outlines_[d]  ,
-                               boxes[i], Y_AXIS, -d);
+  else
+    {
+      Interval x;
+      for (vsize j = 0; j < head_boxes.size (); j++)
+       {
+         x.unite (head_boxes[j][X_AXIS]);
+       }
+      
+      chord_outlines_[key].at (0).height_ = x[dir];
+    }
+      
+  for (vsize i = 0; i < boxes.size (); i++)
+    insert_extent_into_skyline (&chord_outlines_[key]  ,
+                               boxes[i], Y_AXIS, -dir);
 
   if (stem
       && !Stem::is_invisible (stem))
@@ -124,16 +151,16 @@ Tie_formatting_problem::set_chord_outline (Link_array<Item> bounds,
       y.add_point (Stem::head_positions (stem)[-stemdir]
                   * staff_space * .5);
          
-      insert_extent_into_skyline (&chord_outlines_[d], Box (x,y), Y_AXIS, -d);
+      insert_extent_into_skyline (&chord_outlines_[key], Box (x,y), Y_AXIS, -dir);
 
-      stem_extents_[d].unite (Box (x,y));
+      stem_extents_[key].unite (Box (x,y));
 
-      if (d == LEFT)
+      if (dir == LEFT)
        {
          Box flag_box = Stem::get_translated_flag (stem).extent_box ();
          flag_box.translate( Offset (x[RIGHT], X_AXIS));
-         insert_extent_into_skyline (&chord_outlines_[d], flag_box,
-                                     Y_AXIS, -d);
+         insert_extent_into_skyline (&chord_outlines_[key], flag_box,
+                                     Y_AXIS, -dir);
        }
     }
   
@@ -142,29 +169,61 @@ Tie_formatting_problem::set_chord_outline (Link_array<Item> bounds,
     {
       Interval x;
       Interval y;
-      if (boxes.size())
+      if (head_boxes.size())
        {
-         Box b = boxes.boundary (updowndir, 0);
+         Box b = boundary (head_boxes, updowndir, 0);
          x = b[X_AXIS];
-         x[-d] =  b[X_AXIS].linear_combination (-d / 2);
+         x[-dir] =  b[X_AXIS].linear_combination (-dir / 2);
          y[-updowndir] = b[Y_AXIS][updowndir];
          y[updowndir] = updowndir * infinity_f;
        }
 
       if (!x.is_empty ())
-       insert_extent_into_skyline (&chord_outlines_[d],
+       insert_extent_into_skyline (&chord_outlines_[key],
                                    Box (x,y),
-                                   Y_AXIS, -d);
+                                   Y_AXIS, -dir);
     }
   while (flip (&updowndir) != DOWN);
+  
+  head_extents_[key].set_empty ();
+  for (vsize i = 0; i < head_boxes.size (); i++)
+    {
+      head_extents_[key].unite (head_boxes[i]);
+    }
 }
 
+void
+Tie_formatting_problem::set_chord_outline (vector<Item*> bounds,
+                                          Direction dir)
+
+{
+  vector<int> ranks;
+  for (vsize i = 0; i < bounds.size (); i++)
+    ranks.push_back (bounds[i]->get_column ()->get_rank ());
+
+  vector_sort (ranks, default_compare);
+  uniq (ranks);
+
+  for (vsize i = 0; i < ranks.size (); i++)
+    {
+      vector<Item*> col_items;
+      for (vsize j = 0; j < bounds.size (); j ++)
+       {
+         if (bounds[j]->get_column ()->get_rank () == ranks[i])
+           col_items.push_back (bounds[j]);
+       }
+
+      set_column_chord_outline (col_items, dir, ranks[i]);
+    }
+}
+  
+
 
 void
 Tie_formatting_problem::from_tie (Grob *tie)
 {
-  Link_array<Grob> ties;
-  ties.push (tie);
+  vector<Grob*> ties;
+  ties.push_back (tie);
   from_ties (ties);
 
   details_.from_grob (tie);
@@ -177,13 +236,13 @@ Tie_formatting_problem::common_x_refpoint () const
 }
 
 void
-Tie_formatting_problem::from_ties (Link_array<Grob> const &ties)
+Tie_formatting_problem::from_ties (vector<Grob*> const &ties)
 {
-  if (ties.is_empty ())
+  if (ties.empty ())
     return;
   
   x_refpoint_ = ties[0];
-  for (int i = 0; i < ties.size (); i++)
+  for (vsize i = 0; i < ties.size (); i++)
     {
       x_refpoint_ = dynamic_cast<Spanner*> (ties[i])->get_bound (LEFT)->common_refpoint (x_refpoint_, X_AXIS); 
       x_refpoint_ = dynamic_cast<Spanner*> (ties[i])->get_bound (RIGHT)->common_refpoint (x_refpoint_, X_AXIS); 
@@ -194,13 +253,13 @@ Tie_formatting_problem::from_ties (Link_array<Grob> const &ties)
   Direction d = LEFT;
   do
     {
-      Link_array<Item> bounds;
+      vector<Item*> bounds;
       
-      for (int i = 0; i < ties.size (); i++)
+      for (vsize i = 0; i < ties.size (); i++)
        {
          Item *it = dynamic_cast<Spanner*> (ties[i])->get_bound (d);
                                             
-         bounds.push (it);
+         bounds.push_back (it);
        }
       
       set_chord_outline (bounds, d);
@@ -208,7 +267,7 @@ Tie_formatting_problem::from_ties (Link_array<Grob> const &ties)
   while (flip (&d) != LEFT);
 
 
-  for (int i = 0; i < ties.size (); i++)
+  for (vsize i = 0; i < ties.size (); i++)
     {
       Tie_specification spec;
       
@@ -219,27 +278,35 @@ Tie_formatting_problem::from_ties (Link_array<Grob> const &ties)
        }
          
       spec.position_ = Tie::get_position (ties[i]);
-
+      if (scm_is_number (ties[i]->get_property ("staff-position")))
+       {
+         spec.manual_position_ = scm_to_double (ties[i]->get_property ("staff-position"));
+         spec.has_manual_position_ = true;
+         spec.position_ = int (my_round (spec.manual_position_));
+       }
+      
       do
        {
          spec.note_head_drul_[d] = Tie::head (ties[i], d);
+         spec.column_ranks_[d] =
+           dynamic_cast<Spanner*> (ties[i])->get_bound (d)->get_column ()->get_rank ();
        }
       while (flip (&d) != LEFT);
-      
-      specifications_.push (spec);
+      specifications_.push_back (spec);
     }
 }
 
 void
-Tie_formatting_problem::from_lv_ties (Link_array<Grob> const &lv_ties)
+Tie_formatting_problem::from_semi_ties (vector<Grob*> const &lv_ties, Direction head_dir)
 {
-  if (lv_ties.is_empty ())
-    return ;
+  if (lv_ties.empty ())
+    return;
   
   details_.from_grob (lv_ties[0]);
-  Link_array<Item> heads;
-  
-  for (int i = 0; i < lv_ties.size (); i++)
+  vector<Item*> heads;
+
+  int column_rank = -1;
+  for (vsize i = 0; i < lv_ties.size (); i++)
     {
       Tie_specification spec;
       Item *head = unsmob_item (lv_ties[i]->get_object ("note-head"));
@@ -251,32 +318,39 @@ Tie_formatting_problem::from_lv_ties (Link_array<Grob> const &lv_ties)
        {
          spec.position_ = int (Staff_symbol_referencer::get_position (head));
        }
+      
 
-      spec.note_head_drul_[LEFT] = head;
-      heads.push (head);
-      specifications_.push (spec);
+      spec.note_head_drul_[head_dir] = head;
+      column_rank = dynamic_cast<Item*> (head)->get_column ()->get_rank ();
+      spec.column_ranks_ = Drul_array<int> (column_rank, column_rank);
+      heads.push_back (head);
+      specifications_.push_back (spec);
     }
 
   x_refpoint_ = lv_ties [0];
-  for (int i = 0; i < lv_ties.size (); i++)
-    {
-      x_refpoint_ = lv_ties[i]->common_refpoint (x_refpoint_, X_AXIS); 
-    }
+  for (vsize i = 0; i < lv_ties.size (); i++)
+    x_refpoint_ = lv_ties[i]->common_refpoint (x_refpoint_, X_AXIS); 
+  for (vsize i = 0; i < heads.size (); i++)
+    x_refpoint_ = heads[i]->common_refpoint (x_refpoint_, X_AXIS); 
 
-  set_chord_outline (heads, LEFT);
+  set_chord_outline (heads, head_dir);
 
-  Real right_most = - infinity_f;   
+  Real extremal = head_dir * infinity_f;   
 
-  for (int i = 0; i < chord_outlines_[LEFT].size (); i++)
+  Tuple2<int> head_key (column_rank, head_dir);
+  Tuple2<int> open_key (column_rank, -head_dir);
+  
+  for (vsize i = 0; i < chord_outlines_[head_key].size (); i++)
     {
-      right_most = max (right_most, chord_outlines_[LEFT][i].height_);
+      extremal = head_dir * min (head_dir * extremal,
+                                head_dir * chord_outlines_[head_key][i].height_);
     }
 
   Skyline_entry right_entry;
   right_entry.width_.set_full ();
-  right_entry.height_ = right_most + 1.5;
+  right_entry.height_ = extremal - head_dir * 1.5;
   
-  chord_outlines_[RIGHT].push (right_entry);
+  chord_outlines_[open_key].push_back (right_entry);
 }
 
 
@@ -287,41 +361,63 @@ Tie_formatting_problem::get_tie_specification (int i) const
 }
 
 
+/*
+  Return configuration, create it if necessary. 
+*/
 Tie_configuration*
-Tie_formatting_problem::get_configuration (int pos, Direction dir
+Tie_formatting_problem::get_configuration (int pos, Direction dir, Drul_array<int> columns) const
 {
-  pair<int,int> key (pos, dir);
+  int key_components[] = {
+    pos, dir, columns[LEFT], columns[RIGHT]
+  };
+  Tuple<int,4> key (key_components);
+    
   Tie_configuration_map::const_iterator f = possibilities_.find (key);
-                                                             
   if (f != possibilities_.end ())
     {
       return (*f).second;
     }
 
   
-  Tie_configuration *conf = generate_configuration (pos,dir);
-  possibilities_[key] = conf;
+  Tie_configuration *conf = generate_configuration (pos, dir, columns);
+  ((Tie_formatting_problem*) this)->possibilities_[key] = conf;
   return conf;
 }
 
 Tie_configuration*
-Tie_formatting_problem::generate_configuration (int pos, Direction dir) const
+Tie_formatting_problem::generate_configuration (int pos, Direction dir,
+                                               Drul_array<int> columns) const
 {
   Tie_configuration *conf = new Tie_configuration;
   conf->position_ = pos;
   conf->dir_ = dir;
+  
+  conf->column_ranks_ = columns;
+  
   Real y = conf->position_ * 0.5 * details_.staff_space_;
 
+  bool y_tune = true;
   if (dot_positions_.find (pos) != dot_positions_.end ())
     {
-      conf->delta_y_ += 0.25 * details_.staff_space_;
+      conf->delta_y_ += dir * 0.25 * details_.staff_space_;
+      y_tune = false;
     }
   
-  conf->attachment_x_ = get_attachment (y + conf->delta_y_);
+  if (y_tune
+      && max (fabs (get_head_extent (columns[LEFT], LEFT, Y_AXIS)[dir] - y),
+             fabs (get_head_extent (columns[RIGHT], RIGHT, Y_AXIS)[dir] - y)) < 0.25
+      && !Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_, pos))
+    {
+      conf->delta_y_ =
+       (get_head_extent (columns[LEFT], LEFT, Y_AXIS)[dir] - y)
+       + dir * details_.outer_tie_vertical_gap_;
+    }
 
-  Real h =  conf->height (details_);
-  if (!conf->delta_y_)
+  if (y_tune)
     {
+      conf->attachment_x_ = get_attachment (y + conf->delta_y_, conf->column_ranks_);
+      Real h =  conf->height (details_);
+      
       /*
        TODO:
 
@@ -334,7 +430,7 @@ Tie_formatting_problem::generate_configuration (int pos, Direction dir) const
       if (h < details_.intra_space_threshold_ * 0.5 * details_.staff_space_)
        {
          if (!Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_, pos)
-             && fabs (pos) < 2 * Staff_symbol_referencer::staff_radius (details_.staff_symbol_referencer_))
+             && abs (pos) < 2 * Staff_symbol_referencer::staff_radius (details_.staff_symbol_referencer_))
            {
              conf->center_tie_vertically (details_);
            }
@@ -362,42 +458,81 @@ Tie_formatting_problem::generate_configuration (int pos, Direction dir) const
        }
     }
   
-  /*
-    we don't recompute attachment_x_ to take changed Y (through
-    delta_Y) into account. Doing would make ties go into small holes between heads, which
-    means we get collisions with neighboring heads.
-   */
+  conf->attachment_x_ = get_attachment (y + conf->delta_y_, conf->column_ranks_);
+  if (conf->height (details_) < details_.intra_space_threshold_ * 0.5 * details_.staff_space_)
+    {
+      /*
+       This is less sensible for long ties, since those are more
+       horizontal.
+      */
+      Interval close_by = get_attachment (y
+                                         + conf->delta_y_
+                                         + (dir * details_.intra_space_threshold_ * 0.25
+                                            * details_.staff_space_),
+                                         conf->column_ranks_);
+      
+      conf->attachment_x_.intersect (close_by);
+    }
+
   conf->attachment_x_.widen ( - details_.x_gap_);
 
   Direction d = LEFT;
   do
     {
       Real y = conf->position_ * details_.staff_space_ * 0.5 + conf->delta_y_;
-      if (stem_extents_[d][X_AXIS].is_empty ()
-         || !stem_extents_[d][Y_AXIS].contains (y))
+      if (get_stem_extent (conf->column_ranks_[d], d, X_AXIS).is_empty ()
+         || !get_stem_extent (conf->column_ranks_[d], d, Y_AXIS).contains (y))
        continue;
 
       conf->attachment_x_[d] =
-       d* min (d * conf->attachment_x_[d],
-               d * (stem_extents_[d][X_AXIS][-d] - d * details_.stem_gap_));
+       d * min (d * conf->attachment_x_[d],
+                d * (get_stem_extent (conf->column_ranks_[d], d, X_AXIS)[-d] - d * details_.stem_gap_));
     }
   while (flip (&d) != LEFT);
+  
   return conf;
 }
 
+Interval
+Tie_formatting_problem::get_head_extent (int col, Direction d, Axis a) const
+{
+  return (*head_extents_.find (Tuple2<int> (col, int (d)))).second[a];
+}
+
+Interval
+Tie_formatting_problem::get_stem_extent (int col, Direction d, Axis a) const
+{
+  return (*stem_extents_.find (Tuple2<int> (col, int (d)))).second[a];
+}
+
+/**
+   TIE_IDX and TIES_CONF are optional.
+ */
 Real
-Tie_formatting_problem::score_aptitude (Tie_configuration const &conf,
-                                       Tie_specification const &spec) const
+Tie_formatting_problem::score_aptitude (Tie_configuration *conf,
+                                       Tie_specification const &spec,
+                                       Ties_configuration *ties_conf, int tie_idx) const
 {
   Real penalty = 0.0;
-  Real curve_y = conf.position_ * details_.staff_space_ * 0.5 + conf.delta_y_;
+  Real curve_y = conf->position_ * details_.staff_space_ * 0.5 + conf->delta_y_;
   Real tie_y = spec.position_ * details_.staff_space_ * 0.5;
-  if (sign (curve_y - tie_y) != conf.dir_)
-    penalty += details_.wrong_direction_offset_penalty_;
-
-  penalty += details_.vertical_distance_penalty_factor_ * fabs (curve_y - tie_y);
-
+  if (sign (curve_y - tie_y) != conf->dir_)
+    {
+      Real p =  details_.wrong_direction_offset_penalty_;
+      if (ties_conf)
+       ties_conf->add_tie_score (p, tie_idx, "wrong dir");
+      else
+       penalty += p;
+    }
 
+  {
+    Real p = details_.vertical_distance_penalty_factor_ * fabs (curve_y - tie_y);
+    if (ties_conf)
+      ties_conf->add_tie_score (p, tie_idx, "vdist");
+    else
+      penalty += p; 
+  }
+  
   Direction d = LEFT;
   do
     {
@@ -405,47 +540,64 @@ Tie_formatting_problem::score_aptitude (Tie_configuration const &conf,
        continue;
       
       Interval head_x = spec.note_head_drul_[d]->extent (x_refpoint_, X_AXIS);
-      Real dist = head_x.distance (conf.attachment_x_[d]);
-      penalty += details_.horizontal_distance_penalty_factor_ * dist;
+      Real dist = head_x.distance (conf->attachment_x_[d]);
+
+      /*
+       TODO: flatten with log or sqrt.
+       */
+      Real p = details_.horizontal_distance_penalty_factor_ * dist;
+      if (ties_conf)
+       ties_conf->add_tie_score (p, tie_idx,
+                                 (d == LEFT) ? "lhdist" : "rhdist");
+      else
+       penalty += p;
     }
-  while  (flip (&d) != LEFT);
+  while (flip (&d) != LEFT);
 
   return penalty;
 }
 
-Real
-Tie_formatting_problem::score_configuration (Tie_configuration const &conf) const
+void
+Tie_formatting_problem::score_configuration (Tie_configuration *conf) const
 {
-  Real penalty = 0.0;
-  Real length = conf.attachment_x_.length ();
-  if (length < details_.min_length_)
-    penalty += details_.length_penalty_factor_ / max (0.01, length);
+  if (conf->scored_)
+    {
+      return ;
+    }
+  
+  Real length = conf->attachment_x_.length ();
 
-  Real tip_pos = conf.position_ + conf.delta_y_ / 0.5 * details_.staff_space_;
+  conf->add_score (details_.min_length_penalty_factor_
+                  * peak_around (0.33 * details_.min_length_, details_.min_length_, length),
+                  "minlength");
+  
+  Real tip_pos = conf->position_ + conf->delta_y_ / 0.5 * details_.staff_space_;
   Real tip_y = tip_pos * details_.staff_space_ * 0.5;
-  Real height =  conf.height (details_);
+  Real height =  conf->height (details_);
 
-  Real top_y = tip_y + conf.dir_ * height;
+  Real top_y = tip_y + conf->dir_ * height;
   Real top_pos = 2 * top_y / details_.staff_space_;
   Real round_top_pos = rint (top_pos);
   if (Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_,
                                                int (round_top_pos))
       && Staff_symbol_referencer::staff_radius (details_.staff_symbol_referencer_) > top_y)
     {
-      penalty +=
+      conf->add_score (
        details_.staff_line_collision_penalty_
        * peak_around (0.1 * details_.center_staff_line_clearance_,
                     details_.center_staff_line_clearance_,
-                    fabs (top_pos - round_top_pos));
+                      fabs (top_pos - round_top_pos)),
+       "line center");
     }
   
   if (Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_,
                                        int (rint (tip_pos))))
     {
-      penalty += details_.staff_line_collision_penalty_
-       * peak_around (0.1 * details_.tip_staff_line_clearance_,
-                      details_.tip_staff_line_clearance_,
-                      fabs (tip_pos - rint (tip_pos)));
+      conf->add_score (details_.staff_line_collision_penalty_
+                      * peak_around (0.1 * details_.tip_staff_line_clearance_,
+                                     details_.tip_staff_line_clearance_,
+                                     fabs (tip_pos - rint (tip_pos))),
+                      "tipline");
     }
 
   if (!dot_x_.is_empty ())
@@ -453,7 +605,7 @@ Tie_formatting_problem::score_configuration (Tie_configuration const &conf) cons
       /* use left edge? */
       Real x = dot_x_.center ();
       
-      Bezier b = conf.get_transformed_bezier (details_);
+      Bezier b = conf->get_transformed_bezier (details_);
       if (b.control_point_extent (X_AXIS).contains (x))
        {
          Real y = b.get_other_coordinate (X_AXIS, x);
@@ -462,41 +614,50 @@ Tie_formatting_problem::score_configuration (Tie_configuration const &conf) cons
               i != dot_positions_.end (); i ++)
            {
              int dot_pos = (*i);
-             penalty +=
-               details_.dot_collision_penalty_
+             conf->add_score (details_.dot_collision_penalty_
                * peak_around (.1 * details_.dot_collision_clearance_,
                               details_.dot_collision_clearance_,
-                              fabs (dot_pos * details_.staff_space_ * 0.5 - y)); 
+                              fabs (dot_pos * details_.staff_space_ * 0.5 - y)),
+                              "dot collision");
            }
        }
     }
-  
-  return penalty;
+
+  conf->scored_ = true;
 }
 
 Tie_configuration
 Tie_formatting_problem::find_optimal_tie_configuration (Tie_specification const &spec) const
 {
-  Link_array<Tie_configuration> confs;
+  vector<Tie_configuration*> confs;
 
   int pos = spec.position_;
   Direction dir = spec.manual_dir_;
 
-  int region_size = 3;
-  for (int i = 0; i < region_size; i ++)
+  for (int i = 0; i < details_.single_tie_region_size_; i ++)
     {
-      confs.push (generate_configuration (pos + i * dir, dir));
+      confs.push_back (generate_configuration (pos + i * dir, dir,
+                                              spec.column_ranks_));
+      
+      if (spec.has_manual_position_)
+       {
+         confs.back ()->delta_y_
+           = (spec.manual_position_ - spec.position_)
+           * 0.5 * details_.staff_space_;
+
+         break;
+       }
     }
 
-  Array<Real> scores;
+  vector<Real> scores;
 
   int best_idx = -1;
   Real best_score = 1e6;
-  for (int i = 0; i < confs.size (); i ++)
+  for (vsize i = 0; i < confs.size (); i ++)
     {
-      Real score = 0.0;
-      score += score_configuration (*confs[i]);
-      score += score_aptitude (*confs[i], spec);
+      score_configuration (confs[i]);
+      Real score = score_aptitude (confs[i], spec, 0, 0)
+       + confs[i]->score ();
 
       if (score < best_score)
        {
@@ -505,8 +666,13 @@ Tie_formatting_problem::find_optimal_tie_configuration (Tie_specification const
        }
     }
 
-  Tie_configuration best = *confs[best_idx];
-  for (int i = 0; i < confs.size (); i++)
+  if (best_idx < 0)
+    programming_error ("No best tie configuration found.");
+
+  Tie_configuration best
+    = (best_idx >= 0) ?  *confs[best_idx] : *confs[0];
+  
+  for (vsize i = 0; i < confs.size (); i++)
     delete confs[i];
 
   return best;
@@ -521,46 +687,55 @@ Tie_specification::Tie_specification ()
   manual_dir_ = CENTER;
   note_head_drul_[LEFT] =
     note_head_drul_[RIGHT] = 0;
+  column_ranks_[RIGHT] =
+    column_ranks_[LEFT] = 0;
 }
 
+int
+Tie_specification::column_span () const
+{
+  return column_ranks_[RIGHT] - column_ranks_[LEFT];
+}
 
-Real
-Tie_formatting_problem::score_ties_aptitude (Ties_configuration const &ties) const
+void
+Tie_formatting_problem::score_ties_aptitude (Ties_configuration *ties) const
 {
-  Real score = 0.0;
-  if  (ties.size () != specifications_.size ())
+  if  (ties->size () != specifications_.size ())
     {
       programming_error ("Huh? Mismatch between sizes.");
-      return infinity_f;
+      return;
     }
 
-  for (int i = 0; i < ties.size (); i++)
-    score += score_aptitude (ties[i], specifications_[i]);
-
-  return score;
+  for (vsize i = 0; i < ties->size (); i++)
+    score_aptitude (&ties->at (i), specifications_[i],
+                   ties, i);
 }
 
-Real
-Tie_formatting_problem::score_ties (Ties_configuration const &ties) const
+void
+Tie_formatting_problem::score_ties (Ties_configuration *ties) const
 {
-  return score_ties_configuration (ties)
-    + score_ties_aptitude (ties);
+  if (ties->scored_)
+    return;
+  
+  score_ties_configuration (ties);
+  score_ties_aptitude (ties);
+  ties->scored_ = true;
 }
 
-Real
-Tie_formatting_problem::score_ties_configuration (Ties_configuration const &ties) const
+void
+Tie_formatting_problem::score_ties_configuration (Ties_configuration *ties) const
 {
-  Real score = 0.0;
-  for (int i = 0; i < ties.size (); i++)
+  for (vsize i = 0; i < ties->size (); i++)
     {
-      score += score_configuration (ties[i]);
+      score_configuration (&ties->at (i));
+      ties->add_tie_score (ties->at (i).score (), i, "conf");
     }
-
+  
   Real last_edge = 0.0;
   Real last_center = 0.0;
-  for (int i = 0; i < ties.size (); i++)
+  for (vsize i = 0; i < ties->size (); i++)
     {
-      Bezier b (ties[i].get_transformed_bezier (details_));
+      Bezier b (ties->at (i).get_transformed_bezier (details_));
        
       Real center = b.curve_point (0.5)[Y_AXIS];
       Real edge = b.curve_point (0.0)[Y_AXIS];
@@ -568,40 +743,38 @@ Tie_formatting_problem::score_ties_configuration (Ties_configuration const &ties
       if (i)
        {
          if (edge <= last_edge)
-           score += details_.tie_column_monotonicity_penalty_;
+           ties->add_score (details_.tie_column_monotonicity_penalty_, "monoton edge");
          if (center <= last_center)
-           score += details_.tie_column_monotonicity_penalty_;
-
-         score +=
-           details_.tie_tie_collision_penalty_ *
-           peak_around (0.1 * details_.tie_tie_collision_distance_,
-                        details_.tie_tie_collision_distance_,
-                        fabs (center - last_center));
-         score +=
-           details_.tie_tie_collision_penalty_ *
-           peak_around (0.1 * details_.tie_tie_collision_distance_,
-                        details_.tie_tie_collision_distance_,
-                        fabs (edge - last_edge));
+           ties->add_score (details_.tie_column_monotonicity_penalty_, "monoton cent");
+
+         ties->add_score (details_.tie_tie_collision_penalty_ *
+                          peak_around (0.1 * details_.tie_tie_collision_distance_,
+                                       details_.tie_tie_collision_distance_,
+                                       fabs (center - last_center)),
+                          "tietie center");
+         ties->add_score (details_.tie_tie_collision_penalty_ *
+                          peak_around (0.1 * details_.tie_tie_collision_distance_,
+                                       details_.tie_tie_collision_distance_,
+                                       fabs (edge - last_edge)), "tietie edge");
        }
 
       last_edge = edge;
       last_center = center;
     }
 
-
-  score +=
-    details_.outer_tie_length_symmetry_penalty_factor_
-    * fabs (ties[0].attachment_x_.length () - ties.top().attachment_x_.length ());
-  
-  score +=
-    details_.outer_tie_vertical_distance_symmetry_penalty_factor_
-    * (fabs (specifications_[0].position_
-            - (ties[0].position_ * 0.5 * details_.staff_space_ + ties[0].delta_y_))
-       -
-       fabs (specifications_.top ().position_
-            - (ties.top().position_ * 0.5 * details_.staff_space_ + ties.top().delta_y_)));
+  ties->add_score (details_.outer_tie_length_symmetry_penalty_factor_
+                  * fabs (ties->at (0).attachment_x_.length () - ties->back ().attachment_x_.length ()),
+                  "length symm");
   
-  return score;
+  ties->add_score (details_.outer_tie_vertical_distance_symmetry_penalty_factor_
+                  * fabs (fabs (specifications_[0].position_ * 0.5 * details_.staff_space_
+                                - (ties->at (0).position_ * 0.5 * details_.staff_space_
+                                   + ties->at (0).delta_y_))
+                          -
+                          fabs (specifications_.back ().position_ * 0.5 * details_.staff_space_
+                                - (ties->back ().position_ * 0.5 * details_.staff_space_
+                                   + ties->back ().delta_y_))),
+                  "pos symmetry");
 }
 
 /*
@@ -612,16 +785,17 @@ Ties_configuration
 Tie_formatting_problem::generate_ties_configuration (Ties_configuration const &ties_config)
 {
   Ties_configuration copy;
-  for (int i = 0; i < ties_config.size (); i++)
+  for (vsize i = 0; i < ties_config.size (); i++)
     {
-      Tie_configuration * ptr = get_configuration (ties_config[i].position_, ties_config[i].dir_);
+      Tie_configuration * ptr = get_configuration (ties_config[i].position_, ties_config[i].dir_,
+                                                  ties_config[i].column_ranks_);
       if (specifications_[i].has_manual_position_)
        {
          ptr->delta_y_
            = (specifications_[i].manual_position_ - ties_config[i].position_)
            * 0.5 * details_.staff_space_;
        }
-      copy.push (*ptr);
+      copy.push_back (*ptr);
     }
   
   return copy;
@@ -631,7 +805,7 @@ Ties_configuration
 Tie_formatting_problem::generate_base_chord_configuration () 
 {
   Ties_configuration ties_config;
-  for (int i = 0;  i < specifications_.size (); i ++)
+  for (vsize i = 0;  i < specifications_.size (); i ++)
     {
       Tie_configuration conf;
       if (specifications_[i].has_manual_dir_)
@@ -646,11 +820,13 @@ Tie_formatting_problem::generate_base_chord_configuration ()
        {
          conf.position_ = specifications_[i].position_;
        }
-      ties_config.push (conf);
+
+      conf.column_ranks_ = specifications_[i].column_ranks_;
+      ties_config.push_back (conf);
     }
 
   set_ties_config_standard_directions (&ties_config);
-  for (int i = 0; i < ties_config.size (); i++)
+  for (vsize i = 0; i < ties_config.size (); i++)
     if (!specifications_[i].manual_position_)
       ties_config[i].position_ += ties_config[i].dir_;
 
@@ -660,65 +836,89 @@ Tie_formatting_problem::generate_base_chord_configuration ()
 }
 
 Ties_configuration
-Tie_formatting_problem::generate_optimal_chord_configuration ()
+Tie_formatting_problem::find_best_variation (Ties_configuration const &base,
+                                            vector<Tie_configuration_variation> vars)
 {
-  Ties_configuration base = generate_base_chord_configuration ();
-  Array<Tie_configuration_variation> vars = get_variations (base);
-
   Ties_configuration best = base;
-  Real best_score = score_ties (best);
-
+  
   /*
     This simply is 1-opt: we have K substitions, and we try applying
     exactly every one for each.
   */
-  for (int i = 0; i < vars.size (); i++)
+  for (vsize i = 0; i < vars.size (); i++)
     {
-      Ties_configuration variant = base;
+      Ties_configuration variant (base);
       variant[vars[i].index_] = *vars[i].suggestion_;
 
-      Real score = score_ties (variant);
-      if (score < best_score)
+      variant.reset_score ();
+      score_ties (&variant);
+      
+      if (variant.score () < best.score ())
        {
          best = variant;
-         best_score = score;
        }
     }
 
   return best;
 }
+  
+                                      
+
+Ties_configuration
+Tie_formatting_problem::generate_optimal_chord_configuration ()
+{
+  
+  Ties_configuration base = generate_base_chord_configuration ();
+  vector<Tie_configuration_variation> vars = generate_collision_variations (base);
+  
+  score_ties (&base);
+  Ties_configuration best = find_best_variation (base, vars);
+  vars = generate_extremal_tie_variations (best);
+  best = find_best_variation (best, vars);
+
+  return best;
+}
 
 void
 Tie_formatting_problem::set_ties_config_standard_directions (Ties_configuration *tie_configs)
 {
-  if (tie_configs->is_empty ())
+  if (tie_configs->empty ())
     return ;
   
-  if (!tie_configs->elem (0).dir_)
-    tie_configs->elem_ref (0).dir_ = DOWN;
-  if (!tie_configs->top().dir_)
-    tie_configs->top().dir_ = UP;
+  if (!tie_configs->at (0).dir_)
+    tie_configs->at (0).dir_ = DOWN;
+  if (!tie_configs->back ().dir_)
+    tie_configs->back ().dir_ = UP;
 
   /*
     Seconds
    */
-  for (int i = 1; i < tie_configs->size (); i++)
+  for (vsize i = 1; i < tie_configs->size (); i++)
     {
-      Real diff = (tie_configs->elem (i-1).position_
-                  - tie_configs->elem (i).position_);
-
-      if (fabs (diff) <= 1)
+      Real diff = (tie_configs->at (i).position_
+                  -tie_configs->at (i-1).position_);
+                  
+      Real span_diff 
+       = specifications_[i].column_span () - specifications_[i-1].column_span ();
+      if (span_diff && fabs (diff) <= 2)
        {
-         if (!tie_configs->elem (i-1).dir_)
-           tie_configs->elem_ref (i-1).dir_ = DOWN;
-         if (!tie_configs->elem (i).dir_)
-           tie_configs->elem_ref (i).dir_ = UP;
+         if  (span_diff > 0)
+           tie_configs->at (i).dir_ = UP;
+         else if (span_diff < 0)
+           tie_configs->at (i-1).dir_ = DOWN;  
+       }
+      else if (fabs (diff) <= 1)
+       {
+         if (!tie_configs->at (i-1).dir_)
+           tie_configs->at (i-1).dir_ = DOWN;
+         if (!tie_configs->at (i).dir_)
+           tie_configs->at (i).dir_ = UP;
        }
     }
 
-  for (int i = 1; i < tie_configs->size() - 1; i++)
+  for (vsize i = 1; i < tie_configs->size() - 1; i++)
     {
-      Tie_configuration &conf = tie_configs->elem_ref (i);
+      Tie_configuration &conf = tie_configs->at (i);
       if (conf.dir_)
        continue;
 
@@ -737,14 +937,39 @@ Tie_configuration_variation::Tie_configuration_variation ()
   suggestion_ = 0;
 }
 
-Array<Tie_configuration_variation>
-Tie_formatting_problem::get_variations (Ties_configuration const &ties) 
+vector<Tie_configuration_variation>
+Tie_formatting_problem::generate_extremal_tie_variations (Ties_configuration const &ties) const
+{
+  vector<Tie_configuration_variation> vars;
+  Direction d = DOWN;
+  do
+    {
+      if (boundary (ties, d, 0).dir_ == d
+         && !boundary (specifications_, d, 0).has_manual_position_)
+       for (int i = 1; i <= details_.multi_tie_region_size_; i++)
+         {
+           Tie_configuration_variation var;
+           var.index_ = (d == DOWN) ? 0 : ties.size () - 1;
+           var.suggestion_ = get_configuration (boundary (ties, d, 0).position_
+                                                + d * i, d,
+                                                boundary (ties, d, 0).column_ranks_);
+           vars.push_back (var);
+         }
+    }
+  while (flip (&d) !=  DOWN);
+
+  return vars;
+}
+
+
+vector<Tie_configuration_variation>
+Tie_formatting_problem::generate_collision_variations (Ties_configuration const &ties) const
 {
   Real center_distance_tolerance = 0.25;
   
-  Array<Tie_configuration_variation> vars;
+  vector<Tie_configuration_variation> vars;
   Real last_center = 0.0;
-  for (int i = 0; i < ties.size (); i++)
+  for (vsize i = 0; i < ties.size (); i++)
     {
       Bezier b (ties[i].get_transformed_bezier (details_));
        
@@ -760,9 +985,12 @@ Tie_formatting_problem::get_variations (Ties_configuration const &ties)
                  var.index_ = i;
                  var.suggestion_ = get_configuration (specifications_[i].position_
                                                       - ties[i].dir_,
-                                                      -ties[i].dir_);
+                                                      - ties[i].dir_,
+
+                                                      ties[i].column_ranks_
+                                                      );
 
-                 vars.push (var);
+                 vars.push_back (var);
                }
 
              if (!specifications_[i-1].has_manual_dir_)
@@ -771,30 +999,48 @@ Tie_formatting_problem::get_variations (Ties_configuration const &ties)
                  var.index_ = i-1;
                  var.suggestion_ = get_configuration (specifications_[i-1].position_
                                                       - ties[i-1].dir_,
-                                                      - ties[i-1].dir_);
+                                                      - ties[i-1].dir_,
+                                                      specifications_[i-1].column_ranks_);
+
+                 vars.push_back (var);
+               }
 
-                 vars.push (var);
+             if (i == 1 && !specifications_[i-1].has_manual_position_
+                 && ties[i-1].dir_ == DOWN)
+               {
+                 Tie_configuration_variation var;
+                 var.index_ = i-1;
+                 var.suggestion_ = get_configuration (specifications_[i-1].position_ - 1, DOWN,
+                                                      specifications_[i-1].column_ranks_);
+                 vars.push_back (var);
+               }
+             if (i == ties.size() && !specifications_[i].has_manual_position_
+                 && ties[i].dir_ == UP)
+               {
+                 Tie_configuration_variation var;
+                 var.index_ = i;
+                 var.suggestion_ = get_configuration (specifications_[i].position_
+                                                      + 1, UP,
+                                                      specifications_[i].column_ranks_);
+                 vars.push_back (var);
                }
            }
+         else if (dot_positions_.find (ties[i].position_) != dot_positions_.end ()
+                  && !specifications_[i].has_manual_position_)
+           {
+             Tie_configuration_variation var;
+             var.index_ = i;
+             var.suggestion_ = get_configuration (ties[i].position_  + ties[i].dir_,
+                                                  ties[i].dir_,
+                                                  ties[i].column_ranks_);
+             vars.push_back (var);
+           }
+         
        }
 
       last_center = center;
     }
 
-  /*  TODO: switch off? */
-  Direction d = DOWN;
-  do
-    {
-      if (ties.boundary (d, 0).dir_ == d)
-       {
-         Tie_configuration_variation var;
-         var.index_ = (d == DOWN) ? 0 : ties.size () - 1;
-         var.suggestion_ = get_configuration (ties.boundary (d, 0).position_ + d,
-                                              d);
-         vars.push (var);
-       }
-    }
-  while (flip (&d) !=  DOWN);
 
   return vars;
 }
@@ -802,25 +1048,25 @@ Tie_formatting_problem::get_variations (Ties_configuration const &ties)
 void
 Tie_formatting_problem::set_manual_tie_configuration (SCM manual_configs)
 {
-  int k = 0;
+  vsize k = 0;
   for (SCM s = manual_configs;
-       scm_is_pair (s) && k < specifications_.size(); s = scm_cdr (s))
+       scm_is_pair (s) && k < specifications_.size (); s = scm_cdr (s))
     {
       SCM entry = scm_car (s);
       if (scm_is_pair (entry))
        {
          Tie_specification &spec = specifications_[k];
 
-         if (scm_is_number (scm_cdr (entry)))
-           {
-             spec.has_manual_dir_ = true;
-             spec.manual_dir_ = Direction (scm_to_int (scm_cdr (entry)));
-           }
          if (scm_is_number (scm_car (entry)))
            {
              spec.has_manual_position_ = true;
              spec.manual_position_ = scm_to_double (scm_car (entry));
            }
+         if (scm_is_number (scm_cdr (entry)))
+           {
+             spec.has_manual_dir_ = true;
+             spec.manual_dir_ = Direction (scm_to_int (scm_cdr (entry)));
+           }
        }         
       k ++;
     }