]> git.donarmstrong.com Git - lilypond.git/blobdiff - lily/tie-formatting-problem.cc
Run grand-replace (issue 3765)
[lilypond.git] / lily / tie-formatting-problem.cc
index f30a197d470de08b27ca804a5a25311a62851d0f..b15536a863a1bd296054fc5fae75ca7ef75ff635 100644 (file)
 /*
-  tie-formatting-problem.cc -- implement Tie_formatting_problem6
+  This file is part of LilyPond, the GNU music typesetter.
 
-  source file of the GNU LilyPond music typesetter
+  Copyright (C) 2005--2014 Han-Wen Nienhuys <hanwen@xs4all.nl>
 
-  (c) 2005 Han-Wen Nienhuys <hanwen@xs4all.nl>
 
+  LilyPond is free software: you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation, either version 3 of the License, or
+  (at your option) any later version.
+
+  LilyPond is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with LilyPond.  If not, see <http://www.gnu.org/licenses/>.
 */
 
+#include <cstdio>
 #include "tie-formatting-problem.hh"
 
+#include "axis-group-interface.hh"
+#include "paper-column.hh"
+#include "bezier.hh"
 #include "directional-element-interface.hh"
+#include "libc-extension.hh"
+#include "misc.hh"
+#include "note-head.hh"
+#include "rhythmic-head.hh"
+#include "spanner.hh"
 #include "staff-symbol-referencer.hh"
+#include "stem.hh"
+#include "tie-configuration.hh"
 #include "tie.hh"
+#include "warn.hh"
+#include "pointer-group-interface.hh"
+#include "output-def.hh"
 
-#include "item.hh"
-#include "spanner.hh" 
+void
+Tie_formatting_problem::print_ties_configuration (Ties_configuration const *ties)
+{
+  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";
 
-#include "stem.hh"
-#include "note-head.hh"
-#include "rhythmic-head.hh"
+      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;
-  Direction d = LEFT;
-  do
+  Interval attachments (0, 0);
+
+  for (LEFT_and_RIGHT (d))
     {
-      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 ("Cannot find chord outline");
+      else
+        attachments[d] = i->second.height (y);
     }
-  while (flip (&d) != LEFT);
-  
+
   return attachments;
 }
 
-
-
-
-Tie_formatting_problem::Tie_formatting_problem()
+Tie_formatting_problem::Tie_formatting_problem ()
 {
   x_refpoint_ = 0;
-  
+  y_refpoint_ = 0;
+  use_horizontal_spacing_ = true;
+}
+
+Tie_formatting_problem::~Tie_formatting_problem ()
+{
+  for (Tie_configuration_map::const_iterator i (possibilities_.begin ());
+       i != possibilities_.end (); i++)
+    delete (*i).second;
 }
 
 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;
-      
+        continue;
+
       if (!stem)
-       stem = unsmob_grob (head->get_object ("stem"));
-         
+        stem = unsmob_grob (head->get_object ("stem"));
+
       Real p = Staff_symbol_referencer::get_position (head);
-      Interval y ((p-1) * 0.5 * staff_space,
-                 (p+1) * 0.5 * staff_space);
+      Interval y ((p - 1) * 0.5 * staff_space,
+                  (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)
-       {
-         Interval x = dots->extent (x_refpoint_, X_AXIS);
-         Interval y (-0.5, 0.5);
-         y.translate (Staff_symbol_referencer::get_position (dots));
-         y *= staff_space * 0.5;
-         
-         boxes.push (Box (x, y));
-       }
-    }
+      if (dir == LEFT && dots)
+        {
+          Interval x = dots->extent (x_refpoint_, X_AXIS);
+          int p = int (Staff_symbol_referencer::get_position (dots));
 
-  chord_outlines_[d] = empty_skyline (-d);
+          /*
+            TODO: shouldn't this use column-rank dependent key?
+          */
+          dot_positions_.insert (p);
+          dot_x_.unite (x);
 
-  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; 
+          Interval y (dots->extent (dots, Y_AXIS));
+          y.translate (p * staff_space * 0.5);
+
+          boxes.push_back (Box (x, y));
+        }
     }
-         
-  for (int i = 0; i < boxes.size (); i++)
-    insert_extent_into_skyline (&chord_outlines_[d]  ,
-                               boxes[i], Y_AXIS, -d);
 
-  if (stem
-      && !Stem::is_invisible (stem))
+  Tuple2<int> key (column_rank, int (dir));
+
+  if (stem)
     {
-      Interval x;
-      x.add_point (stem->relative_coordinate (x_refpoint_, X_AXIS));
-      x.widen (staff_space / 20); // ugh.
-      Interval y;
-      y.add_point (Stem::stem_end_position (stem) * staff_space * .5);
+      if (Stem::is_normal_stem (stem))
+        {
+          Interval x;
+          x.add_point (stem->relative_coordinate (x_refpoint_, X_AXIS));
+          x.widen (staff_space / 20); // ugh.
+          Interval y;
+
+          Real stem_end_position = 0.0;
+          if (Stem::is_cross_staff (stem))
+            stem_end_position = get_grob_direction (stem) * infinity_f;
+          else
+            {
+              if (use_horizontal_spacing_ || !Stem::get_beam (stem))
+                stem_end_position = stem->extent (stem, Y_AXIS)[get_grob_direction (stem)];
+              else
+                // May want to change this to the stem's pure height...
+                stem_end_position = Stem::note_head_positions (stem)[get_grob_direction (stem)]
+                                    * staff_space * .5;
+            }
+
+          y.add_point (stem_end_position);
+
+          Direction stemdir = get_grob_direction (stem);
+          y.add_point (Stem::head_positions (stem)[-stemdir]
+                       * staff_space * .5);
+
+          /*
+            add extents of stem.
+          */
+          boxes.push_back (Box (x, y));
+
+          stem_extents_[key].unite (Box (x, y));
+
+          if (dir == LEFT)
+            {
+              Grob *flag = Stem::flag (stem);
+              if (flag)
+                {
+                  Grob *commony = stem->common_refpoint (flag, Y_AXIS);
+                  boxes.push_back (Box (flag->extent (x_refpoint_, X_AXIS),
+                                        flag->extent (commony, Y_AXIS)));
+                }
+            }
+        }
+      else
+        {
+          Grob *head = Stem::support_head (stem);
+
+          /*
+            In case of invisible stem, don't pass x-center of heads.
+          */
+          Real x_center = head->extent (x_refpoint_, X_AXIS).center ();
+          Interval x_ext;
+          x_ext[-dir] = x_center;
+          x_ext[dir] = infinity_f * dir;
+          Interval y_ext;
+          for (vsize j = 0; j < head_boxes.size (); j++)
+            y_ext.unite (head_boxes[j][Y_AXIS]);
+
+          boxes.push_back (Box (x_ext, y_ext));
+        }
 
-      Direction stemdir = get_grob_direction (stem);
-      y.add_point (Stem::head_positions (stem)[-stemdir]
-                  * staff_space * .5);
-         
-      insert_extent_into_skyline (&chord_outlines_[d], Box (x,y), Y_AXIS, -d);
+      extract_grob_set (stem, "note-heads", heads);
+      for (vsize i = 0; i < heads.size (); i++)
+        {
+          if (find (bounds.begin (), bounds.end (), dynamic_cast<Item *> (heads[i])) == bounds.end ())
+            {
+              /*
+                other untied notes in the same chord.
+              */
 
+              Interval y = Staff_symbol_referencer::extent_in_staff (heads[i]);
+              Interval x = heads[i]->extent (x_refpoint_, X_AXIS);
+              boxes.push_back (Box (x, y));
+            }
 
+          Grob *acc = unsmob_grob (heads[i]->get_object ("accidental-grob"));
+          if (acc)
+            acc->get_property ("stencil"); /* trigger tie-related suicide */
+
+          if (acc && acc->is_live () && dir == RIGHT)
+            {
+              boxes.push_back (Box (acc->extent (x_refpoint_, X_AXIS),
+                                    Staff_symbol_referencer::extent_in_staff (acc)));
+            }
+
+          head_positions_[column_rank].add_point (int (Staff_symbol_referencer::get_position (heads[i])));
+        }
 
-      if (d == 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);
-       }
     }
-  
-  Direction updowndir = DOWN;
-  do
+
+  for (DOWN_and_UP (updowndir))
     {
-      Interval x ;
+      Interval x;
       Interval y;
-      if (boxes.size())
-       {
-         Box b = boxes.boundary (updowndir, 0);
-         x = b[X_AXIS];
-         x[-d] =  b[X_AXIS].linear_combination (-d / 2);
-         y[-updowndir] = b[Y_AXIS][updowndir];
-         y[updowndir] = updowndir * infinity_f;
-       }
+      if (head_boxes.size ())
+        {
+          Box b = boundary (head_boxes, updowndir, 0);
+          x = b[X_AXIS];
+          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],
-                                   Box (x,y),
-                                   Y_AXIS, -d);
+        boxes.push_back (Box (x, y));
     }
-  while (flip (&updowndir) != DOWN);
 
-  for (int i = 0; i < bounds.size (); i++)
+  chord_outlines_[key] = Skyline (boxes, Y_AXIS, -dir).padded (details_.skyline_padding_);
+  if (bounds[0]->break_status_dir ())
     {
-      if (!Note_head::has_interface (bounds[i]))
-       continue;
+      Interval iv (Axis_group_interface::staff_extent (bounds[0], x_refpoint_, X_AXIS, y_refpoint_, Y_AXIS));
+      if (iv.is_empty ())
+        iv.add_point (bounds[0]->relative_coordinate (x_refpoint_, X_AXIS));
 
-      
-      Grob *dots = unsmob_grob (bounds[i]->get_object ("dot"));
-      if (dots && d == LEFT)
-       {
-         Interval x = dots->extent (x_refpoint_, X_AXIS);
-         Real p = Staff_symbol_referencer::get_position (dots);
-             
-         Interval y (-1,1);
-         y *= (staff_space /4);
-         y.translate (p * staff_space * .5);
+      chord_outlines_[key].set_minimum_height (iv[-dir]);
+    }
+  else
+    {
+      Interval x;
+      for (vsize j = 0; j < head_boxes.size (); j++)
+        {
+          x.unite (head_boxes[j][X_AXIS]);
+        }
 
-         insert_extent_into_skyline (&chord_outlines_[d],
-                                     Box (x,y), Y_AXIS, -d);
-       }
+      chord_outlines_[key].set_minimum_height (x[dir]);
+    }
+
+  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, less<int> ());
+  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);
 }
 
 Grob *
@@ -178,66 +312,920 @@ 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++)
-    {
-      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); 
-    }
-  
-  Direction d = LEFT;
-  do
-    {
-      Link_array<Item> bounds;
-      
-      for (int i = 0; i < ties.size (); i++)
-       {
-         Item *it = dynamic_cast<Spanner*> (ties[i])->get_bound (d);
-                                            
-         bounds.push (it);
-       }
-      
+  y_refpoint_ = ties[0];
+  for (vsize i = 0; i < ties.size (); i++)
+    {
+      Spanner *tie = dynamic_cast<Spanner *> (ties[i]);
+      Item *l = tie->get_bound (LEFT);
+      Item *r = tie->get_bound (RIGHT);
+
+      x_refpoint_ = l->common_refpoint (x_refpoint_, X_AXIS);
+      x_refpoint_ = r->common_refpoint (x_refpoint_, X_AXIS);
+
+      if (!l->break_status_dir ())
+        y_refpoint_ = l->common_refpoint (y_refpoint_, Y_AXIS);
+      if (!r->break_status_dir ())
+        y_refpoint_ = r->common_refpoint (y_refpoint_, Y_AXIS);
+    }
+
+  details_.from_grob (ties[0]);
+
+  for (LEFT_and_RIGHT (d))
+    {
+      vector<Item *> bounds;
+
+      for (vsize i = 0; i < ties.size (); i++)
+        {
+          Item *it = dynamic_cast<Spanner *> (ties[i])->get_bound (d);
+          if (it->break_status_dir ())
+            it = it->get_column ();
+
+          bounds.push_back (it);
+        }
+
       set_chord_outline (bounds, d);
     }
-  while (flip (&d) != LEFT);
+
+  for (vsize i = 0; i < ties.size (); i++)
+    {
+      Tie_specification spec;
+      spec.from_grob (ties[i]);
+
+      for (LEFT_and_RIGHT (d))
+        {
+          spec.note_head_drul_[d] = Tie::head (ties[i], d);
+          spec.column_ranks_[d] = Tie::get_column_rank (ties[i], d);
+        }
+      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 &semi_ties, Direction head_dir)
+{
+  if (semi_ties.empty ())
+    return;
+
+  use_horizontal_spacing_ = false;
+  details_.from_grob (semi_ties[0]);
+  vector<Item *> heads;
+
+  int column_rank = -1;
+  for (vsize i = 0; i < semi_ties.size (); i++)
+    {
+      Tie_specification spec;
+      Item *head = unsmob_item (semi_ties[i]->get_object ("note-head"));
+
+      if (!head)
+        programming_error ("LV tie without head?!");
+
+      if (head)
+        {
+          spec.position_ = int (Staff_symbol_referencer::get_position (head));
+        }
+
+      spec.from_grob (semi_ties[i]);
+
+      spec.note_head_drul_[head_dir] = head;
+      column_rank = Tie::get_column_rank (semi_ties[i], head_dir);
+      spec.column_ranks_ = Drul_array<int> (column_rank, column_rank);
+      heads.push_back (head);
+      specifications_.push_back (spec);
+    }
+
+  x_refpoint_ = semi_ties[0];
+  y_refpoint_ = semi_ties[0];
+
+  for (vsize i = 0; i < semi_ties.size (); i++)
+    {
+      x_refpoint_ = semi_ties[i]->common_refpoint (x_refpoint_, X_AXIS);
+      y_refpoint_ = semi_ties[i]->common_refpoint (y_refpoint_, Y_AXIS);
+    }
+  for (vsize i = 0; i < heads.size (); i++)
+    {
+      x_refpoint_ = heads[i]->common_refpoint (x_refpoint_, X_AXIS);
+      y_refpoint_ = heads[i]->common_refpoint (y_refpoint_, Y_AXIS);
+    }
+
+  set_chord_outline (heads, head_dir);
+
+  Tuple2<int> head_key (column_rank, head_dir);
+  Tuple2<int> open_key (column_rank, -head_dir);
+  Real extremal = chord_outlines_[head_key].max_height ();
+
+  chord_outlines_[open_key] = Skyline (head_dir);
+  chord_outlines_[open_key].set_minimum_height (extremal - head_dir * 1.5);
+}
+
+Tie_specification
+Tie_formatting_problem::get_tie_specification (int i) const
+{
+  return specifications_[i];
+}
+
+/*
+  Return configuration, create it if necessary.
+*/
+Tie_configuration *
+Tie_formatting_problem::get_configuration (int pos, Direction dir, Drul_array<int> columns,
+                                           bool tune_dy) const
 {
-  if (lv_ties.is_empty ())
-    return ;
-  
-  Link_array<Item> heads;
-  for (int i = 0; i < lv_ties.size (); i++)
+  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, columns, tune_dy);
+  ((Tie_formatting_problem *) this)->possibilities_[key] = conf;
+  return conf;
+}
+
+Tie_configuration *
+Tie_formatting_problem::generate_configuration (int pos, Direction dir,
+                                                Drul_array<int> columns, bool y_tune) 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_;
+
+  if (dot_positions_.find (pos) != dot_positions_.end ())
+    {
+      conf->delta_y_ += dir * 0.25 * details_.staff_space_;
+      y_tune = false;
+    }
+
+  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))
     {
-      Item *head = unsmob_item (lv_ties[i]->get_object ("note-head"));
-      heads.push (head);
+      conf->delta_y_
+        = (get_head_extent (columns[LEFT], LEFT, Y_AXIS)[dir] - y)
+          + dir * details_.outer_tie_vertical_gap_;
     }
 
-  x_refpoint_ = lv_ties [0];
-  for (int i = 0; i < lv_ties.size (); i++)
+  if (y_tune)
     {
-      x_refpoint_ = lv_ties[i]->common_refpoint (x_refpoint_, X_AXIS); 
+      conf->attachment_x_ = get_attachment (y + conf->delta_y_, conf->column_ranks_);
+      Real h = conf->height (details_);
+
+      /*
+        TODO:
+
+        - should make sliding criterion, should flatten ties if
+
+        - they're just the wrong (ie. touching line at top & bottom)
+        size.
+
+       */
+      Interval staff_span
+        = Staff_symbol_referencer::staff_span (details_.staff_symbol_referencer_);
+      staff_span.widen (-1);
+      bool const within_staff = staff_span.contains (pos);
+      if (head_positions_slice (columns[LEFT]).contains (pos)
+          || head_positions_slice (columns[RIGHT]).contains (pos)
+          || within_staff)
+        {
+          if (h < details_.intra_space_threshold_ * 0.5 * details_.staff_space_)
+            {
+              if (Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_, pos))
+                {
+                  conf->delta_y_ += dir *
+                                    details_.tip_staff_line_clearance_ * 0.5 * details_.staff_space_;
+                }
+              else if (within_staff)
+                {
+                  conf->center_tie_vertically (details_);
+                }
+            }
+          else
+            {
+              Real top_y = y + conf->delta_y_ + conf->dir_ * h;
+              Real top_pos = top_y / (0.5 * details_.staff_space_);
+              int round_pos = int (my_round (top_pos));
+
+              /* TODO: should use other variable? */
+              Real clearance = details_.center_staff_line_clearance_;
+              if (fabs (top_pos - round_pos) < clearance
+                  && Staff_symbol_referencer::on_staff_line (details_.staff_symbol_referencer_,
+                                                             round_pos))
+                {
+                  Real new_y = (round_pos + clearance * conf->dir_) * 0.5 * details_.staff_space_;
+                  conf->delta_y_ = (new_y - top_y);
+                }
+            }
+        }
+    }
+  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_);
+
+  if (conf->column_span_length ())
+    {
+      /*
+        avoid the stems that we attach to as well. We don't do this
+        for semities (span length = 0)
+
+        It would be better to check D against HEAD-DIRECTION if
+        applicable.
+      */
+      for (LEFT_and_RIGHT (d))
+        {
+          Real y = conf->position_ * details_.staff_space_ * 0.5 + conf->delta_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 * (get_stem_extent (conf->column_ranks_[d], d, X_AXIS)[-d] - d * details_.stem_gap_));
+        }
+    }
+  return conf;
+}
+
+Interval
+Tie_formatting_problem::get_head_extent (int col, Direction d, Axis a) const
+{
+  Column_extent_map::const_iterator i = head_extents_.find (Tuple2<int> (col, int (d)));
+  if (i != head_extents_.end ())
+    return (*i).second[a];
+  else
+    return Interval ();
+}
+
+Interval
+Tie_formatting_problem::get_stem_extent (int col, Direction d, Axis a) const
+{
+  Column_extent_map::const_iterator i = stem_extents_.find (Tuple2<int> (col, int (d)));
+  if (i != stem_extents_.end ())
+    return (*i).second[a];
+  else
+    return Interval ();
+}
+
+/**
+   TIE_IDX and TIES_CONF are optional.
+ */
+Real
+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 tie_y = spec.position_ * details_.staff_space_ * 0.5;
+  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;
     }
 
-  set_chord_outline (heads, LEFT);
+  {
+    Real relevant_dist = max (fabs (curve_y - tie_y) - 0.5, 0.0);
+    Real p = details_.vertical_distance_penalty_factor_ * convex_amplifier (1.0, 0.9, relevant_dist);
+    if (ties_conf)
+      ties_conf->add_tie_score (p, tie_idx, "vdist");
+    else
+      penalty += p;
+  }
+
+  for (LEFT_and_RIGHT (d))
+    {
+      if (!spec.note_head_drul_[d])
+        continue;
 
-  Real right_most = - infinity_f;   
+      Interval head_x = spec.note_head_drul_[d]->extent (x_refpoint_, X_AXIS);
+      Real dist = head_x.distance (conf->attachment_x_[d]);
 
-  for (int i = 0; i < chord_outlines_[LEFT].size (); i++)
+      /*
+        TODO: flatten with log or sqrt.
+       */
+      Real p = details_.horizontal_distance_penalty_factor_
+               * convex_amplifier (1.25, 1.0, dist);
+      if (ties_conf)
+        ties_conf->add_tie_score (p, tie_idx,
+                                  (d == LEFT) ? "lhdist" : "rhdist");
+      else
+        penalty += p;
+
+    }
+
+  if (ties_conf
+      && ties_conf->size () == 1)
     {
-      right_most = max (right_most, chord_outlines_[LEFT][i].height_);
+      Drul_array<Grob *> stems (0, 0);
+      for (LEFT_and_RIGHT (d))
+        {
+          if (!spec.note_head_drul_[d])
+            continue;
+
+          Grob *stem = unsmob_grob (spec.note_head_drul_[d]->get_object ("stem"));
+          if (stem
+              && Stem::is_normal_stem (stem))
+            stems[d] = stem;
+        }
+
+      bool tie_stem_dir_ok = true;
+      bool tie_position_dir_ok = true;
+      if (stems[LEFT] && !stems[RIGHT])
+        tie_stem_dir_ok = conf->dir_ != get_grob_direction (stems[LEFT]);
+      else if (!stems[LEFT] && stems[RIGHT])
+        tie_stem_dir_ok = conf->dir_ != get_grob_direction (stems[RIGHT]);
+      else if (stems[LEFT] && stems[RIGHT]
+               && get_grob_direction (stems[LEFT]) == get_grob_direction (stems[RIGHT]))
+        tie_stem_dir_ok = conf->dir_ != get_grob_direction (stems[LEFT]);
+      else if (spec.position_)
+        tie_position_dir_ok = conf->dir_ == sign (spec.position_);
+
+      if (!tie_stem_dir_ok)
+        ties_conf->add_score (details_.same_dir_as_stem_penalty_, "tie/stem dir");
+      if (!tie_position_dir_ok)
+        ties_conf->add_score (details_.same_dir_as_stem_penalty_, "tie/pos dir");
     }
 
-  Skyline_entry right_entry;
-  right_entry.width_.set_full ();
-  right_entry.height_ = right_most + 1.5;
-  
-  chord_outlines_[RIGHT].push (right_entry);
+  return penalty;
+}
+
+Slice
+Tie_formatting_problem::head_positions_slice (int rank) const
+{
+  Position_extent_map::const_iterator i (head_positions_.find (rank));
+  if (i != head_positions_.end ())
+    {
+      return (*i).second;
+    }
+  Slice empty;
+  return empty;
+}
+
+/*
+  Score a configuration, ie. how well these ties looks without regard
+  to the note heads that they should connect to.
+ */
+void
+Tie_formatting_problem::score_configuration (Tie_configuration *conf) const
+{
+  if (conf->scored_)
+    {
+      return;
+    }
+
+  Real length = conf->attachment_x_.length ();
+
+  Real length_penalty
+    = peak_around (0.33 * details_.min_length_, details_.min_length_, length);
+  conf->add_score (details_.min_length_penalty_factor_
+                   * length_penalty, "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 top_y = tip_y + conf->dir_ * height;
+  Real top_pos = 2 * top_y / details_.staff_space_;
+  Real round_top_pos = rint (top_pos);
+  Interval staff_span
+    = Staff_symbol_referencer::staff_span (details_.staff_symbol_referencer_);
+  if (Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_,
+                                        int (round_top_pos))
+      && staff_span[UP] * 0.5 > top_y)
+    {
+      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)),
+                       "line center");
+    }
+
+  int rounded_tip_pos = int (rint (tip_pos));
+  staff_span.widen (-1);
+  if (Staff_symbol_referencer::on_line (details_.staff_symbol_referencer_, rounded_tip_pos)
+      && (head_positions_slice (conf->column_ranks_[LEFT]).contains (rounded_tip_pos)
+          || head_positions_slice (conf->column_ranks_[RIGHT]).contains (rounded_tip_pos)
+          || staff_span.contains (rounded_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 ())
+    {
+      /* use left edge? */
+      Real x = dot_x_.center ();
+
+      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);
+
+          for (set<int>::const_iterator i (dot_positions_.begin ());
+               i != dot_positions_.end (); i++)
+            {
+              int dot_pos = (*i);
+              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)),
+                               "dot collision");
+            }
+        }
+    }
+
+  conf->scored_ = true;
+}
+
+void
+Tie_formatting_problem::score_ties_aptitude (Ties_configuration *ties) const
+{
+  if (ties->size () != specifications_.size ())
+    {
+      programming_error ("Huh? Mismatch between sizes.");
+      return;
+    }
+
+  for (vsize i = 0; i < ties->size (); i++)
+    score_aptitude (&ties->at (i), specifications_[i],
+                    ties, i);
+}
+
+void
+Tie_formatting_problem::score_ties (Ties_configuration *ties) const
+{
+  if (ties->scored_)
+    return;
+
+  score_ties_configuration (ties);
+  score_ties_aptitude (ties);
+  ties->scored_ = true;
+}
+
+void
+Tie_formatting_problem::score_ties_configuration (Ties_configuration *ties) const
+{
+  for (vsize i = 0; i < ties->size (); 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 (vsize i = 0; i < ties->size (); i++)
+    {
+      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];
+
+      if (i)
+        {
+          if (edge <= last_edge)
+            ties->add_score (details_.tie_column_monotonicity_penalty_, "monoton edge");
+          if (center <= last_center)
+            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;
+    }
+
+  if (ties->size () > 1)
+    {
+      ties->add_score (details_.outer_tie_length_symmetry_penalty_factor_
+                       * fabs (ties->at (0).attachment_x_.length () - ties->back ().attachment_x_.length ()),
+                       "length symm");
+
+      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");
+    }
+}
+
+/*
+  Generate with correct X-attachments and beziers, copying delta_y_
+  from TIES_CONFIG if necessary.
+*/
+Ties_configuration
+Tie_formatting_problem::generate_ties_configuration (Ties_configuration const &ties_config)
+{
+  Ties_configuration copy;
+  for (vsize i = 0; i < ties_config.size (); i++)
+    {
+      Tie_configuration *ptr = get_configuration (ties_config[i].position_, ties_config[i].dir_,
+                                                  ties_config[i].column_ranks_,
+                                                  !specifications_[i].has_manual_delta_y_);
+      if (specifications_[i].has_manual_delta_y_)
+        {
+          ptr->delta_y_
+            = (specifications_[i].manual_position_ - ties_config[i].position_)
+              * 0.5 * details_.staff_space_;
+        }
+      copy.push_back (*ptr);
+    }
+
+  return copy;
+}
+
+Ties_configuration
+Tie_formatting_problem::generate_base_chord_configuration ()
+{
+  Ties_configuration ties_config;
+  for (vsize i = 0; i < specifications_.size (); i++)
+    {
+      Tie_configuration conf;
+      if (specifications_[i].has_manual_dir_)
+        conf.dir_ = specifications_[i].manual_dir_;
+      if (specifications_[i].has_manual_position_)
+        {
+          conf.position_ = (int) my_round (specifications_[i].manual_position_);
+          if (specifications_[i].has_manual_delta_y_)
+            conf.delta_y_ = (specifications_[i].manual_position_ - conf.position_)
+                            * 0.5 * details_.staff_space_;
+        }
+      else
+        {
+          conf.position_ = specifications_[i].position_;
+        }
+
+      conf.column_ranks_ = specifications_[i].column_ranks_;
+      ties_config.push_back (conf);
+    }
+
+  set_ties_config_standard_directions (&ties_config);
+  for (vsize i = 0; i < ties_config.size (); i++)
+    if (!specifications_[i].manual_position_)
+      ties_config[i].position_ += ties_config[i].dir_;
+
+  ties_config = generate_ties_configuration (ties_config);
+
+  return ties_config;
+}
+
+Ties_configuration
+Tie_formatting_problem::find_best_variation (Ties_configuration const &base,
+                                             vector<Tie_configuration_variation> const &vars)
+{
+  Ties_configuration best = base;
+
+  /*
+    This simply is 1-opt: we have K substitions, and we try applying
+    exactly every one for each.
+  */
+  for (vsize i = 0; i < vars.size (); i++)
+    {
+      Ties_configuration variant (base);
+      for (vsize j = 0; j < vars[i].index_suggestion_pairs_.size (); j++)
+        variant[vars[i].index_suggestion_pairs_[j].first] = *vars[i].index_suggestion_pairs_[j].second;
+
+      variant.reset_score ();
+      score_ties (&variant);
+
+      if (variant.score () < best.score ())
+        {
+          best = variant;
+        }
+    }
+
+  return best;
+}
+
+Ties_configuration
+Tie_formatting_problem::generate_optimal_configuration ()
+{
+  Ties_configuration base = generate_base_chord_configuration ();
+  score_ties (&base);
+
+  vector<Tie_configuration_variation> vars;
+  if (specifications_.size () > 1)
+    vars = generate_collision_variations (base);
+  else
+    vars = generate_single_tie_variations (base);
+
+  Ties_configuration best = find_best_variation (base, vars);
+
+  if (specifications_.size () > 1)
+    {
+      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->empty ())
+    return;
+
+  if (!tie_configs->at (0).dir_)
+    {
+      if (tie_configs->size () == 1)
+        tie_configs->at (0).dir_ = Direction (sign (tie_configs->at (0).position_));
+
+      if (!tie_configs->at (0).dir_)
+        tie_configs->at (0).dir_
+          = (tie_configs->size () > 1) ? DOWN : details_.neutral_direction_;
+    }
+
+  if (!tie_configs->back ().dir_)
+    tie_configs->back ().dir_ = UP;
+
+  /*
+    Seconds
+   */
+  for (vsize i = 1; i < tie_configs->size (); i++)
+    {
+      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 (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 (vsize i = 1; i + 1 < tie_configs->size (); i++)
+    {
+      Tie_configuration &conf = tie_configs->at (i);
+      if (conf.dir_)
+        continue;
+
+      Direction position_dir
+        = Direction (sign (conf.position_));
+      if (!position_dir)
+        position_dir = DOWN;
+
+      conf.dir_ = position_dir;
+    }
+}
+
+vector<Tie_configuration_variation>
+Tie_formatting_problem::generate_extremal_tie_variations (Ties_configuration const &ties) const
+{
+  vector<Tie_configuration_variation> vars;
+  for (int i = 1; i <= details_.multi_tie_region_size_; i++)
+    {
+      Drul_array<Tie_configuration *> configs (0, 0);
+      for (DOWN_and_UP (d))
+        {
+          const Tie_configuration &config = boundary (ties, d, 0);
+          if (config.dir_ == d
+              && !boundary (specifications_, d, 0).has_manual_position_)
+            {
+              Tie_configuration_variation var;
+              configs[d] = get_configuration (config.position_ + d * i, d,
+                                              config.column_ranks_,
+                                              true);
+              var.add_suggestion ((d == DOWN) ? 0 : ties.size () - 1,
+                                  configs[d]);
+              vars.push_back (var);
+            }
+        }
+      if (configs[LEFT] && configs[RIGHT])
+        {
+          Tie_configuration_variation var;
+          var.add_suggestion (0, configs[DOWN]);
+          var.add_suggestion (ties.size () - 1, configs[UP]);
+          vars.push_back (var);
+        }
+    }
+
+  return vars;
+}
+
+vector<Tie_configuration_variation>
+Tie_formatting_problem::generate_single_tie_variations (Ties_configuration const &ties) const
+{
+  vector<Tie_configuration_variation> vars;
+
+  int sz = details_.single_tie_region_size_;
+  if (specifications_[0].has_manual_position_)
+    sz = 1;
+  for (int i = 0; i < sz; i++)
+    {
+      for (LEFT_and_RIGHT (d))
+        {
+          if (i == 0
+              && ties[0].dir_ == d)
+            continue;
+
+          int p = ties[0].position_ + i * d;
+
+          if (!specifications_[0].has_manual_dir_
+              || d == specifications_[0].manual_dir_)
+            {
+              Tie_configuration_variation var;
+              var.add_suggestion (0,
+                                  get_configuration (p,
+                                                     d, specifications_[0].column_ranks_,
+                                                     !specifications_[0].has_manual_delta_y_));
+              vars.push_back (var);
+            }
+        }
+    }
+  return vars;
+}
+
+vector<Tie_configuration_variation>
+Tie_formatting_problem::generate_collision_variations (Ties_configuration const &ties) const
+{
+  Real center_distance_tolerance = 0.25;
+
+  vector<Tie_configuration_variation> vars;
+  Real last_center = 0.0;
+  for (vsize i = 0; i < ties.size (); i++)
+    {
+      Bezier b (ties[i].get_transformed_bezier (details_));
+
+      Real center = b.curve_point (0.5)[Y_AXIS];
+
+      if (i)
+        {
+          if (center <= last_center + center_distance_tolerance)
+            {
+              if (!specifications_[i].has_manual_dir_)
+                {
+                  Tie_configuration_variation var;
+                  var.add_suggestion (i,
+                                      get_configuration (specifications_[i].position_
+                                                         - ties[i].dir_,
+                                                         - ties[i].dir_,
+
+                                                         ties[i].column_ranks_,
+                                                         !specifications_[i].has_manual_delta_y_
+                                                        ));
+
+                  vars.push_back (var);
+                }
+
+              if (!specifications_[i - 1].has_manual_dir_)
+                {
+                  Tie_configuration_variation var;
+                  var.add_suggestion (i - 1,
+                                      get_configuration (specifications_[i - 1].position_
+                                                         - ties[i - 1].dir_,
+                                                         - ties[i - 1].dir_,
+                                                         specifications_[i - 1].column_ranks_,
+                                                         !specifications_[i - 1].has_manual_delta_y_));
+
+                  vars.push_back (var);
+                }
+
+              if (i == 1 && !specifications_[i - 1].has_manual_position_
+                  && ties[i - 1].dir_ == DOWN)
+                {
+                  Tie_configuration_variation var;
+                  var.add_suggestion (i - 1,
+                                      get_configuration (specifications_[i - 1].position_ - 1, DOWN,
+                                                         specifications_[i - 1].column_ranks_,
+                                                         !specifications_[i - 1].has_manual_delta_y_
+                                                        ));
+                  vars.push_back (var);
+                }
+              if (i == ties.size () && !specifications_[i].has_manual_position_
+                  && ties[i].dir_ == UP)
+                {
+                  Tie_configuration_variation var;
+                  var.add_suggestion (i,
+                                      get_configuration (specifications_[i].position_
+                                                         + 1, UP,
+                                                         specifications_[i].column_ranks_,
+                                                         !specifications_[i].has_manual_delta_y_
+                                                        ));
+                  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.add_suggestion (i,
+                                  get_configuration (ties[i].position_ + ties[i].dir_,
+                                                     ties[i].dir_,
+                                                     ties[i].column_ranks_,
+                                                     !specifications_[i].has_manual_delta_y_
+                                                    ));
+              vars.push_back (var);
+            }
+
+        }
+
+      last_center = center;
+    }
+
+  return vars;
+}
+
+void
+Tie_formatting_problem::set_manual_tie_configuration (SCM manual_configs)
+{
+  vsize k = 0;
+  for (SCM s = manual_configs;
+       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_car (entry)))
+            {
+              spec.has_manual_position_ = true;
+              spec.manual_position_ = scm_to_double (scm_car (entry));
+              spec.has_manual_delta_y_ = (scm_inexact_p (scm_car (entry)) == SCM_BOOL_T);
+            }
+
+          if (scm_is_number (scm_cdr (entry)))
+            {
+              spec.has_manual_dir_ = true;
+              spec.manual_dir_ = Direction (scm_to_int (scm_cdr (entry)));
+            }
+        }
+      k++;
+    }
+}
+
+void
+Tie_formatting_problem::set_debug_scoring (Ties_configuration const &base)
+{
+#if DEBUG_TIE_SCORING
+  if (to_boolean (x_refpoint_->layout ()
+                  ->lookup_variable (ly_symbol2scm ("debug-tie-scoring"))))
+    {
+      for (vsize i = 0; i < base.size (); i++)
+        {
+          string card = base.complete_tie_card (i);
+          specifications_[i].tie_grob_->set_property ("annotation",
+                                                      ly_string2scm (card));
+        }
+    }
+#endif
 }