[lilypond.git] / lily / beam.cc

/*
  beam.cc -- implement Beam
  
  source file of the GNU LilyPond music typesetter
  
  (c) 1997--2004 Han-Wen Nienhuys <hanwen@cs.uu.nl>
  Jan Nieuwenhuizen <janneke@gnu.org>
*/

/*
TODO:

  - Determine auto knees based on positions if it's set by the user.

  - the code is littered with * and / staff_space calls for
    #'positions. Consider moving to real-world coordinates?

    Problematic issue is user tweaks (user tweaks are in staff-coordinates.) 
  
Notes:

 - Stems run to the Y-center of the beam.
  
 - beam_translation is the offset between Y centers of the beam.

*/


#include <math.h> // tanh.

#include "stencil.hh" 
#include "directional-element-interface.hh"
#include "beaming.hh"
#include "beam.hh"
#include "misc.hh"
#include "least-squares.hh"
#include "stem.hh"
#include "output-def.hh"
#include "lookup.hh"
#include "group-interface.hh"
#include "staff-symbol-referencer.hh"
#include "item.hh"
#include "spanner.hh"
#include "warn.hh"


#if DEBUG_QUANTING
#include "text-item.hh"  // debug output.
#include "font-interface.hh"  // debug output.
#endif


void
Beam::add_stem (Grob *me, Grob *s)
{
  Pointer_group_interface::add_grob (me, ly_symbol2scm ("stems"), s);
  
  s->add_dependency (me);

  assert (!Stem::get_beam (s));
  s->set_property ("beam", me->self_scm ());

  add_bound_item (dynamic_cast<Spanner*> (me), dynamic_cast<Item*> (s));
}


Real
Beam::get_thickness (Grob * me)
{
  return robust_scm2double (me->get_property ("thickness"), 0)
    * Staff_symbol_referencer::staff_space (me);
}

/* Return the translation between 2 adjoining beams. */
Real
Beam::get_beam_translation (Grob *me)
{
  SCM func = me->get_property ("space-function");

  if (ly_c_procedure_p (func))
    {
      SCM s = scm_call_2 (func, me->self_scm (), scm_int2num (get_beam_count (me)));
      return scm_to_double (s);
    }
  else
    {
      return 0.81;
    }
}

/* Maximum beam_count. */
int
Beam::get_beam_count (Grob *me) 
{
  int m = 0;
  for (SCM s = me->get_property ("stems"); ly_c_pair_p (s); s = ly_cdr (s))
    {
      Grob *stem = unsmob_grob (ly_car (s));
      m = m >? (Stem::beam_multiplicity (stem).length () + 1);
    }
  return m;
}


/*
  Space return space between beams.
 */
MAKE_SCHEME_CALLBACK (Beam, space_function, 2);
SCM
Beam::space_function (SCM smob, SCM beam_count)
{
  Grob *me = unsmob_grob (smob);
  
  Real staff_space = Staff_symbol_referencer::staff_space (me);
  Real line = Staff_symbol_referencer::line_thickness (me);
  Real thickness = get_thickness (me);
  
  Real beam_translation = scm_to_int (beam_count) < 4
    ? (2*staff_space + line - thickness) / 2.0
    : (3*staff_space + line - thickness) / 3.0;
  
  return scm_make_real (beam_translation);
}


/* After pre-processing all directions should be set.
   Several post-processing routines (stem, slur, script) need stem/beam
   direction.
   Currenly, this means that beam has set all stem's directions.
   [Alternatively, stems could set its own directions, according to
   their beam, during 'final-pre-processing'.] */
MAKE_SCHEME_CALLBACK (Beam, before_line_breaking, 1);
SCM
Beam::before_line_breaking (SCM smob)
{
  Grob *me =  unsmob_grob (smob);

  /* Beams with less than 2 two stems don't make much sense, but could happen
     when you do
     
     [r8 c8 r8].
     
    For a beam that  only has one stem, we try to do some disappearance magic:
    we revert the flag, and move on to The Eternal Engraving Fields. */

  int count = visible_stem_count (me);
  if (count < 2)
    {
      me->warning (_ ("beam has less than two visible stems"));

      SCM stems = me->get_property ("stems");
      if (scm_ilength (stems) == 1)
        {
          me->warning (_ ("removing beam with less than two stems"));

          unsmob_grob (ly_car (stems))->set_property ("beam", SCM_EOL);
          me->suicide ();

          return SCM_UNSPECIFIED;
        }
      else if (scm_ilength (stems) == 0)
        {
          me->suicide ();
          return SCM_UNSPECIFIED;         
        }
    }
  if (count >= 1)
    {
      Direction d = get_default_dir (me);

      consider_auto_knees (me);
      set_stem_directions (me, d);

      connect_beams (me);

      set_stem_shorten (me);
    }

  return SCM_EOL;
}


/*
  We want a maximal number of shared beams, but if there is choice, we
  take the one that is closest to the end of the stem. This is for situations like

       x
      |
      |
  |===|
  |=
  |
  x

  
 */
int
position_with_maximal_common_beams (SCM left_beaming, SCM right_beaming,
                                    Direction left_dir,
                                    Direction right_dir)
{
  Slice lslice = int_list_to_slice (ly_cdr (left_beaming));

  int best_count = 0;
  int best_start = 0;
  for (int i = lslice[-left_dir];
       (i - lslice[left_dir])* left_dir <= 0 ; i+= left_dir) 
    {
      int count =0;
      for ( SCM s = ly_car (right_beaming); ly_c_pair_p (s); s = ly_cdr (s))
        {
          int k = - right_dir * scm_to_int (ly_car (s)) + i;
          if (scm_c_memq (scm_int2num (k), left_beaming) != SCM_BOOL_F)
            count ++;
        }

      if (count >= best_count)
        {
          best_count = count; 
          best_start = i;
        }
    }

  return best_start;
}

void
Beam::connect_beams (Grob *me)
{
  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");

  Slice last_int;
  last_int.set_empty ();
  SCM last_beaming = SCM_EOL;
  Direction last_dir = CENTER;
  for (int i = 0; i< stems.size (); i++)
    {
      Grob *this_stem = stems[i];
      SCM this_beaming = this_stem->get_property ("beaming");

      Direction this_dir = get_grob_direction (this_stem);
      if (ly_c_pair_p (last_beaming) && ly_c_pair_p (this_beaming))
        {
          int start_point = position_with_maximal_common_beams
            (last_beaming, this_beaming,
             last_dir, this_dir);
          
          Direction d = LEFT;
          Slice new_slice ; 
          do
            {
              if (d == RIGHT && i == stems.size ()-1)
                continue;
              
              new_slice.set_empty ();
              SCM s = index_get_cell (this_beaming, d);
              for (; ly_c_pair_p (s); s = ly_cdr (s))
                {
                  int new_beam_pos =
                    start_point - this_dir * scm_to_int (ly_car (s));

                  new_slice.add_point (new_beam_pos);
                  scm_set_car_x (s, scm_int2num (new_beam_pos));
                }


            }
          while (flip (&d) != LEFT);

          if (!new_slice.is_empty ())
            last_int =  new_slice;
        }
      else
        {
          scm_set_car_x ( this_beaming, SCM_EOL);
          SCM s = ly_cdr (this_beaming);
          for (; ly_c_pair_p (s); s = ly_cdr (s))
            {
              int np = - this_dir * scm_to_int (ly_car (s));
              scm_set_car_x (s, scm_int2num (np));
              last_int.add_point (np);
            }
        }

      if (i == stems.size () -1)
        {
          scm_set_cdr_x (this_beaming, SCM_EOL);
        }

      if (scm_ilength (ly_cdr (this_beaming)) > 0)
        {
          last_beaming = this_beaming;
          last_dir = this_dir;
        }
    }
 }


/*
  TODO: should not make beams per stem, but per Y-level.
 */
MAKE_SCHEME_CALLBACK (Beam, print, 1);
SCM
Beam::print (SCM grob)
{
  Spanner *me = unsmob_spanner (grob);
  position_beam (me);
  
  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
  Grob* xcommon = common_refpoint_of_array (stems, me, X_AXIS);

  xcommon = me->get_bound (LEFT)->common_refpoint (xcommon, X_AXIS);
  xcommon = me->get_bound (RIGHT)->common_refpoint (xcommon, X_AXIS);

  Real x0, dx;
  if (visible_stem_count (me))
    {
      // ugh -> use commonx
      x0 = first_visible_stem (me)->relative_coordinate (xcommon, X_AXIS);
      dx = last_visible_stem (me)->relative_coordinate (xcommon, X_AXIS) - x0;
    }
  else
    {
      x0 = stems[0]->relative_coordinate (xcommon, X_AXIS);
      dx = stems.top ()->relative_coordinate (xcommon, X_AXIS) - x0;
    }

  SCM posns = me->get_property ("positions");
  Drul_array<Real> pos;
  if (!is_number_pair (posns))
    {
      programming_error ("No beam posns");
      pos = Interval (0,0);
    }
  else
    pos= ly_scm2realdrul (posns);

  scale_drul (&pos,  Staff_symbol_referencer::staff_space (me));
  
  Real dy = pos[RIGHT] - pos[LEFT];
  Real slope = (dy && dx) ? dy/dx : 0;
  
  Real thick = get_thickness (me);
  Real bdy = get_beam_translation (me);

  SCM last_beaming = SCM_EOL;
  Real last_xposn = -1;
  Real last_stem_width = -1 ;

  Real gap_length = robust_scm2double (me->get_property ("gap"), 0.0);
  
  Stencil the_beam;
  Real lt = me->get_paper ()->get_dimension (ly_symbol2scm ("linethickness"));
  
  for (int i = 0; i<= stems.size (); i++)
    {
      Grob * st = (i < stems.size ()) ? stems[i] : 0;
      
      SCM this_beaming = st ? st->get_property ("beaming") : SCM_EOL;
      Real xposn = st ? st->relative_coordinate (xcommon, X_AXIS) : 0.0;
      Real stem_width = st ? robust_scm2double (st->get_property ("thickness"), 1.0) *lt : 0 ;
      Direction stem_dir = st ? to_dir (st->get_property ("direction")) : CENTER;
      /*
        We do the space left of ST, with lfliebertjes pointing to the
        right from the left stem, and rfliebertjes pointing left from
        right stem.
       */
      SCM left = (i > 0) ? ly_cdr (last_beaming) : SCM_EOL;
      SCM right = st ? ly_car (this_beaming) : SCM_EOL;

      Array<int> full_beams;
      Array<int> lfliebertjes;
      Array<int> rfliebertjes;    

      for (SCM s = left;
           ly_c_pair_p (s); s =ly_cdr (s))
        {
          int b = scm_to_int (ly_car (s));
          if (scm_c_memq (ly_car (s), right) != SCM_BOOL_F)
            {
              full_beams.push (b);
            }
          else
            {
              lfliebertjes.push (b); 
            }
        }
      for (SCM s = right;
           ly_c_pair_p (s); s =ly_cdr (s))
        {
          int b = scm_to_int (ly_car (s));
          if (scm_c_memq (ly_car (s), left) == SCM_BOOL_F)
            {
              rfliebertjes.push (b);
            }
        }

      /*
        how much to stick out for beams across linebreaks
       */
      Real break_overshoot = 3.0;
      Real w = (i > 0 && st) ? (xposn - last_xposn) : break_overshoot;

      Real stem_offset =0.0;
      if (i > 0)
        {
          w += last_stem_width / 2;
          stem_offset = -last_stem_width / 2;
        }

      if (st)
        w += stem_width/ 2 ;
      

      Real blot = me->get_paper ()->get_dimension (ly_symbol2scm ("blotdiameter"));
      Stencil whole = Lookup::beam (slope, w, thick, blot);
      Stencil gapped;

      int gap_count = 0;
      if (scm_is_number (me->get_property ("gap-count")))
        {
          gap_count = scm_to_int (me->get_property ("gap-count"));
          gapped = Lookup::beam (slope, w - 2 * gap_length, thick, blot);

          full_beams.sort (default_compare);
          if (stem_dir == UP)
            full_beams.reverse ();
        }

      int k = 0;
      for (int j = full_beams.size (); j--;)
        {
          Stencil b (whole);
          
          if (k++ < gap_count)
            {
              b = gapped;
              b.translate_axis (gap_length, X_AXIS);
            }
          b.translate_axis (last_xposn -  x0 + stem_offset, X_AXIS);
          b.translate_axis (slope * (last_xposn - x0) + bdy * full_beams[j], Y_AXIS);

          the_beam.add_stencil (b);           
        }
          
      if (lfliebertjes.size () || rfliebertjes.size ())
        {
          Real nw_f;

          if (st)
            {
              int t = Stem::duration_log (st); 

              SCM proc = me->get_property ("flag-width-function");
              SCM result = scm_call_1 (proc, scm_int2num (t));
              nw_f = scm_to_double (result);
            }
          else
            nw_f = break_overshoot / 2;
              
          /* Half beam should be one note-width,
             but let's make sure two half-beams never touch */
          Real lw = nw_f;
          Real rw = nw_f;
          if (i > 0)
            rw = nw_f <? ( (xposn - last_xposn) / 2);
          else
            /*
              TODO: 0.5 is a guess.
            */
            rw = xposn - me->get_bound (LEFT)->extent (xcommon, X_AXIS)[RIGHT]
              - 0.5;
          
          if (st)
            lw = nw_f <? ( (xposn - last_xposn) / 2);
          else
            lw = me->get_bound (RIGHT)->relative_coordinate (xcommon, X_AXIS)
              - last_xposn;

          Stencil rhalf = Lookup::beam (slope, rw, thick, blot);
          Stencil lhalf = Lookup::beam (slope, lw, thick, blot);
          for (int j = lfliebertjes.size (); j--;)
            {
              Stencil b (lhalf);
              b.translate_axis (last_xposn -  x0, X_AXIS);
              b.translate_axis (slope * (last_xposn-x0) + bdy * lfliebertjes[j], Y_AXIS);
              the_beam.add_stencil (b);       
            }
          for (int j = rfliebertjes.size (); j--;)
            {
              Stencil b (rhalf);
              b.translate_axis (xposn -  x0 - rw , X_AXIS);
              b.translate_axis (slope * (xposn-x0 -rw) + bdy * rfliebertjes[j], Y_AXIS);
              the_beam.add_stencil (b);       
            }
        }


      last_xposn = xposn;
      last_stem_width = stem_width;
      last_beaming = this_beaming;
    }

  the_beam.translate_axis (x0 - me->relative_coordinate (xcommon, X_AXIS), X_AXIS);
  the_beam.translate_axis (pos[LEFT], Y_AXIS);

#if (DEBUG_QUANTING)
  SCM quant_score = me->get_property ("quant-score");
  if (to_boolean (me->get_paper ()->lookup_variable (ly_symbol2scm ("debug-beam-quanting")))
      && scm_is_string (quant_score))
    {
      
      /*
        This code prints the demerits for each beam. Perhaps this
        should be switchable for those who want to twiddle with the
        parameters.
      */
      String str;
      SCM properties = Font_interface::text_font_alist_chain (me);

      Direction stem_dir = stems.size() ? to_dir (stems[0]->get_property ("direction")) : UP;
    
      Stencil tm = *unsmob_stencil (Text_item::interpret_markup
         (me->get_paper ()->self_scm (), properties, quant_score));
      the_beam.add_at_edge (Y_AXIS, stem_dir, tm, 1.0, 0);
    }
#endif
  
  return the_beam.smobbed_copy ();
}
  



Direction
Beam::get_default_dir (Grob *me) 
{
  Drul_array<int> total;
  total[UP]  = total[DOWN] = 0;
  Drul_array<int> count; 
  count[UP]  = count[DOWN] = 0;
  Direction d = DOWN;

  Link_array<Grob> stems=
        Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");

  for (int i=0; i < stems.size (); i++)
    do {
      Grob *s = stems[i];
      Direction sd = get_grob_direction (s);

      int center_distance = int (- d * Stem::head_positions (s) [-d]) >? 0;
      int current = sd  ? (1 + d * sd)/2 : center_distance;

      if (current)
        {
          total[d] += current;
          count[d] ++;
        }
    } while (flip (&d) != DOWN);
  
  SCM func = me->get_property ("dir-function");
  SCM s = scm_call_2 (func,
                    scm_cons (scm_int2num (count[UP]),
                             scm_int2num (count[DOWN])),
                    scm_cons (scm_int2num (total[UP]),
                             scm_int2num (total[DOWN])));

  if (scm_is_number (s) && scm_to_int (s))
    return to_dir (s);
  
  /* If dir is not determined: get default */
  return to_dir (me->get_property ("neutral-direction"));
}


/* Set all stems with non-forced direction to beam direction.
   Urg: non-forced should become `without/with unforced' direction,
   once stem gets cleaned-up. */
void
Beam::set_stem_directions (Grob *me, Direction d)
{
  Link_array<Grob> stems
    =Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
  
  for (int i=0; i <stems.size (); i++)
    {
      Grob *s = stems[i];
  
      SCM forcedir = s->get_property ("direction");
      if (!to_dir (forcedir))
        set_grob_direction (s,  d);
    }
}

/*
  A union of intervals in the real line.

  Abysmal performance (quadratic) for large N, hopefully we don't have
  that large N. In any case, this should probably be rewritten to use
  a balanced tree.
 */
struct Int_set
{
  Array<Interval> allowed_regions_;

  Int_set ()
  {
    set_full ();
  }

  void set_full ()
  {
    allowed_regions_.clear ();
    Interval s;
    s.set_full ();
    allowed_regions_.push (s);
  }

  void remove_interval (Interval rm)
  {
    for (int i = 0; i < allowed_regions_.size (); )
      {
        Interval s = rm;

        s.intersect (allowed_regions_[i]);

        if (!s.is_empty ())
          {
            Interval before = allowed_regions_[i];
            Interval after = allowed_regions_[i];

            before[RIGHT] = s[LEFT];
            after[LEFT] = s[RIGHT];

            if (!before.is_empty () && before.length () > 0.0)
              {
                allowed_regions_.insert (before, i);
                i++;
              }
            allowed_regions_.del (i);
            if (!after.is_empty () && after.length () > 0.0)
              {
                allowed_regions_.insert (after, i);
                i++;
              }
          }
        else
          i++;
      }
  }
};


/*
  Only try horizontal beams for knees.  No reliable detection of
  anything else is possible here, since we don't know funky-beaming
  settings, or X-distances (slopes!)  People that want sloped
  knee-beams, should set the directions manually.
 */
void
Beam::consider_auto_knees (Grob* me)
{
  SCM scm = me->get_property ("auto-knee-gap");
  if (!scm_is_number (scm))
    return ;

  Real threshold = scm_to_double (scm);
  
  Int_set gaps;

  gaps.set_full ();

  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
      
  Grob *common = common_refpoint_of_array (stems, me,  Y_AXIS);
  Real staff_space = Staff_symbol_referencer::staff_space (me);
  
  Array<Interval> hps_array;  
  for (int i=0; i < stems.size (); i++)
    {
      Grob* stem = stems[i];
      if (Stem::is_invisible (stem))
        continue;

      Interval hps = Stem::head_positions (stem);
      if (!hps.is_empty ())
        {
          hps[LEFT] += -1;
          hps[RIGHT] += 1; 
          hps *= staff_space * 0.5 ;

          /*
            We could subtract beam Y position, but this routine only
            sets stem directions, a constant shift does not have an
            influence.
            
           */
          hps += stem->relative_coordinate (common, Y_AXIS);

          if (to_dir (stem->get_property ("direction")))
            {
              Direction stemdir = to_dir (stem->get_property ("direction"));
              hps[-stemdir] = - stemdir * infinity_f;
            }
        }
      hps_array.push (hps);

      gaps.remove_interval (hps);
    }

  Interval max_gap;
  Real max_gap_len =0.0;

  for (int i  = gaps.allowed_regions_.size () -1;  i >=  0 ; i--)
    {
      Interval gap = gaps.allowed_regions_[i];

      /*
        the outer gaps are not knees.
       */
      if (isinf (gap[LEFT]) || isinf (gap[RIGHT]))
        continue;
      
      if (gap.length () >= max_gap_len)
        {
          max_gap_len = gap.length ();
          max_gap = gap;
        }
    }

  if (max_gap_len > threshold)
    {
      int j = 0;
      for (int i = 0; i < stems.size (); i++)
        {
          Grob* stem = stems[i];
          if (Stem::is_invisible (stem))
            continue;

          Interval hps = hps_array[j++];


          Direction d =  (hps.center () < max_gap.center ()) ?
            UP : DOWN ;
          
          stem->set_property ("direction", scm_int2num (d));
          
          hps.intersect (max_gap);
          assert (hps.is_empty () || hps.length () < 1e-6 );
        }
    }
}



/* Set stem's shorten property if unset.

 TODO:
   take some y-position (chord/beam/nearest?) into account
   scmify forced-fraction
 
  This is done in beam because the shorten has to be uniform over the
  entire beam.

*/
void
Beam::set_stem_shorten (Grob *me)
{
  /*
    shortening looks silly for x staff beams
   */
  if (is_knee (me))
    return ;
  
  Real forced_fraction = 1.0 * forced_stem_count (me)
    / visible_stem_count (me);

  int beam_count = get_beam_count (me);

  SCM shorten_list = me->get_property ("beamed-stem-shorten");
  if (shorten_list == SCM_EOL)
    return;

  Real staff_space = Staff_symbol_referencer::staff_space (me);
  
  SCM shorten_elt =
    robust_list_ref (beam_count -1, shorten_list);
  Real shorten_f = scm_to_double (shorten_elt) * staff_space;

  /* your similar cute comment here */
  shorten_f *= forced_fraction;

  if (shorten_f)
    me->set_property ("shorten", scm_make_real (shorten_f));
}

/*  Call list of y-dy-callbacks, that handle setting of
    grob-properties

*/
MAKE_SCHEME_CALLBACK (Beam, after_line_breaking, 1);
SCM
Beam::after_line_breaking (SCM smob)
{
  Grob *me = unsmob_grob (smob);

  position_beam (me);
  return SCM_UNSPECIFIED;
}

void
Beam::position_beam (Grob *me)
{
  if (to_boolean (me->get_property ("positioning-done")))
    return ;

  me->set_property ("positioning-done", SCM_BOOL_T);

  /* Copy to mutable list. */
  SCM s = ly_deep_copy (me->get_property ("positions"));
  me->set_property ("positions", s);

  if (ly_car (s) == SCM_BOOL_F)
    {
      // one wonders if such genericity is necessary  --hwn.
      SCM callbacks = me->get_property ("position-callbacks");
      for (SCM i = callbacks; ly_c_pair_p (i); i = ly_cdr (i))
        scm_call_1 (ly_car (i), me->self_scm ());
    }

  set_stem_lengths (me);  
}


void
set_minimum_dy (Grob *me, Real * dy)
{
  if (*dy)
    {
      /*
        If dy is smaller than the smallest quant, we
        get absurd direction-sign penalties. 
      */
          
      Real ss = Staff_symbol_referencer::staff_space (me);
      Real thickness = Beam::get_thickness (me) / ss ;
      Real slt = Staff_symbol_referencer::line_thickness (me) / ss;
      Real sit = (thickness - slt) / 2;
      Real inter = 0.5;
      Real hang = 1.0 - (thickness - slt) / 2;
          
      *dy = sign (*dy) * (fabs (*dy)
                        >?
                        (sit <? inter <? hang));
    }
}

/*
  Compute  a first approximation to the beam slope.
 */
MAKE_SCHEME_CALLBACK (Beam, least_squares, 1);
SCM
Beam::least_squares (SCM smob)
{
  Grob *me = unsmob_grob (smob);

  int count = visible_stem_count (me);
  Interval pos (0, 0);
  
  if (count < 1)
    {
      me->set_property ("positions", ly_interval2scm (pos));
      return SCM_UNSPECIFIED;
    }


  Array<Real> x_posns ;
  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
  Grob *commonx = common_refpoint_of_array (stems, me, X_AXIS);
  Grob *commony = common_refpoint_of_array (stems, me, Y_AXIS);  

  Real my_y = me->relative_coordinate (commony, Y_AXIS);
  
  Grob *fvs  = first_visible_stem (me);
  Grob *lvs  = last_visible_stem (me);
  
  Interval ideal (Stem::get_stem_info (fvs).ideal_y_
                  + fvs->relative_coordinate (commony, Y_AXIS) -my_y,
                  Stem::get_stem_info (lvs).ideal_y_
                  + lvs->relative_coordinate (commony, Y_AXIS) - my_y);
  
  Real x0 = first_visible_stem (me)->relative_coordinate (commonx, X_AXIS);
  for (int i=0; i < stems.size (); i++)
    {
      Grob* s = stems[i];

      Real x = s->relative_coordinate (commonx, X_AXIS) - x0;
      x_posns.push (x);
    }
  Real dx = last_visible_stem (me)->relative_coordinate (commonx, X_AXIS) - x0;

  
  Real y =0;  
  Real slope = 0;
  Real dy = 0;
  
  if (!ideal.delta ())
    {
      Interval chord (Stem::chord_start_y (first_visible_stem (me)),
                      Stem::chord_start_y (last_visible_stem (me)));

      /* Simple beams (2 stems) on middle line should be allowed to be
         slightly sloped.
         
         However, if both stems reach middle line,
         ideal[LEFT] == ideal[RIGHT] and ideal.delta () == 0.

         For that case, we apply artificial slope */
      if (!ideal[LEFT] && chord.delta () && count == 2)
        {
          /* FIXME. -> UP */
          Direction d = (Direction) (sign (chord.delta ()) * UP);
          pos[d] = get_thickness (me) / 2;
          pos[-d] = - pos[d];
        }
      else
        {
          pos = ideal;
        }

      /*
        For broken beams this doesn't work well. In this case, the
        slope esp. of the first part of a broken beam should predict
        where the second part goes.
      */
      me->set_property ("least-squares-dy",
                        scm_make_real (pos[RIGHT] - pos[LEFT]));
    }
  else
    {
      Array<Offset> ideals;
      for (int i=0; i < stems.size (); i++)
        {
          Grob* s = stems[i];
          if (Stem::is_invisible (s))
            continue;
          ideals.push (Offset (x_posns[i],
                               Stem::get_stem_info (s).ideal_y_
                               + s->relative_coordinate (commony, Y_AXIS)
                               - my_y));
        }
      
      minimise_least_squares (&slope, &y, ideals);

      dy = slope * dx;

      set_minimum_dy (me,&dy);
      me->set_property ("least-squares-dy", scm_make_real (dy));
      pos = Interval (y, (y+dy));
    }

  /*
    "position" is relative to the staff.
   */
  scale_drul (&pos,  1/ Staff_symbol_referencer::staff_space (me)); 
  
  me->set_property ("positions", ly_interval2scm (pos));
 
  return SCM_UNSPECIFIED;
}


/*
  We can't combine with previous function, since check concave and
  slope damping comes first.

  TODO: we should use the concaveness to control the amount of damping
  applied.
  
*/
MAKE_SCHEME_CALLBACK (Beam, shift_region_to_valid, 1);
SCM
Beam::shift_region_to_valid (SCM grob)
{
  Grob *me = unsmob_grob (grob);
  /*
    Code dup.
   */
  Array<Real> x_posns ;
  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
  Grob *commonx = common_refpoint_of_array (stems, me, X_AXIS);
  Grob *commony = common_refpoint_of_array (stems, me, Y_AXIS);  

  Grob *fvs = first_visible_stem (me);

  if (!fvs)
    return SCM_UNSPECIFIED;
    
  Real x0 =fvs->relative_coordinate (commonx, X_AXIS);
  for (int i=0; i < stems.size (); i++)
    {
      Grob* s = stems[i];

      Real x = s->relative_coordinate (commonx, X_AXIS) - x0;
      x_posns.push (x);
    }

  Grob *lvs = last_visible_stem (me);
  if (!lvs)
    return SCM_UNSPECIFIED;
  
  Real dx = lvs->relative_coordinate (commonx, X_AXIS) - x0;

  Drul_array<Real> pos = ly_scm2interval ( me->get_property ("positions"));

  scale_drul (&pos,  Staff_symbol_referencer::staff_space (me));
  
  Real dy = pos[RIGHT] - pos[LEFT];
  Real y = pos[LEFT];
  Real slope =dy/dx;

  
  /*
    Shift the positions so that we have a chance of finding good
    quants (i.e. no short stem failures.)
   */
  Interval feasible_left_point;
  feasible_left_point.set_full ();
  for (int i=0; i < stems.size (); i++)
    {
      Grob* s = stems[i];
      if (Stem::is_invisible (s))
        continue;

      Direction d = Stem::get_direction (s);

      Real left_y =
        Stem::get_stem_info (s).shortest_y_
        - slope * x_posns [i];

      /*
        left_y is now relative to the stem S. We want relative to
        ourselves, so translate:
       */
      left_y += 
        + s->relative_coordinate (commony, Y_AXIS)
        - me->relative_coordinate (commony, Y_AXIS);

      Interval flp ;
      flp.set_full ();
      flp[-d] = left_y;

      feasible_left_point.intersect (flp);
    }
      
  if (feasible_left_point.is_empty ())
    warning (_ ("no viable initial configuration found: may not find good beam slope"));
  else if (!feasible_left_point.contains (y))
    {
      if (isinf (feasible_left_point[DOWN]))
        y = feasible_left_point[UP] - REGION_SIZE;
      else if (isinf (feasible_left_point[UP]))
        y = feasible_left_point[DOWN]+ REGION_SIZE;
      else
        y = feasible_left_point.center ();
    }
  
  pos = Drul_array<Real> (y, (y+dy));
  scale_drul (&pos, 1/ Staff_symbol_referencer::staff_space (me));
  
  me->set_property ("positions", ly_interval2scm (pos));
  return SCM_UNSPECIFIED;
}

/* This neat trick is by Werner Lemberg,
   damped = tanh (slope)
   corresponds with some tables in [Wanske] CHECKME */
MAKE_SCHEME_CALLBACK (Beam, slope_damping, 1);
SCM
Beam::slope_damping (SCM smob)
{
  Grob *me = unsmob_grob (smob);

  if (visible_stem_count (me) <= 1)
    return SCM_UNSPECIFIED;

  SCM s = me->get_property ("damping"); 
  Real damping = scm_to_double (s);

  if (damping)
    {
      Drul_array<Real> pos = ly_scm2interval (me->get_property ("positions"));
      scale_drul (&pos,  Staff_symbol_referencer::staff_space (me));
      
      Real dy = pos[RIGHT] - pos[LEFT];

      Grob *fvs  = first_visible_stem (me);
      Grob *lvs  = last_visible_stem (me);

      Grob *commonx = fvs->common_refpoint (lvs, X_AXIS);


      Real dx = last_visible_stem (me)->relative_coordinate (commonx, X_AXIS)
        - first_visible_stem (me)->relative_coordinate (commonx, X_AXIS);

      Real slope = dy && dx ? dy/dx : 0;

      Real concaveness = robust_scm2double (me->get_property ("concaveness"), 0.0);
      
      slope = 0.6 * tanh (slope) / (damping + concaveness);

      Real damped_dy = slope * dx;

      set_minimum_dy (me, &damped_dy);
      
      pos[LEFT] += (dy - damped_dy) / 2;
      pos[RIGHT] -= (dy - damped_dy) / 2;

      scale_drul (&pos, 1/Staff_symbol_referencer::staff_space (me));
      
      me->set_property ("positions", ly_interval2scm (pos));
    }
  return SCM_UNSPECIFIED;
}

/*
  Report slice containing the numbers that are both in (car BEAMING)
  and (cdr BEAMING)
 */
Slice
where_are_the_whole_beams (SCM beaming)
{
  Slice l; 
  
  for ( SCM s = ly_car (beaming); ly_c_pair_p (s) ; s = ly_cdr (s))
    {
      if (scm_c_memq (ly_car (s), ly_cdr (beaming)) != SCM_BOOL_F)
        
        l.add_point (scm_to_int (ly_car (s)));
    }

  return l;
}

/* Return the Y position of the stem-end, given the Y-left, Y-right
   in POS for stem S.  This Y position is relative to S. */
Real
Beam::calc_stem_y (Grob *me, Grob* s, Grob ** common,
                   Real xl, Real xr,
                   Drul_array<Real> pos, bool french) 
{
  Real beam_translation = get_beam_translation (me);

    
  Real r = s->relative_coordinate (common[X_AXIS], X_AXIS) - xl;
  Real dy = pos[RIGHT] - pos[LEFT];
  Real dx = xr - xl;
  Real stem_y_beam0 = (dy && dx
                       ? r / dx
                       * dy
                       : 0) + pos[LEFT];
  
  Direction my_dir = get_grob_direction (s);
  SCM beaming = s->get_property ("beaming");
 
  Real stem_y = stem_y_beam0;
  if (french)
    {
      Slice bm = where_are_the_whole_beams (beaming);
      if (!bm.is_empty ())
        stem_y += beam_translation * bm[-my_dir];
    }
  else
    {
      Slice bm = Stem::beam_multiplicity (s);
      if (!bm.is_empty ())
        stem_y +=bm[my_dir] * beam_translation;
    }
  
  Real id = me->relative_coordinate (common[Y_AXIS], Y_AXIS)
    - s->relative_coordinate (common[Y_AXIS], Y_AXIS);
  
  return stem_y + id;
}

/*
  Hmm.  At this time, beam position and slope are determined.  Maybe,
  stem directions and length should set to relative to the chord's
  position of the beam.  */
void
Beam::set_stem_lengths (Grob *me)
{
  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");

  if (!stems.size ())
    return;
  
  Grob *common[2];
  for (int a = 2; a--;)
    common[a] = common_refpoint_of_array (stems, me, Axis (a));
  
  Drul_array<Real> pos = ly_scm2realdrul (me->get_property ("positions"));
  Real staff_space = Staff_symbol_referencer::staff_space (me);
  scale_drul (&pos,  staff_space);

  bool gap = false;
  Real thick =0.0;
  if (scm_is_number (me->get_property ("gap-count"))
      &&scm_to_int (me->get_property ("gap-count")))
    {
      gap = true;
      thick = get_thickness (me);
    }
      
  // ugh -> use commonx
  Grob * fvs = first_visible_stem (me);
  Grob *lvs = last_visible_stem (me);
    
  Real xl = fvs ? fvs->relative_coordinate (common[X_AXIS], X_AXIS) : 0.0;
  Real xr = lvs ? lvs->relative_coordinate (common[X_AXIS], X_AXIS) : 0.0;
  
  for (int i=0; i < stems.size (); i++)
    {
      Grob* s = stems[i];
      if (Stem::is_invisible (s))
        continue;

      bool french = to_boolean (s->get_property ("french-beaming"));
      Real stem_y = calc_stem_y (me, s, common,
                                 xl, xr,
                                 pos, french && s != lvs && s!= fvs);

      /*
        Make the stems go up to the end of the beam. This doesn't matter
        for normal beams, but for tremolo beams it looks silly otherwise.
       */
      if (gap)
        stem_y += thick * 0.5 * get_grob_direction (s);

      Stem::set_stemend (s, 2* stem_y / staff_space);
    }
}

void
Beam::set_beaming (Grob *me, Beaming_info_list *beaming)
{
  Link_array<Grob> stems=
    Pointer_group_interface__extract_grobs (me, (Grob *)0, "stems");
  
  Direction d = LEFT;
  for (int i=0; i  < stems.size (); i++)
    {
      /*
        Don't overwrite user settings.
       */
      
      do
        {
          /* Don't set beaming for outside of outer stems */      
          if ( (d == LEFT && i == 0)
              || (d == RIGHT && i == stems.size () -1))
            continue;

          Grob *st =  stems[i];
          SCM beaming_prop = st->get_property ("beaming");
          if (beaming_prop == SCM_EOL ||
              index_get_cell (beaming_prop, d) == SCM_EOL)
            {
              int b = beaming->infos_.elem (i).beams_i_drul_[d];
              if (i>0
                  && i < stems.size () -1
                  && Stem::is_invisible (st))
                b = b <? beaming->infos_.elem (i).beams_i_drul_[-d];
              
              Stem::set_beaming (st, b, d);
            }
        }
      while (flip (&d) != LEFT);
    }
}

int
Beam::forced_stem_count (Grob *me) 
{
  Link_array<Grob>stems = 
    Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
  int f = 0;
  for (int i=0; i < stems.size (); i++)
    {
      Grob *s = stems[i];

      if (Stem::is_invisible (s))
        continue;

      /* I can imagine counting those boundaries as a half forced stem,
         but let's count them full for now. */
      if (abs (Stem::chord_start_y (s)) > 0.1
        && (Stem::get_direction (s) != Stem::get_default_dir (s)))
        f++;
    }
  return f;
}




int
Beam::visible_stem_count (Grob *me) 
{
  Link_array<Grob>stems = 
    Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
  int c = 0;
  for (int i = stems.size (); i--;)
    {
      if (!Stem::is_invisible (stems[i]))
        c++;
    }
  return c;
}

Grob*
Beam::first_visible_stem (Grob *me) 
{
  Link_array<Grob>stems = 
    Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
  
  for (int i = 0; i < stems.size (); i++)
    {
      if (!Stem::is_invisible (stems[i]))
        return stems[i];
    }
  return 0;
}

Grob*
Beam::last_visible_stem (Grob *me) 
{
  Link_array<Grob>stems = 
    Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
  for (int i = stems.size (); i--;)
    {
      if (!Stem::is_invisible (stems[i]))
        return stems[i];
    }
  return 0;
}


/*
  [TODO]
  
  handle rest under beam (do_post: beams are calculated now)
  what about combination of collisions and rest under beam.

  Should lookup
    
    rest -> stem -> beam -> interpolate_y_position ()
*/
MAKE_SCHEME_CALLBACK (Beam, rest_collision_callback, 2);
SCM
Beam::rest_collision_callback (SCM element_smob, SCM axis)
{
  Grob *rest = unsmob_grob (element_smob);
  Axis a = (Axis) scm_to_int (axis);

  if (scm_is_number (rest->get_property ("staff-position")))
    return scm_int2num (0);
  
  assert (a == Y_AXIS);

  Grob *st = unsmob_grob (rest->get_property ("stem"));
  Grob *stem = st;
  if (!stem)
    return scm_make_real (0.0);
  Grob *beam = unsmob_grob (stem->get_property ("beam"));
  if (!beam
      || !Beam::has_interface (beam)
      || !Beam::visible_stem_count (beam))
    return scm_make_real (0.0);

  Drul_array<Real> pos (0, 0);
  SCM s = beam->get_property ("positions");
  if (ly_c_pair_p (s) && scm_is_number (ly_car (s)))
    pos = ly_scm2interval (s);
  Real staff_space = Staff_symbol_referencer::staff_space (rest);

  scale_drul (&pos, staff_space);
  

  Real dy = pos[RIGHT] - pos[LEFT];
  
  // ugh -> use commonx
  Real x0 = first_visible_stem (beam)->relative_coordinate (0, X_AXIS);
  Real dx = last_visible_stem (beam)->relative_coordinate (0, X_AXIS) - x0;
  Real slope = dy && dx ? dy/dx : 0;
  
  Direction d = Stem::get_direction (stem);
  Real stem_y = pos[LEFT] + (stem->relative_coordinate (0, X_AXIS) - x0) * slope;
  
  Real beam_translation = get_beam_translation (beam);
  Real beam_thickness = Beam::get_thickness (beam);
  
  int beam_count = get_direction_beam_count (beam, d);
  Real height_of_my_beams = beam_thickness / 2
    + (beam_count - 1) * beam_translation;
  Real beam_y = stem_y - d * height_of_my_beams;

  Grob *common_y = rest->common_refpoint (beam, Y_AXIS);

  Real rest_dim = rest->extent (common_y, Y_AXIS)[d];
  Real minimum_distance =
    staff_space * robust_scm2double (rest->get_property ("minimum-distance"), 0.0);

  Real shift = d * ( ((beam_y - d * minimum_distance) - rest_dim) * d  <? 0.0);

  shift /= staff_space;
  Real rad = Staff_symbol_referencer::line_count (rest) * staff_space / 2;

  /* Always move discretely by half spaces */
  shift = ceil (fabs (shift * 2.0)) / 2.0 * sign (shift);

  /* Inside staff, move by whole spaces*/
  if ( (rest->extent (common_y, Y_AXIS)[d] + staff_space * shift) * d
      < rad
      || (rest->extent (common_y, Y_AXIS)[-d] + staff_space * shift) * -d
      < rad)
    shift = ceil (fabs (shift)) *sign (shift);

  return scm_make_real (staff_space * shift);
}

bool
Beam::is_knee (Grob* me)
{
  SCM k = me->get_property ("knee");
  if (scm_is_bool (k))
    return ly_scm2bool (k);

  bool knee = false;
  int d = 0;
  for (SCM s = me->get_property ("stems"); ly_c_pair_p (s); s = ly_cdr (s))
    {
      Direction dir = get_grob_direction (unsmob_grob (ly_car (s)));
      if (d && d != dir)
        {
          knee = true;
          break;
        }
      d = dir;
    }
  
  me->set_property ("knee", ly_bool2scm (knee));

  return knee;
}

int
Beam::get_direction_beam_count (Grob *me, Direction d )
{
  Link_array<Grob>stems = 
    Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
  int bc = 0;
  
  for (int i = stems.size (); i--;)
    {
      /*
        Should we take invisible stems into account?
       */
      if (Stem::get_direction (stems[i]) == d)
        bc = bc >? (Stem::beam_multiplicity (stems[i]).length () + 1);
    }

  return bc;
}


ADD_INTERFACE (Beam, "beam-interface",
               "A beam. \n\n"
               "The @code{thickness} property is the weight of beams, and is measured "
               "in  staffspace"
               ,
               "knee positioning-done position-callbacks "
               "concaveness dir-function quant-score auto-knee-gap gap "
               "gap-count chord-tremolo beamed-stem-shorten shorten least-squares-dy "
               "damping inspect-quants flag-width-function neutral-direction positions space-function "
               "thickness");