CVSROOT:        /cvsroot/lilypond
Module name:    lilypond
Branch:         lilypond_2_6
Changes by:     Han-Wen Nienhuys <[EMAIL PROTECTED]>    05/08/04 15:57:47

Modified files:
        .              : ChangeLog 
        lily           : beam.cc 

Log message:
        (shift_region_to_valid): prevent division by
        zero. Fixes beams across line breaks with 1 stem after the break.

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/lilypond/lilypond/ChangeLog.diff?only_with_tag=lilypond_2_6&tr1=1.3836.2.17&tr2=1.3836.2.18&r1=text&r2=text
http://savannah.gnu.org/cgi-bin/viewcvs/lilypond/lilypond/lily/beam.cc.diff?only_with_tag=lilypond_2_6&tr1=1.302&tr2=1.302.2.1&r1=text&r2=text

Patches:
Index: lilypond/ChangeLog
diff -u lilypond/ChangeLog:1.3836.2.17 lilypond/ChangeLog:1.3836.2.18
--- lilypond/ChangeLog:1.3836.2.17      Thu Aug  4 11:11:29 2005
+++ lilypond/ChangeLog  Thu Aug  4 15:57:47 2005
@@ -1,5 +1,10 @@
 2005-08-04  Han-Wen Nienhuys  <[EMAIL PROTECTED]>
- 
+
+       * lily/beam.cc (shift_region_to_valid): prevent division by
+       zero. Fixes beams across line breaks with 1 stem after the break.  
+
+       * VERSION: release 2.6.3
+       
        * lily/auto-beam-engraver.cc (derived_mark): new method. Yes. We
        have to protect even those unlikely-to-be-corrupted data members.  
   
Index: lilypond/lily/beam.cc
diff -u /dev/null lilypond/lily/beam.cc:1.302.2.1
--- /dev/null   Thu Aug  4 15:57:48 2005
+++ lilypond/lily/beam.cc       Thu Aug  4 15:57:47 2005
@@ -0,0 +1,1413 @@
+/*
+  beam.cc -- implement Beam
+
+  source file of the GNU LilyPond music typesetter
+
+  (c) 1997--2005 Han-Wen Nienhuys <[EMAIL PROTECTED]>
+  Jan Nieuwenhuizen <[EMAIL PROTECTED]>
+*/
+
+/*
+  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 "beam.hh"
+#include "interval-set.hh"
+#include "directional-element-interface.hh"
+#include "beaming.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-interface.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"); scm_is_pair (s); s = scm_cdr (s))
+    {
+      Grob *stem = unsmob_grob (scm_car (s));
+      m = max (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)
+    {
+      SCM stems = me->get_property ("stems");
+      if (scm_ilength (stems) == 1)
+       {
+         me->warning (_ ("removing beam with less than two stems"));
+
+         unsmob_grob (scm_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 (scm_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 = scm_car (right_beaming); scm_is_pair (s); s = scm_cdr (s))
+       {
+         int k = -right_dir * scm_to_int (scm_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
+    = extract_grob_array (me, ly_symbol2scm ("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 (scm_is_pair (last_beaming) && scm_is_pair (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 (; scm_is_pair (s); s = scm_cdr (s))
+               {
+                 int new_beam_pos
+                   = start_point - this_dir * scm_to_int (scm_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 = scm_cdr (this_beaming);
+         for (; scm_is_pair (s); s = scm_cdr (s))
+           {
+             int np = -this_dir * scm_to_int (scm_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 (scm_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
+    = extract_grob_array (me, ly_symbol2scm ("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 positions?");
+      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_layout ()->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) ? scm_cdr (last_beaming) : SCM_EOL;
+      SCM right = st ? scm_car (this_beaming) : SCM_EOL;
+
+      Array<int> full_beams;
+      Array<int> lfliebertjes;
+      Array<int> rfliebertjes;
+
+      for (SCM s = left;
+          scm_is_pair (s); s = scm_cdr (s))
+       {
+         int b = scm_to_int (scm_car (s));
+         if (scm_c_memq (scm_car (s), right) != SCM_BOOL_F)
+           {
+             full_beams.push (b);
+           }
+         else
+           {
+             lfliebertjes.push (b);
+           }
+       }
+      for (SCM s = right;
+          scm_is_pair (s); s = scm_cdr (s))
+       {
+         int b = scm_to_int (scm_car (s));
+         if (scm_c_memq (scm_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_layout ()->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 = min (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 = min (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_layout ()->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_interface::interpret_markup
+                                   (me->get_layout ()->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
+    = extract_grob_array (me, ly_symbol2scm ("stems"));
+
+  for (int i = 0; i < stems.size (); i++)
+    do
+      {
+       Grob *s = stems[i];
+       Direction sd = get_grob_direction (s);
+
+       int center_distance = max (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
+    = extract_grob_array (me, ly_symbol2scm ("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);
+    }
+}
+
+/*
+  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.
+
+
+  TODO:
+
+  this routine should take into account the stemlength scoring
+  of a possible knee/nonknee beam.
+*/
+void
+Beam::consider_auto_knees (Grob *me)
+{
+  SCM scm = me->get_property ("auto-knee-gap");
+  if (!scm_is_number (scm))
+    return;
+
+  Interval_set gaps;
+
+  gaps.set_full ();
+
+  Link_array<Grob> stems
+    = extract_grob_array (me, ly_symbol2scm ("stems"));
+
+  Grob *common = common_refpoint_of_array (stems, me, Y_AXIS);
+  Real staff_space = Staff_symbol_referencer::staff_space (me);
+
+  Array<Interval> head_extents_array;
+  for (int i = 0; i < stems.size (); i++)
+    {
+      Grob *stem = stems[i];
+      if (Stem::is_invisible (stem))
+       continue;
+
+      Interval head_extents = Stem::head_positions (stem);
+      if (!head_extents.is_empty ())
+       {
+         head_extents[LEFT] += -1;
+         head_extents[RIGHT] += 1;
+         head_extents *= 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.
+         */
+         head_extents += stem->relative_coordinate (common, Y_AXIS);
+
+         if (to_dir (stem->get_property ("direction")))
+           {
+             Direction stemdir = to_dir (stem->get_property ("direction"));
+             head_extents[-stemdir] = -stemdir * infinity_f;
+           }
+       }
+      head_extents_array.push (head_extents);
+
+      gaps.remove_interval (head_extents);
+    }
+
+  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;
+       }
+    }
+
+  Real beam_translation = get_beam_translation (me);
+  Real beam_thickness = Beam::get_thickness (me);
+  int beam_count = Beam::get_beam_count (me);
+  Real height_of_beams = beam_thickness / 2
+    + (beam_count - 1) * beam_translation;
+  Real threshold = scm_to_double (scm) + height_of_beams;
+
+  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 head_extents = head_extents_array[j++];
+
+         Direction d = (head_extents.center () < max_gap.center ())
+           ? UP : DOWN;
+
+         stem->set_property ("direction", scm_int2num (d));
+
+         head_extents.intersect (max_gap);
+         assert (head_extents.is_empty () || head_extents.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 (!me->is_live ())
+    return;
+  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 (scm_car (s) == SCM_BOOL_F)
+    {
+      // one wonders if such genericity is necessary  --hwn.
+      SCM callbacks = me->get_property ("position-callbacks");
+      for (SCM i = callbacks; scm_is_pair (i); i = scm_cdr (i))
+       scm_call_1 (scm_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) * max (fabs (*dy),
+                             min (min (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
+    = extract_grob_array (me, ly_symbol2scm ("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
+    = extract_grob_array (me, ly_symbol2scm ("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 = dx ?  dy / dx : 0.0;
+
+  /*
+    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 = scm_car (beaming); scm_is_pair (s); s = scm_cdr (s))
+    {
+      if (scm_c_memq (scm_car (s), scm_cdr (beaming)) != SCM_BOOL_F)
+
+       l.add_point (scm_to_int (scm_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
+    = extract_grob_array (me, ly_symbol2scm ("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
+    = extract_grob_array (me, ly_symbol2scm ("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 = min (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
+    = extract_grob_array (me, ly_symbol2scm ("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
+    = extract_grob_array (me, ly_symbol2scm ("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
+    = extract_grob_array (me, ly_symbol2scm ("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
+    = extract_grob_array (me, ly_symbol2scm ("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);
+  (void) axis;
+
+  if (scm_is_number (rest->get_property ("staff-position")))
+    return scm_int2num (0);
+
+  assert (scm_to_int (axis) == 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 (scm_is_pair (s) && scm_is_number (scm_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);
+
+  /*
+    TODO: this is not strictly correct for 16th knee beams.
+  */
+  int beam_count
+    = Stem::beam_multiplicity (stem).length () + 1;
+
+  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 (stem->get_property 
("stemlet-length"), 0.0)
+                      + robust_scm2double (rest->get_property 
("minimum-distance"), 0.0));
+
+  Real shift = d * min (((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"); scm_is_pair (s); s = scm_cdr (s))
+    {
+      Direction dir = get_grob_direction (unsmob_grob (scm_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
+    = extract_grob_array (me, ly_symbol2scm ("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 = max (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");
+


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