source file of the GNU LilyPond music typesetter
- (c) 1997--2002 Han-Wen Nienhuys <hanwen@cs.uu.nl>
+ (c) 1997--2004 Han-Wen Nienhuys <hanwen@cs.uu.nl>
Jan Nieuwenhuizen <janneke@gnu.org>
-
*/
/*
- [TODO]
+TODO:
- * Fix TODO
-
- * Junk stem_info.
-
- * Remove #'direction from beam. A beam has no direction per se.
- It may only set directions for stems.
+ - Determine auto knees based on positions if it's set by the user.
- * Rewrite stem_beams.
+ - the code is littered with * and / staff_space calls for
+ #'positions. Consider moving to real-world coordinates?
- * Use Number_pair i.s.o Interval to represent (yl, yr).
+ 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.
+*/
-/* snapnie now also works */
-#define SNAPNIE
#include <math.h> // tanh.
#include "spanner.hh"
#include "warn.hh"
-
-#define DEBUG_QUANTING 0
+bool debug_beam_quanting_flag;
#if DEBUG_QUANTING
#endif
-const int INTER_QUANT_PENALTY = 1000;
-const int SECONDARY_BEAM_DEMERIT = 15;
-const int STEM_LENGTH_DEMERIT_FACTOR = 5;
-// possibly ridiculous, but too short stems just won't do
-const int STEM_LENGTH_LIMIT_PENALTY = 5000;
-const int DAMPING_DIRECTIION_PENALTY = 800;
-const int MUSICAL_DIRECTION_FACTOR = 400;
-const int IDEAL_SLOPE_FACTOR = 10;
-
-
-static Real
-shrink_extra_weight (Real x)
-{
- return fabs (x) * ((x < 0) ? 1.5 : 1.0);
-}
-
void
Beam::add_stem (Grob *me, Grob *s)
{
s->add_dependency (me);
- assert (!Stem::beam_l (s));
+ assert (!Stem::get_beam (s));
s->set_grob_property ("beam", me->self_scm ());
add_bound_item (dynamic_cast<Spanner*> (me), dynamic_cast<Item*> (s));
}
+
Real
-Beam::get_interbeam (Grob *me)
+Beam::get_thickness (Grob * me)
+{
+ return robust_scm2double (me->get_grob_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_grob_property ("space-function");
- SCM s = gh_call2 (func, me->self_scm (), gh_int2scm (get_multiplicity (me)));
- return gh_scm2double (s);
+
+ if (gh_procedure_p (func))
+ {
+ SCM s = gh_call2 (func, me->self_scm (), scm_int2num (get_beam_count (me)));
+ return gh_scm2double (s);
+ }
+ else
+ {
+ return 0.81;
+ }
}
-/*
- Maximum multiplicity.
- */
+/* Maximum beam_count. */
int
-Beam::get_multiplicity (Grob *me)
+Beam::get_beam_count (Grob *me)
{
int m = 0;
for (SCM s = me->get_grob_property ("stems"); gh_pair_p (s); s = ly_cdr (s))
{
- Grob *sc = unsmob_grob (ly_car (s));
-
- if (Stem::has_interface (sc))
- m = m >? Stem::beam_count (sc, LEFT) >? Stem::beam_count (sc, RIGHT);
+ 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 multiplicity)
+Beam::space_function (SCM smob, SCM beam_count)
{
Grob *me = unsmob_grob (smob);
Real staff_space = Staff_symbol_referencer::staff_space (me);
- Real line = me->paper_l ()->get_var ("linethickness");
- Real thickness = gh_scm2double (me->get_grob_property ("thickness"))
- * staff_space;
+ Real line = Staff_symbol_referencer::line_thickness (me);
+ Real thickness = get_thickness (me);
- Real interbeam = gh_scm2int (multiplicity) < 4
+ Real beam_translation = gh_scm2int (beam_count) < 4
? (2*staff_space + line - thickness) / 2.0
: (3*staff_space + line - thickness) / 3.0;
- return gh_double2scm (interbeam);
+ return gh_double2scm (beam_translation);
}
{
me->warning (_ ("Beam has less than two stems. Removing beam."));
- unsmob_grob (gh_car (stems))->remove_grob_property ("beam");
+ unsmob_grob (gh_car (stems))->set_grob_property ("beam", SCM_EOL);
me->suicide ();
return SCM_UNSPECIFIED;
{
Direction d = get_default_dir (me);
- consider_auto_knees (me, d);
+ 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 (gh_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 = gh_car (right_beaming); gh_pair_p (s); s = gh_cdr (s))
+ {
+ int k = - right_dir * gh_scm2int (gh_car (s)) + i;
+ if (scm_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_grob_property ("beaming");
+
+ Direction this_dir = get_grob_direction (this_stem);
+ if (gh_pair_p (last_beaming) && gh_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 (; gh_pair_p (s); s = gh_cdr (s))
+ {
+ int new_beam_pos =
+ start_point - this_dir * gh_scm2int (gh_car (s));
+
+ new_slice.add_point (new_beam_pos);
+ gh_set_car_x (s, scm_int2num (new_beam_pos));
+ }
+
+
+ }
+ while (flip (&d) != LEFT);
+
+ if (!new_slice.is_empty ())
+ last_int = new_slice;
+ }
+ else
+ {
+ gh_set_car_x ( this_beaming, SCM_EOL);
+ SCM s = gh_cdr (this_beaming);
+ for (; gh_pair_p (s); s = gh_cdr (s))
+ {
+ int np = - this_dir * gh_scm2int (gh_car(s));
+ gh_set_car_x (s, scm_int2num (np));
+ last_int.add_point (np);
+ }
+ }
+
+ if (i == stems.size () -1)
+ {
+ gh_set_cdr_x (this_beaming, SCM_EOL);
+ }
+
+ if (scm_ilength (gh_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, brew_molecule, 1);
+SCM
+Beam::brew_molecule (SCM grob)
+{
+ Grob *me = unsmob_grob (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);
+
+ 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_grob_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 dydx = (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_grob_property ("gap"), 0.0);
+
+ Molecule the_beam;
+ Real lt = me->get_paper ()->get_realvar (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_grob_property ("beaming") : SCM_EOL;
+ Real xposn = st ? st->relative_coordinate (xcommon, X_AXIS) : 0.0;
+ Real stem_width = st ? robust_scm2double (st->get_grob_property ("thickness"), 1.0) *lt : 0 ;
+ Direction stem_dir = st ? to_dir (st->get_grob_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) ? gh_cdr (last_beaming) : SCM_EOL;
+ SCM right = st ? gh_car (this_beaming) : SCM_EOL;
+
+ Array<int> full_beams;
+ Array<int> lfliebertjes;
+ Array<int> rfliebertjes;
+
+ for (SCM s = left;
+ gh_pair_p (s); s =gh_cdr (s))
+ {
+ int b = gh_scm2int (gh_car (s));
+ if (scm_memq (gh_car(s), right) != SCM_BOOL_F)
+ {
+ full_beams.push (b);
+ }
+ else
+ {
+ lfliebertjes.push (b);
+ }
+ }
+ for (SCM s = right;
+ gh_pair_p (s); s =gh_cdr (s))
+ {
+ int b = gh_scm2int (gh_car (s));
+ if (scm_memq (gh_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_realvar (ly_symbol2scm ("blotdiameter"));
+ Molecule whole = Lookup::beam (dydx, w, thick, blot);
+ Molecule gapped;
+
+ int gap_count = 0;
+ if (gh_number_p (me->get_grob_property ("gap-count")))
+ {
+ gap_count = gh_scm2int (me->get_grob_property ("gap-count"));
+ gapped = Lookup::beam (dydx, 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--;)
+ {
+ Molecule 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 (dydx * (last_xposn - x0) + bdy * full_beams[j], Y_AXIS);
+
+ the_beam.add_molecule (b);
+ }
+
+
+
+ if (lfliebertjes.size() || rfliebertjes.size())
+ {
+ Real nw_f;
+
+ if (st)
+ {
+ int t = Stem::duration_log (st);
+
+ SCM proc = me->get_grob_property ("flag-width-function");
+ SCM result = gh_call1 (proc, scm_int2num (t));
+ nw_f = gh_scm2double (result);
+ }
+ else
+ nw_f = break_overshoot;
+
+ /* Half beam should be one note-width,
+ but let's make sure two half-beams never touch */
+ Real w = (i>0 && st) ? (xposn - last_xposn) : break_overshoot;
+ w = w/2 <? nw_f;
+
+ Molecule half = Lookup::beam (dydx, w, thick, blot);
+ for (int j = lfliebertjes.size(); j--;)
+ {
+ Molecule b (half);
+ b.translate_axis (last_xposn - x0, X_AXIS);
+ b.translate_axis (dydx * (last_xposn-x0) + bdy * lfliebertjes[j], Y_AXIS);
+ the_beam.add_molecule (b);
+ }
+ for (int j = rfliebertjes.size(); j--;)
+ {
+ Molecule b (half);
+ b.translate_axis (xposn - x0 - w , X_AXIS);
+ b.translate_axis (dydx * (xposn-x0 -w) + bdy * rfliebertjes[j], Y_AXIS);
+ the_beam.add_molecule (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_grob_property ("quant-score");
+ if (debug_beam_quanting_flag
+ && gh_string_p (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::font_alist_chain (me);
+
+ Molecule tm = *unsmob_molecule (Text_item::interpret_markup
+ (me->get_paper ()->self_scm (), properties, quant_score));
+ the_beam.add_at_edge (Y_AXIS, UP, tm, 5.0, 0);
+ }
+#endif
+
+
+
+ return the_beam.smobbed_copy();
+}
+
+
+
+
Direction
Beam::get_default_dir (Grob *me)
{
count[UP] = count[DOWN] = 0;
Direction d = DOWN;
- Link_array<Item> stems=
- Pointer_group_interface__extract_grobs (me, (Item*)0, "stems");
+ 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 = Directional_element_interface::get (s);
+ 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;
SCM func = me->get_grob_property ("dir-function");
SCM s = gh_call2 (func,
- gh_cons (gh_int2scm (count[UP]),
- gh_int2scm (count[DOWN])),
- gh_cons (gh_int2scm (total[UP]),
- gh_int2scm (total[DOWN])));
+ gh_cons (scm_int2num (count[UP]),
+ scm_int2num (count[DOWN])),
+ gh_cons (scm_int2num (total[UP]),
+ scm_int2num (total[DOWN])));
if (gh_number_p (s) && gh_scm2int (s))
return to_dir (s);
void
Beam::set_stem_directions (Grob *me, Direction d)
{
- Link_array<Item> stems
- =Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
+ 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 force = s->remove_grob_property ("dir-forced");
- if (!gh_boolean_p (force) || !gh_scm2bool (force))
- Directional_element_interface::set (s, d);
+
+ SCM forcedir = s->get_grob_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++;
+ }
+ }
+};
-/* Simplistic auto-knees; only consider vertical gap between two
- adjacent chords.
- `Forced' stem directions are ignored. If you don't want auto-knees,
- don't set, or unset auto-knee-gap. */
+/*
+ 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, Direction d)
+Beam::consider_auto_knees (Grob* me)
{
SCM scm = me->get_grob_property ("auto-knee-gap");
+ if (!gh_number_p (scm))
+ return ;
- if (gh_number_p (scm))
- {
- bool knee_b = false;
- Real knee_y = 0;
- Real staff_space = Staff_symbol_referencer::staff_space (me);
- Real gap = gh_scm2double (scm) / staff_space;
+ Real threshold = gh_scm2double (scm);
+
+ Int_set gaps;
+ gaps.set_full ();
- Link_array<Item> stems=
- Pointer_group_interface__extract_grobs (me, (Item*)0, "stems");
+ Link_array<Grob> stems=
+ Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
- Grob *common = me->common_refpoint (stems[0], Y_AXIS);
- for (int i=1; i < stems.size (); i++)
- if (!Stem::invisible_b (stems[i]))
- common = common->common_refpoint (stems[i], Y_AXIS);
-
- int l = 0;
- for (int i=1; i < stems.size (); i++)
- {
- if (!Stem::invisible_b (stems[i-1]))
- l = i - 1;
- if (Stem::invisible_b (stems[l]))
- continue;
- if (Stem::invisible_b (stems[i]))
- continue;
-
- Real left = Stem::extremal_heads (stems[l])[d]
- ->relative_coordinate (common, Y_AXIS);
- Real right = Stem::extremal_heads (stems[i])[-d]
- ->relative_coordinate (common, Y_AXIS);
+ 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::invisible_b (stem))
+ continue;
- Real dy = right - left;
+ Interval hps = Stem::head_positions (stem);
+ if(!hps.is_empty ())
+ {
+ hps[LEFT] += -1;
+ hps[RIGHT] += 1;
+ hps *= staff_space * 0.5 ;
- if (abs (dy) >= gap)
+ /*
+ 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_grob_property ("direction")))
{
- knee_y = (right + left) / 2;
- knee_b = true;
- break;
+ Direction stemdir = to_dir (stem->get_grob_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 (knee_b)
+ if (gap.length () >= max_gap_len)
{
- for (int i=0; i < stems.size (); i++)
- {
- if (Stem::invisible_b (stems[i]))
- continue;
- Item *s = stems[i];
- Real y = Stem::extremal_heads (stems[i])[d]
- ->relative_coordinate (common, Y_AXIS);
+ max_gap_len = gap.length();
+ max_gap = gap;
+ }
+ }
- Directional_element_interface::set (s, y < knee_y ? UP : DOWN);
- s->set_grob_property ("dir-forced", SCM_BOOL_T);
- }
+ if (max_gap_len > threshold)
+ {
+ int j = 0;
+ for (int i = 0; i < stems.size(); i++)
+ {
+ Grob* stem = stems[i];
+ if (Stem::invisible_b (stem))
+ continue;
+
+ Interval hps = hps_array[j++];
+
+
+ Direction d = (hps.center () < max_gap.center()) ?
+ UP : DOWN ;
+
+ stem->set_grob_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
-
- TODO:
-
- why is shorten stored in beam, and not directly in stem?
+
+ This is done in beam because the shorten has to be uniform over the
+ entire beam.
*/
void
-Beam::set_stem_shorten (Grob *m)
+Beam::set_stem_shorten (Grob *me)
{
- Spanner*me = dynamic_cast<Spanner*> (m);
-
- Real forced_fraction = forced_stem_count (me) / visible_stem_count (me);
+ /*
+ shortening looks silly for x staff beams
+ */
+ if (knee_b(me))
+ return ;
+
+ Real forced_fraction = 1.0 * forced_stem_count (me)
+ / visible_stem_count (me);
- int multiplicity = get_multiplicity (me);
+ int beam_count = get_beam_count (me);
- SCM shorten = me->get_grob_property ("beamed-stem-shorten");
- if (shorten == SCM_EOL)
+ SCM shorten_list = me->get_grob_property ("beamed-stem-shorten");
+ if (shorten_list == SCM_EOL)
return;
- int sz = scm_ilength (shorten);
-
Real staff_space = Staff_symbol_referencer::staff_space (me);
- SCM shorten_elt = scm_list_ref (shorten,
- gh_int2scm (multiplicity <? (sz - 1)));
+
+ SCM shorten_elt =
+ robust_list_ref (beam_count -1, shorten_list);
Real shorten_f = gh_scm2double (shorten_elt) * staff_space;
/* your similar cute comment here */
}
/* Call list of y-dy-callbacks, that handle setting of
- grob-properties y, dy.
-
- User may set grob-properties: y-position-hs and height-hs
- (to be fixed) that override the calculated y and dy.
-
- Because y and dy cannot be calculated and quanted separately, we
- always calculate both, then check for user override. */
+ grob-properties
+
+*/
MAKE_SCHEME_CALLBACK (Beam, after_line_breaking, 1);
SCM
Beam::after_line_breaking (SCM smob)
{
Grob *me = unsmob_grob (smob);
-
- /* Copy to mutable list. */
- SCM s = ly_deep_copy (me->get_grob_property ("positions"));
- me->set_grob_property ("positions", s);
-
- if (ly_car (s) != SCM_BOOL_F)
- return SCM_UNSPECIFIED;
-
- // one wonders if such genericity is necessary --hwn.
- SCM callbacks = me->get_grob_property ("position-callbacks");
- for (SCM i = callbacks; gh_pair_p (i); i = ly_cdr (i))
- gh_call1 (ly_car (i), smob);
- set_stem_lengths (me);
+ position_beam (me);
return SCM_UNSPECIFIED;
}
-struct Quant_score
+void
+Beam::position_beam (Grob *me)
{
- Real yl;
- Real yr;
- Real demerits;
-};
+ if (to_boolean (me->get_grob_property ("positioning-done")))
+ return ;
+ me->set_grob_property ("positioning-done", SCM_BOOL_T);
-/*
- TODO:
-
- - Make all demerits customisable
+ /* Copy to mutable list. */
+ SCM s = ly_deep_copy (me->get_grob_property ("positions"));
+ me->set_grob_property ("positions", s);
- - One sensible check per demerit (what's this --hwn)
+ if (ly_car (s) == SCM_BOOL_F)
+ {
+ // one wonders if such genericity is necessary --hwn.
+ SCM callbacks = me->get_grob_property ("position-callbacks");
+ for (SCM i = callbacks; gh_pair_p (i); i = ly_cdr (i))
+ gh_call1 (ly_car (i), me->self_scm ());
+ }
- - Add demerits for quants per se, as to forbid a specific quant
- entirely
+ set_stem_lengths (me);
+}
-*/
-MAKE_SCHEME_CALLBACK (Beam, quanting, 1);
+
+/*
+ Compute a first approximation to the beam slope.
+ */
+MAKE_SCHEME_CALLBACK (Beam, least_squares, 1);
SCM
-Beam::quanting (SCM smob)
+Beam::least_squares (SCM smob)
{
Grob *me = unsmob_grob (smob);
- SCM s = me->get_grob_property ("positions");
- Real yl = gh_scm2double (gh_car (s));
- Real yr = gh_scm2double (gh_cdr (s));
-
- Real ss = Staff_symbol_referencer::staff_space (me);
- Real thickness = gh_scm2double (me->get_grob_property ("thickness")) / ss;
- Real slt = me->paper_l ()->get_var ("linethickness") / ss;
-
-
- SCM sdy = me->get_grob_property ("least-squares-dy");
- Real dy_mus = gh_number_p (sdy) ? gh_scm2double (sdy) : 0.0;
-
- Real straddle = 0.0;
- Real sit = (thickness - slt) / 2;
- Real inter = 0.5;
- Real hang = 1.0 - (thickness - slt) / 2;
- Real quants [] = {straddle, sit, inter, hang };
-
- int num_quants = int (sizeof (quants)/sizeof (Real));
- Array<Real> quantsl;
- Array<Real> quantsr;
-
- /*
- going to REGION_SIZE == 2, yields another 0.6 second with
- wtk1-fugue2.
-
-
- (result indexes between 70 and 575) ? --hwn.
-
- */
-
-
+ int count = visible_stem_count (me);
+ Interval pos (0, 0);
- /*
- Do stem computations. These depend on YL and YR linearly, so we can
- precompute for every stem 2 factors.
- */
- Link_array<Grob> stems=
- Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
- Array<Stem_info> stem_infos;
- Array<Real> lbase_lengths;
- Array<Real> rbase_lengths;
-
- Drul_array<bool> dirs_found(0,0);
- for (int i= 0; i < stems.size(); i++)
+ if (count < 1)
{
- Grob*s = stems[i];
- stem_infos.push (Stem::calc_stem_info (s));
- dirs_found[stem_infos.top ().dir_] = true;
-
-#ifdef SNAPNIE
- Real b = calc_stem_y (me, s, Interval (1,0), false);
- lbase_lengths.push (b);
-
- Real a = calc_stem_y (me, s, Interval (0,1), false);
- rbase_lengths.push (a);
-#endif
+ me->set_grob_property ("positions", ly_interval2scm (pos));
+ return SCM_UNSPECIFIED;
}
- Direction ldir = Direction (stem_infos[0].dir_);
- Direction rdir = Direction (stem_infos.top ().dir_);
- bool knee_b = dirs_found[LEFT] && dirs_found[RIGHT];
-
- /*
- This
-
- \score {
- \context Staff \notes {
- \stemDown [e'8 e e']
- }
- }
-
- breaks with REGION_SIZE < 4
- */
- int REGION_SIZE = 4;
-
- /*
- Knees are harder, lets try some more possibilities for knees.
- */
- if (knee_b)
- REGION_SIZE += 2;
-
- for (int i = -REGION_SIZE ; i < REGION_SIZE; i++)
- for (int j = 0; j < num_quants; j++)
- {
- quantsl.push (i + quants[j] + int (yl));
- quantsr.push (i + quants[j] + int (yr));
- }
-
- Array<Quant_score> qscores;
-
- for (int l =0; l < quantsl.size (); l++)
- for (int r =0; r < quantsr.size (); r++)
- {
- Quant_score qs;
- qs.yl = quantsl[l];
- qs.yr = quantsr[r];
- qs.demerits = 0.0;
-
- qscores.push (qs);
- }
-
- /*
- This is a longish function, but we don't separate this out into
- neat modular separate subfunctions, as the subfunctions would be
- called for many values of YL, YR. By precomputing various
- parameters outside of the loop, we can save a lot of time.
-
- */
- for (int i = qscores.size (); i--;)
- if (qscores[i].demerits < 100)
- {
- qscores[i].demerits
- += score_slopes_dy (me, qscores[i].yl, qscores[i].yr,
- dy_mus, yr- yl);
- }
-
- Real rad = Staff_symbol_referencer::staff_radius (me);
- int multiplicity = get_multiplicity (me);
- Real interbeam = multiplicity < 4
- ? (2*ss + slt - thickness) / 2.0
- : (3*ss + slt - thickness) / 3.0;
-
- for (int i = qscores.size (); i--;)
- if (qscores[i].demerits < 100)
- {
- qscores[i].demerits
- += score_forbidden_quants (me, qscores[i].yl, qscores[i].yr,
- rad, slt, thickness, interbeam,
- multiplicity, ldir, rdir);
- }
-
-
- for (int i = qscores.size (); i--;)
- if (qscores[i].demerits < 100)
- {
- qscores[i].demerits
- += score_stem_lengths (stems, stem_infos,
- lbase_lengths, rbase_lengths,
- knee_b,
- me, qscores[i].yl, qscores[i].yr);
- }
-
-
- Real best = 1e6;
- int best_idx = -1;
- for (int i = qscores.size (); i--;)
- {
- if (qscores[i].demerits < best)
- {
- best = qscores [i].demerits ;
- best_idx = i;
- }
- }
+ 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);
- me->set_grob_property ("positions",
- gh_cons (gh_double2scm (qscores[best_idx].yl),
- gh_double2scm (qscores[best_idx].yr))
- );
-
-#if DEBUG_QUANTING
-
- // debug quanting
- me->set_grob_property ("quant-score",
- gh_double2scm (qscores[best_idx].demerits));
- me->set_grob_property ("best-idx", gh_int2scm (best_idx));
-#endif
-
- return SCM_UNSPECIFIED;
-}
-
-Real
-Beam::score_stem_lengths (Link_array<Grob>stems,
- Array<Stem_info> stem_infos,
- Array<Real> left_factor,
- Array<Real> right_factor,
- bool knee,
- Grob*me,
- Real yl, Real yr)
-{
- Real demerit_score = 0.0 ;
- Real pen = STEM_LENGTH_LIMIT_PENALTY;
+ Grob *fvs = first_visible_stem (me);
+ Grob *lvs = last_visible_stem (me);
-#if 0
- if (knee)
- pen = sqrt(pen);
-#endif
+ 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 (0, X_AXIS);
- Real dx = last_visible_stem (me)->relative_coordinate (0, X_AXIS) - x0;
-
+ Real x0 = first_visible_stem (me)->relative_coordinate (commonx, X_AXIS);
for (int i=0; i < stems.size (); i++)
{
Grob* s = stems[i];
- if (Stem::invisible_b (s))
- continue;
-
-#ifdef SNAPNIE
- /* for a two-stemmed, interstaff beam knee up/down:
- \score {
- \context PianoStaff \notes\relative c' <
- \context Staff = lh {
- \stemDown [c8 \translator Staff = rh \stemUp a'' ]
- }
- \context Staff = rh \relative c' s4
- >
- }
-
- with yl = -5.8 (about ideal)
- and yr = -1 (ridiculous pos)
- this yields current_y = -8.1 (about ideal) */
-
- Real current_y =
- yl * left_factor[i] + right_factor[i]* yr;
-#else
- Real f = (s->relative_coordinate (0, X_AXIS) - x0) / dx;
- Real current_y = yl + f * (yr - yl);
-#endif
-
- Stem_info info = stem_infos[i];
- Direction d = info.dir_;
-
- demerit_score += pen
- * ( 0 >? (info.dir_ * (info.shortest_y_ - current_y)));
-
- demerit_score += STEM_LENGTH_DEMERIT_FACTOR
- * shrink_extra_weight (d * current_y - info.dir_ * info.ideal_y_);
- }
-
- demerit_score *= 2.0 / stems.size ();
-
- return demerit_score;
-}
-
-Real
-Beam::score_slopes_dy (Grob *me,
- Real yl, Real yr,
- Real dy_mus, Real dy_damp)
-{
- Real dy = yr - yl;
-
- Real dem = 0.0;
- if (sign (dy_damp) != sign (dy))
- {
- dem += DAMPING_DIRECTIION_PENALTY;
+ 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;
- dem += MUSICAL_DIRECTION_FACTOR * (0 >? (fabs (dy) - fabs (dy_mus)));
- dem += shrink_extra_weight (fabs (dy_damp) - fabs (dy))* IDEAL_SLOPE_FACTOR;
-
- return dem;
-}
-
-static Real
-my_modf (Real x)
-{
- return x - floor (x);
-}
-
-Real
-Beam::score_forbidden_quants (Grob*me,
- Real yl, Real yr,
- Real rad,
- Real slt,
- Real thickness, Real interbeam,
- int multiplicity,
- Direction ldir, Direction rdir)
-{
- Real dy = yr - yl;
-
- Real dem = 0.0;
- if (fabs (yl) < rad && fabs ( my_modf (yl) - 0.5) < 1e-3)
- dem += INTER_QUANT_PENALTY;
- if (fabs (yr) < rad && fabs ( my_modf (yr) - 0.5) < 1e-3)
- dem += INTER_QUANT_PENALTY;
-
- // todo: use multiplicity of outer stems.
- if (multiplicity >= 2)
+
+ Real y =0;
+ Real dydx = 0;
+ Real dy = 0;
+
+ if (!ideal.delta ())
{
-
- Real straddle = 0.0;
- Real sit = (thickness - slt) / 2;
- Real inter = 0.5;
- Real hang = 1.0 - (thickness - slt) / 2;
-
-
- if (fabs (yl - ldir * interbeam) < rad
- && fabs (my_modf (yl) - inter) < 1e-3)
- dem += SECONDARY_BEAM_DEMERIT;
- if (fabs (yr - rdir * interbeam) < rad
- && fabs (my_modf (yr) - inter) < 1e-3)
- dem += SECONDARY_BEAM_DEMERIT;
-
- Real eps = 1e-3;
-
- /*
- Can't we simply compute the distance between the nearest
- staffline and the secondary beam? That would get rid of the
- silly case analysis here (which is probably not when we have
- different beam-thicknesses.)
-
- --hwn
- */
+ 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.
- // hmm, without Interval/Drul_array, you get ~ 4x same code...
- if (fabs (yl - ldir * interbeam) < rad + inter)
+ For that case, we apply artificial slope */
+ if (!ideal[LEFT] && chord.delta () && count == 2)
{
- if (ldir == UP && dy <= eps
- && fabs (my_modf (yl) - sit) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
-
- if (ldir == DOWN && dy >= eps
- && fabs (my_modf (yl) - hang) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
+ /* FIXME. -> UP */
+ Direction d = (Direction) (sign (chord.delta ()) * UP);
+ pos[d] = get_thickness (me) / 2;
+ pos[-d] = - pos[d];
}
-
- if (fabs (yr - rdir * interbeam) < rad + inter)
+ else
{
- if (rdir == UP && dy >= eps
- && fabs (my_modf (yr) - sit) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
-
- if (rdir == DOWN && dy <= eps
- && fabs (my_modf (yr) - hang) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
+ pos = ideal;
}
-
- if (multiplicity >= 3)
+
+ /*
+ 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_grob_property ("least-squares-dy",
+ gh_double2scm (pos[RIGHT] - pos[LEFT]));
+ }
+ else
+ {
+ Array<Offset> ideals;
+ for (int i=0; i < stems.size (); i++)
{
- if (fabs (yl - 2 * ldir * interbeam) < rad + inter)
- {
- if (ldir == UP && dy <= eps
- && fabs (my_modf (yl) - straddle) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
-
- if (ldir == DOWN && dy >= eps
- && fabs (my_modf (yl) - straddle) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
- }
-
- if (fabs (yr - 2 * rdir * interbeam) < rad + inter)
- {
- if (rdir == UP && dy >= eps
- && fabs (my_modf (yr) - straddle) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
-
- if (rdir == DOWN && dy <= eps
- && fabs (my_modf (yr) - straddle) < eps)
- dem += SECONDARY_BEAM_DEMERIT;
- }
+ Grob* s = stems[i];
+ if (Stem::invisible_b (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 (&dydx, &y, ideals);
+
+ dy = dydx * dx;
+ me->set_grob_property ("least-squares-dy", gh_double2scm (dy));
+ pos = Interval (y, (y+dy));
}
+
+ /*
+ "position" is relative to the staff.
+ */
+ scale_drul (&pos, 1/ Staff_symbol_referencer::staff_space (me));
- return dem;
+ me->set_grob_property ("positions", ly_interval2scm (pos));
+
+ return SCM_UNSPECIFIED;
}
-
-MAKE_SCHEME_CALLBACK (Beam, least_squares, 1);
+/*
+ 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::least_squares (SCM smob)
+Beam::shift_region_to_valid (SCM grob)
{
- Grob *me = unsmob_grob (smob);
+ 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);
- int count = visible_stem_count (me);
- Interval pos (0, 0);
-
- if (count <= 1)
+ 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++)
{
- me->set_grob_property ("positions", ly_interval2scm (pos));
- return SCM_UNSPECIFIED;
+ Grob* s = stems[i];
+
+ Real x = s->relative_coordinate (commonx, X_AXIS) - x0;
+ x_posns.push (x);
}
- Interval ideal (Stem::calc_stem_info (first_visible_stem (me)).ideal_y_,
- Stem::calc_stem_info (last_visible_stem (me)).ideal_y_);
+ 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_grob_property ("positions"));
+
+ scale_drul (&pos, Staff_symbol_referencer::staff_space (me));
- if (!ideal.delta ())
+ Real dy = pos[RIGHT] - pos[LEFT];
+ Real y = pos[LEFT];
+ Real dydx =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++)
{
- Interval chord (Stem::chord_start_y (first_visible_stem (me)),
- Stem::chord_start_y (last_visible_stem (me)));
+ Grob* s = stems[i];
+ if (Stem::invisible_b (s))
+ continue;
+ Direction d = Stem::get_direction (s);
- /*
- TODO : use scoring for this.
+ Real left_y =
+ Stem::get_stem_info (s).shortest_y_
+ - dydx * x_posns [i];
- complicated, because we take stem-info.ideal for determining
- beam slopes.
-
+ /*
+ left_y is now relative to the stem S. We want relative to
+ ourselves, so translate:
*/
- /* Make simple beam on middle line have small tilt */
- if (!ideal[LEFT] && chord.delta () && count == 2)
- {
+ left_y +=
+ + s->relative_coordinate (commony, Y_AXIS)
+ - me->relative_coordinate (commony, Y_AXIS);
- /*
- FIXME. -> UP
- */
- Direction d = (Direction) (sign (chord.delta ()) * UP);
- pos[d] = gh_scm2double (me->get_grob_property ("thickness")) / 2;
- // * dir;
- pos[-d] = - pos[d];
- }
- else
- {
- pos = ideal;
- }
+ Interval flp ;
+ flp.set_full ();
+ flp[-d] = left_y;
+
+ feasible_left_point.intersect (flp);
}
- else
+
+ if (feasible_left_point.is_empty ())
{
- Array<Offset> ideals;
-
- // ugh -> use commonx
- Real x0 = first_visible_stem (me)->relative_coordinate (0, X_AXIS);
- Link_array<Item> stems=
- Pointer_group_interface__extract_grobs (me, (Item*)0, "stems");
-
- for (int i=0; i < stems.size (); i++)
- {
- Item* s = stems[i];
- if (Stem::invisible_b (s))
- continue;
- ideals.push (Offset (s->relative_coordinate (0, X_AXIS) - x0,
- Stem::calc_stem_info (s).ideal_y_));
- }
- Real y;
- Real dydx;
- minimise_least_squares (&dydx, &y, ideals);
-
- Real dx = last_visible_stem (me)->relative_coordinate (0, X_AXIS) - x0;
- Real dy = dydx * dx;
- me->set_grob_property ("least-squares-dy", gh_double2scm (dy));
-
- pos = Interval (y, (y+dy));
+ warning (_("Not sure that we can find a nice beam slope (no viable initial configuration found)."));
}
-
+ 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_grob_property ("positions", ly_interval2scm (pos));
return SCM_UNSPECIFIED;
}
+
MAKE_SCHEME_CALLBACK (Beam, check_concave, 1);
SCM
Beam::check_concave (SCM smob)
{
Grob *me = unsmob_grob (smob);
- Link_array<Item> stems =
- Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
+ Link_array<Grob> stems =
+ Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
for (int i = 0; i < stems.size ();)
{
concave *= dir;
concaveness2 = concave / (stems.size () - 2);
- /* ugh: this is the a kludge to get
- input/regression/beam-concave.ly to behave as
- baerenreiter. */
+ /*
+
+ ugh: this is the a kludge to get
+ input/regression/beam-concave.ly to behave as
+ baerenreiter.
+
+ */
/*
huh? we're dividing twice (which is not scalable) meaning that
/* TODO: some sort of damping iso -> plain horizontal */
if (concaveness1 || concaveness2 > r2)
{
- Interval pos = ly_scm2interval (me->get_grob_property ("positions"));
- Real r = pos.linear_combination (0);
- me->set_grob_property ("positions", ly_interval2scm (Interval (r, r)));
+ Drul_array<Real> pos = ly_scm2interval (me->get_grob_property ("positions"));
+ Real r = linear_combination (pos, 0);
+
+ r /= Staff_symbol_referencer::staff_space (me);
+ me->set_grob_property ("positions", ly_interval2scm (Drul_array<Real> (r, r)));
me->set_grob_property ("least-squares-dy", gh_double2scm (0));
}
if (damping)
{
- Interval pos = ly_scm2interval (me->get_grob_property ("positions"));
- Real dy = pos.delta ();
+ Drul_array<Real> pos = ly_scm2interval (me->get_grob_property ("positions"));
+ scale_drul (&pos, Staff_symbol_referencer::staff_space (me));
- // ugh -> use commonx
- Real dx = last_visible_stem (me)->relative_coordinate (0, X_AXIS)
- - first_visible_stem (me)->relative_coordinate (0, X_AXIS);
+ 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 dydx = dy && dx ? dy/dx : 0;
dydx = 0.6 * tanh (dydx) / damping;
Real damped_dy = dydx * dx;
pos[LEFT] += (dy - damped_dy) / 2;
pos[RIGHT] -= (dy - damped_dy) / 2;
+
+ scale_drul (&pos, 1/Staff_symbol_referencer::staff_space (me));
me->set_grob_property ("positions", ly_interval2scm (pos));
}
}
/*
- Calculate the Y position of the stem-end, given the Y-left, Y-right
- in POS, and for stem S.
-
- If CORRECT, correct for multiplicity of beam in case of knees.
+ Report slice containing the numbers that are both in (car BEAMING)
+ and (cdr BEAMING)
*/
-Real
-Beam::calc_stem_y (Grob *me, Grob* s, Interval pos, bool correct)
+Slice
+where_are_the_whole_beams(SCM beaming)
{
- int beam_multiplicity = get_multiplicity (me);
- int stem_multiplicity = (Stem::duration_log (s) - 2) >? 0;
+ Slice l;
- int first_multiplicity = (Stem::duration_log (first_visible_stem (me))
- - 2) >? 0;
- int last_multiplicity = (Stem::duration_log (last_visible_stem (me))
- - 2) >? 0;
-
- Real thick = gh_scm2double (me->get_grob_property ("thickness"));
- Real interbeam = get_interbeam (me);
-
- // ugh -> use commonx
- Grob * fvs = first_visible_stem (me);
- Grob *lvs = last_visible_stem (me);
-
- Real x0 = fvs ? fvs->relative_coordinate (0, X_AXIS) : 0.0;
- Real dx = fvs ? lvs->relative_coordinate (0, X_AXIS) - x0 : 0.0;
- Real r = s->relative_coordinate (0, X_AXIS) - x0;
- Real dy = pos.delta ();
- Real stem_y = (dy && dx
- ? r / dx
- * dy
- : 0) + pos[LEFT];
-
- Direction my_dir = Directional_element_interface::get (s);
- Direction first_dir = fvs? Directional_element_interface::get (fvs) : my_dir;
-
- if (correct && my_dir != first_dir)
+ for( SCM s = gh_car (beaming); gh_pair_p (s) ; s = gh_cdr (s))
{
- /*
- WTF is happening here ?
-
- It looks as if this is some kind of fixup for multiple kneed
- beams to get a piece of stem at the #.
-
-
- x
- |
- =======|
- |======#
- |
- |
- x
-
- Rules for this kind of stuff are hairy. In any event, the
- current stem should look at the multiplicity of its
- predecessor.
-
- --hwn.
+ if (scm_memq (gh_car (s), gh_cdr (beaming)) != SCM_BOOL_F)
- */
-
- // FIXME, hairy stuff
- stem_y += my_dir * (thick / 2 + (beam_multiplicity - 1) * interbeam);
+ l.add_point (gh_scm2int (gh_car (s)));
+ }
- // huh, why not for first visible?
+ return l;
+}
- /*
- What the heck is happening here??
- */
- Grob *last_visible = last_visible_stem (me);
- if (last_visible)
- {
- if ( Staff_symbol_referencer::staff_symbol_l (s)
- != Staff_symbol_referencer::staff_symbol_l (last_visible))
- stem_y += Directional_element_interface::get (me)
- * (beam_multiplicity - stem_multiplicity) * interbeam;
- }
- else
- programming_error ("No last visible stem");
+/* 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_grob_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;
}
- return stem_y;
+
+ Real id = me->relative_coordinate (common[Y_AXIS], Y_AXIS)
+ - s->relative_coordinate (common[Y_AXIS], Y_AXIS);
+
+ return stem_y + id;
}
/*
void
Beam::set_stem_lengths (Grob *me)
{
- Link_array<Item> stems=
- Pointer_group_interface__extract_grobs (me, (Item*)0, "stems");
+ Link_array<Grob> stems=
+ Pointer_group_interface__extract_grobs (me, (Grob*)0, "stems");
- if (stems.size () <= 1)
+ if (!stems.size ())
return;
- Grob *common = me->common_refpoint (stems[0], Y_AXIS);
- for (int i=1; i < stems.size (); i++)
- if (!Stem::invisible_b (stems[i]))
- common = common->common_refpoint (stems[i], Y_AXIS);
-
- Interval pos = ly_scm2interval (me->get_grob_property ("positions"));
+ 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_grob_property ("positions"));
Real staff_space = Staff_symbol_referencer::staff_space (me);
+ scale_drul (&pos, staff_space);
- /*
- DOCUMENT THIS.
- */
-#if 0
- Real thick = gh_scm2double (me->get_grob_property ("thickness"));
- Direction dir = Directional_element_interface::get (me);
- bool ps_testing = to_boolean (ly_symbol2scm ("ps-testing"));
-#endif
+ bool gap = false;
+ Real thick =0.0;
+ if (gh_number_p (me->get_grob_property ("gap-count"))
+ &&gh_scm2int (me->get_grob_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++)
{
- Item* s = stems[i];
+ Grob* s = stems[i];
if (Stem::invisible_b (s))
continue;
- Real stem_y = calc_stem_y (me, s, pos, true);
+ bool french = to_boolean (s->get_grob_property ("french-beaming"));
+ Real stem_y = calc_stem_y (me, s, common,
+ xl, xr,
+ pos, french && s != lvs && s!= fvs);
-#if 0
- // doesn't play well with dvips
- if (ps_testing)
- if (Stem::get_direction (s) == dir)
- stem_y += Stem::get_direction (s) * thick / 2;
-#endif
-
- /* caution: stem measures in staff-positions */
- Real id = me->relative_coordinate (common, Y_AXIS)
- - stems[i]->relative_coordinate (common, Y_AXIS);
- Stem::set_stemend (s, (stem_y + id) / staff_space * 2);
+ /*
+ 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);
}
}
Direction d = LEFT;
for (int i=0; i < stems.size (); i++)
{
+ /*
+ Don't overwrite user settings.
+ */
+
do
{
- /* Don't overwrite user override (?) */
- if (Stem::beam_count (stems[i], d) == -1
- /* Don't set beaming for outside of outer stems */
- && ! (d == LEFT && i == 0)
- && ! (d == RIGHT && i == stems.size () -1))
+ /* 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_grob_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];
- Stem::set_beaming (stems[i], b, d);
+ if (i>0
+ && i < stems.size() -1
+ && Stem::invisible_b (st))
+ b = b <? beaming->infos_.elem(i).beams_i_drul_[-d];
+
+ Stem::set_beaming (st, b, d);
}
}
while (flip (&d) != LEFT);
}
}
-
-
-/*
- beams to go with one stem.
-
- FIXME: clean me up:
-
- The beam should be constructed by one function that knows where the
- X and Y points are, and only inspects the stems to obtain
- multiplicity and stem directions.
-
- */
-Molecule
-Beam::stem_beams (Grob *me, Item *here, Item *next, Item *prev, Real dydx)
-{
- // ugh -> use commonx
- if ((next
- && ! (next->relative_coordinate (0, X_AXIS)
- > here->relative_coordinate (0, X_AXIS)))
- || (prev
- && ! (prev->relative_coordinate (0, X_AXIS)
- < here->relative_coordinate (0, X_AXIS))))
- programming_error ("Beams are not left-to-right");
-
- Real thick = gh_scm2double (me->get_grob_property ("thickness"));
- Real bdy = get_interbeam (me);
-
- Molecule leftbeams;
- Molecule rightbeams;
-
- Real nw_f;
- if (!Stem::first_head (here))
- nw_f = 0;
- else
- {
- int t = Stem::duration_log (here);
-
- SCM proc = me->get_grob_property ("flag-width-function");
- SCM result = gh_call1 (proc, gh_int2scm (t));
- nw_f = gh_scm2double (result);
- }
-
-
- /* [Tremolo] beams on whole notes may not have direction set? */
- Direction dir = Directional_element_interface::get (here);
-
- /* half beams extending to the left. */
- if (prev)
- {
- int lhalfs= lhalfs = Stem::beam_count (here, LEFT)
- - Stem::beam_count (prev, RIGHT);
- int lwholebeams= Stem::beam_count (here, LEFT)
- <? Stem::beam_count (prev, RIGHT);
-
- /* Half beam should be one note-width,
- but let's make sure two half-beams never touch */
-
- // FIXME: TODO (check) stem width / sloped beams
- Real w = here->relative_coordinate (0, X_AXIS)
- - prev->relative_coordinate (0, X_AXIS);
- Real stem_w = gh_scm2double (prev->get_grob_property ("thickness"))
- // URG
- * me->paper_l ()->get_var ("linethickness");
-
- w = w/2 <? nw_f;
- Molecule a;
- if (lhalfs) // generates warnings if not
- a = Lookup::beam (dydx, w + stem_w, thick);
- a.translate (Offset (-w, -w * dydx));
- a.translate_axis (-stem_w/2, X_AXIS);
- for (int j = 0; j < lhalfs; j++)
- {
- Molecule b (a);
- b.translate_axis (-dir * bdy * (lwholebeams+j), Y_AXIS);
- leftbeams.add_molecule (b);
- }
- }
-
- if (next)
- {
- int rhalfs = Stem::beam_count (here, RIGHT)
- - Stem::beam_count (next, LEFT);
- int rwholebeams= Stem::beam_count (here, RIGHT)
- <? Stem::beam_count (next, LEFT);
-
- Real w = next->relative_coordinate (0, X_AXIS)
- - here->relative_coordinate (0, X_AXIS);
-
- Real stem_w = gh_scm2double (next->get_grob_property ("thickness"))
- // URG
- * me->paper_l ()->get_var ("linethickness");
-
- Molecule a = Lookup::beam (dydx, w + stem_w, thick);
- a.translate_axis (- stem_w/2, X_AXIS);
- int j = 0;
- Real gap_f = 0;
-
- SCM gap = me->get_grob_property ("gap");
- if (gh_number_p (gap))
- {
- int gap_i = gh_scm2int ((gap));
- int nogap = rwholebeams - gap_i;
-
- for (; j < nogap; j++)
- {
- Molecule b (a);
- b.translate_axis (-dir * bdy * j, Y_AXIS);
- rightbeams.add_molecule (b);
- }
- if (Stem::invisible_b (here))
- gap_f = nw_f;
- else
- gap_f = nw_f / 2;
- w -= 2 * gap_f;
- a = Lookup::beam (dydx, w + stem_w, thick);
- }
-
- for (; j < rwholebeams; j++)
- {
- Molecule b (a);
- Real tx = 0;
- if (Stem::invisible_b (here))
- // ugh, see chord-tremolo.ly
- tx = (-dir + 1) / 2 * nw_f * 1.5 + gap_f/4;
- else
- tx = gap_f;
- b.translate (Offset (tx, -dir * bdy * j));
- rightbeams.add_molecule (b);
- }
-
- w = w/2 <? nw_f;
- if (rhalfs)
- a = Lookup::beam (dydx, w, thick);
-
- for (; j < rwholebeams + rhalfs; j++)
- {
- Molecule b (a);
- b.translate_axis (- dir * bdy * j, Y_AXIS);
- rightbeams.add_molecule (b);
- }
-
- }
- leftbeams.add_molecule (rightbeams);
-
- return leftbeams;
-}
-
-
-MAKE_SCHEME_CALLBACK (Beam, brew_molecule, 1);
-SCM
-Beam::brew_molecule (SCM smob)
-{
- Grob *me =unsmob_grob (smob);
-
- Molecule mol;
- if (!gh_pair_p (me->get_grob_property ("stems")))
- return SCM_EOL;
- Real x0, dx;
- Link_array<Item>stems =
- Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
- if (visible_stem_count (me))
- {
- // ugh -> use commonx
- x0 = first_visible_stem (me)->relative_coordinate (0, X_AXIS);
- dx = last_visible_stem (me)->relative_coordinate (0, X_AXIS) - x0;
- }
- else
- {
- x0 = stems[0]->relative_coordinate (0, X_AXIS);
- dx = stems.top ()->relative_coordinate (0, X_AXIS) - x0;
- }
-
- SCM posns = me->get_grob_property ("positions");
- Interval pos;
- if (!ly_number_pair_p (posns))
- {
- programming_error ("No beam posns");
- pos = Interval (0,0);
- }
- else
- pos= ly_scm2interval (posns);
- Real dy = pos.delta ();
- Real dydx = dy && dx ? dy/dx : 0;
-
-
- for (int i=0; i < stems.size (); i++)
- {
- Item *item = stems[i];
- Item *prev = (i > 0)? stems[i-1] : 0;
- Item *next = (i < stems.size ()-1) ? stems[i+1] :0;
-
-
-
- Molecule sb = stem_beams (me, item, next, prev, dydx);
- Real x = item->relative_coordinate (0, X_AXIS) - x0;
- sb.translate (Offset (x, x * dydx + pos[LEFT]));
-
-
- mol.add_molecule (sb);
- }
-
- mol.translate_axis (x0
- - dynamic_cast<Spanner*> (me)
- ->get_bound (LEFT)->relative_coordinate (0, X_AXIS),
- X_AXIS);
-
-#if (DEBUG_QUANTING)
- {
- /*
- This code prints the demerits for each beam. Perhaps this
- should be switchable for those who want to twiddle with the
- parameters.
- */
- String str;
- if (1)
- {
- str += to_str (gh_scm2int (me->get_grob_property ("best-idx")));
- str += ":";
- }
- str += to_str (gh_scm2double (me->get_grob_property ("quant-score")),
- "%.2f");
-
- SCM properties = Font_interface::font_alist_chain (me);
-
-
- Molecule tm = Text_item::text2molecule (me, ly_str02scm (str.ch_C ()), properties);
- mol.add_at_edge (Y_AXIS, UP, tm, 5.0);
- }
-#endif
-
- return mol.smobbed_copy ();
-}
-
int
Beam::forced_stem_count (Grob *me)
{
- Link_array<Item>stems =
- Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
+ Link_array<Grob>stems =
+ Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
int f = 0;
for (int i=0; i < stems.size (); i++)
{
- Item *s = stems[i];
+ Grob *s = stems[i];
if (Stem::invisible_b (s))
continue;
- if (((int)Stem::chord_start_y (s))
+ /* 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++;
}
int
Beam::visible_stem_count (Grob *me)
{
- Link_array<Item>stems =
- Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
+ Link_array<Grob>stems =
+ Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
int c = 0;
for (int i = stems.size (); i--;)
{
return c;
}
-Item*
+Grob*
Beam::first_visible_stem (Grob *me)
{
- Link_array<Item>stems =
- Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
+ Link_array<Grob>stems =
+ Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
for (int i = 0; i < stems.size (); i++)
{
return 0;
}
-Item*
+Grob*
Beam::last_visible_stem (Grob *me)
{
- Link_array<Item>stems =
- Pointer_group_interface__extract_grobs (me, (Item*) 0, "stems");
+ Link_array<Grob>stems =
+ Pointer_group_interface__extract_grobs (me, (Grob*) 0, "stems");
for (int i = stems.size (); i--;)
{
if (!Stem::invisible_b (stems[i]))
{
Grob *rest = unsmob_grob (element_smob);
Axis a = (Axis) gh_scm2int (axis);
+
+ if (gh_number_p (rest->get_grob_property ("staff-position")))
+ return gh_int2scm (0);
assert (a == Y_AXIS);
|| !Beam::visible_stem_count (beam))
return gh_double2scm (0.0);
- // make callback for rest from this.
- // todo: make sure this calced already.
-
- // Interval pos = ly_scm2interval (beam->get_grob_property ("positions"));
- Interval pos (0, 0);
+ Drul_array<Real> pos (0, 0);
SCM s = beam->get_grob_property ("positions");
if (gh_pair_p (s) && gh_number_p (ly_car (s)))
pos = ly_scm2interval (s);
+ Real staff_space = Staff_symbol_referencer::staff_space (rest);
+
+ scale_drul (&pos, staff_space);
+
- Real dy = pos.delta ();
+ 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 dydx = dy && dx ? dy/dx : 0;
Direction d = Stem::get_direction (stem);
- Real beamy = (stem->relative_coordinate (0, X_AXIS) - x0) * dydx + pos[LEFT];
-
- Real staff_space = Staff_symbol_referencer::staff_space (rest);
-
+ Real stem_y = pos[LEFT] + (stem->relative_coordinate (0, X_AXIS) - x0) * dydx;
- Real rest_dim = rest->extent (rest, Y_AXIS)[d]*2.0 / staff_space; // refp??
-
- Real minimum_dist
- = gh_scm2double (rest->get_grob_property ("minimum-beam-collision-distance"));
- Real dist =
- minimum_dist + -d * (beamy - rest_dim) >? 0;
+ 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;
- int stafflines = Staff_symbol_referencer::line_count (rest);
+ Grob *common_y = rest->common_refpoint (beam, Y_AXIS);
- // move discretely by half spaces.
- int discrete_dist = int (ceil (dist));
+ Real rest_dim = rest->extent (common_y, Y_AXIS)[d];
+ Real minimum_distance =
+ staff_space * robust_scm2double (rest->get_grob_property ("minimum-distance"), 0.0);
- // move by whole spaces inside the staff.
- if (discrete_dist < stafflines+1)
- discrete_dist = int (ceil (discrete_dist / 2.0)* 2.0);
+ Real shift = d * (((beam_y - d * minimum_distance) - rest_dim) * d <? 0.0);
- return gh_double2scm (-d * discrete_dist);
-}
+ 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 gh_double2scm (staff_space * shift);
+}
-ADD_INTERFACE (Beam, "beam-interface",
- "A beam.
+bool
+Beam::knee_b (Grob* me)
+{
+ SCM k = me->get_grob_property ("knee");
+ if (gh_boolean_p (k))
+ return gh_scm2bool (k);
-#'thickness= weight of beams, in staffspace
+ bool knee = false;
+ int d = 0;
+ for (SCM s = me->get_grob_property ("stems"); gh_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_grob_property ("knee", gh_bool2scm (knee));
+ return knee;
+}
-We take the least squares line through the ideal-length stems, and
-then damp that using
+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);
+ }
- damped = tanh (slope)
+ return bc;
+}
-this gives an unquantized left and right position for the beam end.
-Then we take all combinations of quantings near these left and right
-positions, and give them a score (according to how close they are to
-the ideal slope, how close the result is to the ideal stems, etc.). We
-take the best scoring combination.
-",
- "position-callbacks concaveness-gap concaveness-threshold dir-function quant-score auto-knee-gap gap chord-tremolo beamed-stem-shorten shorten least-squares-dy damping flag-width-function neutral-direction positions space-function thickness");
+ADD_INTERFACE (Beam, "beam-interface",
+ "A beam. \n\n"
+" "
+"#'thickness= weight of beams, in staffspace "
+" "
+" "
+"We take the least squares line through the ideal-length stems, and "
+"then damp that using "
+" \n"
+" damped = tanh (slope) \n"
+" \n"
+"this gives an unquantized left and right position for the beam end. "
+"Then we take all combinations of quantings near these left and right "
+"positions, and give them a score (according to how close they are to "
+"the ideal slope, how close the result is to the ideal stems, etc.). We "
+"take the best scoring combination. "
+,
+ "knee positioning-done position-callbacks concaveness-gap concaveness-threshold dir-function quant-score auto-knee-gap gap gap-count chord-tremolo beamed-stem-shorten shorten least-squares-dy damping flag-width-function neutral-direction positions space-function thickness");