-Interval
-Beam::no_visible_stem_positions (Grob *me, Interval default_value)
-{
- extract_grob_set (me, "stems", stems);
- if (stems.empty ())
- return default_value;
-
- Interval head_positions;
- Slice multiplicity;
- for (vsize i = 0; i < stems.size (); i++)
- {
- head_positions.unite (Stem::head_positions (stems[i]));
- multiplicity.unite (Stem::beam_multiplicity (stems[i]));
- }
-
- Direction dir = get_grob_direction (me);
-
- if (!dir)
- programming_error ("The beam should have a direction by now.");
-
- Real y = head_positions.linear_combination (dir)
- * 0.5 * Staff_symbol_referencer::staff_space (me)
- + dir * get_beam_translation (me) * (multiplicity.length () + 1);
-
- y /= Staff_symbol_referencer::staff_space (me);
- return Interval (y, y);
-}
-
-/*
- Compute a first approximation to the beam slope.
-*/
-MAKE_SCHEME_CALLBACK (Beam, calc_least_squares_positions, 2);
-SCM
-Beam::calc_least_squares_positions (SCM smob, SCM /* posns */)
-{
- Grob *me = unsmob_grob (smob);
-
- int count = normal_stem_count (me);
- Interval pos (0, 0);
- if (count < 1)
- return ly_interval2scm (no_visible_stem_positions (me, pos));
-
- vector<Real> x_posns;
- extract_grob_set (me, "normal-stems", 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_normal_stem (me);
- Grob *lvs = last_normal_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_normal_stem (me)->relative_coordinate (commonx, X_AXIS);
- for (vsize i = 0; i < stems.size (); i++)
- {
- Grob *s = stems[i];
-
- Real x = s->relative_coordinate (commonx, X_AXIS) - x0;
- x_posns.push_back (x);
- }
- Real dx = last_normal_stem (me)->relative_coordinate (commonx, X_AXIS) - x0;
-
- Real y = 0;
- Real slope = 0;
- Real dy = 0;
- Real ldy = 0.0;
- if (!ideal.delta ())
- {
- Interval chord (Stem::chord_start_y (stems[0]),
- Stem::chord_start_y (stems.back ()));
-
- /* 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_beam_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.
- */
- ldy = pos[RIGHT] - pos[LEFT];
- }
- else
- {
- vector<Offset> ideals;
- for (vsize i = 0; i < stems.size (); i++)
- {
- Grob *s = stems[i];
- ideals.push_back (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);
-
- ldy = 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 ("least-squares-dy", scm_from_double (ldy));
- return ly_interval2scm (pos);
-}
-
-// Assuming V is not empty, pick a 'reasonable' point inside V.
-static Real
-point_in_interval (Interval v, Real dist)
-{
- if (isinf (v[DOWN]))
- return v[UP] - dist;
- else if (isinf (v[UP]))
- return v[DOWN] + dist;
- else
- return v.center ();
-}
-
-/*
- 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, 2);
-SCM
-Beam::shift_region_to_valid (SCM grob, SCM posns)
-{
- Grob *me = unsmob_grob (grob);
-
- /*
- Code dup.
- */
- vector<Real> x_posns;
- extract_grob_set (me, "stems", stems);
- extract_grob_set (me, "covered-grobs", covered);
-
- Grob *common[NO_AXES] = { me, me };
- for (Axis a = X_AXIS; a < NO_AXES; incr (a))
- {
- common[a] = common_refpoint_of_array (stems, me, a);
- common[a] = common_refpoint_of_array (covered, common[a], a);
- }
- Grob *fvs = first_normal_stem (me);
-
- if (!fvs)
- return posns;
- Interval x_span;
- x_span[LEFT] = fvs->relative_coordinate (common[X_AXIS], X_AXIS);
- for (vsize i = 0; i < stems.size (); i++)
- {
- Grob *s = stems[i];
-
- Real x = s->relative_coordinate (common[X_AXIS], X_AXIS) - x_span[LEFT];
- x_posns.push_back (x);
- }
-
- Grob *lvs = last_normal_stem (me);
- x_span[RIGHT] = lvs->relative_coordinate (common[X_AXIS], X_AXIS);
-
- Drul_array<Real> pos = ly_scm2interval (posns);
-
- scale_drul (&pos, Staff_symbol_referencer::staff_space (me));
-
- Real beam_dy = pos[RIGHT] - pos[LEFT];
- Real beam_left_y = pos[LEFT];
- Real slope = x_span.delta () ? (beam_dy / x_span.delta ()) : 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 (vsize i = 0; i < stems.size (); i++)
- {
- Grob *s = stems[i];
- if (Stem::is_invisible (s))
- continue;
-
- Direction d = get_grob_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 (common[Y_AXIS], Y_AXIS)
- - me->relative_coordinate (common[Y_AXIS], Y_AXIS);
-
- Interval flp;
- flp.set_full ();
- flp[-d] = left_y;
-
- feasible_left_point.intersect (flp);
- }
-
- vector<Grob *> filtered;
- /*
- We only update these for objects that are too large for quanting
- to find a workaround. Typically, these are notes with
- stems, and timesig/keysig/clef, which take out the entire area
- inside the staff as feasible.
-
- The code below disregards the thickness and multiplicity of the
- beam. This should not be a problem, as the beam quanting will
- take care of computing the impact those exactly.
- */
- Real min_y_size = 2.0;
-
- // A list of intervals into which beams may not fall
- vector<Interval> forbidden_intervals;
-
- for (vsize i = 0; i < covered.size (); i++)
- {
- if (!covered[i]->is_live ())
- continue;
-
- if (Beam::has_interface (covered[i]) && is_cross_staff (covered[i]))
- continue;
-
- Box b;
- for (Axis a = X_AXIS; a < NO_AXES; incr (a))
- b[a] = covered[i]->extent (common[a], a);
-
- if (b[X_AXIS].is_empty () || b[Y_AXIS].is_empty ())
- continue;
-
- if (intersection (b[X_AXIS], x_span).is_empty ())
- continue;
-
- filtered.push_back (covered[i]);
- Grob *head_stem = Rhythmic_head::get_stem (covered[i]);
- if (head_stem && Stem::is_normal_stem (head_stem)
- && Note_head::has_interface (covered[i]))
- {
- if (Stem::get_beam (head_stem))
- {
- /*
- We must assume that stems are infinitely long in this
- case, as asking for the length of the stem typically
- leads to circular dependencies.
-
- This strategy assumes that we don't want to handle the
- collision of beams in opposite non-forced directions
- with this code, where shortening the stems of both
- would resolve the problem, eg.
-
- x x
- | |
- =====
-
- =====
- | |
- x x
-
- Such beams would need a coordinating grob to resolve
- the collision, since both will likely want to occupy
- the centerline.
- */
- Direction stemdir = get_grob_direction (head_stem);
- b[Y_AXIS][stemdir] = stemdir * infinity_f;
- }
- else
- {
- // TODO - should we include the extent of the stem here?
- }
- }
-
- if (b[Y_AXIS].length () < min_y_size)
- continue;
-
- Direction d = LEFT;
- do
- {
- Real x = b[X_AXIS][d] - x_span[LEFT];
- Real dy = slope * x;
-
- Direction yd = DOWN;
- Interval disallowed;
- do
- {
- Real left_y = b[Y_AXIS][yd];
-
- left_y -= dy;
-
- // Translate back to beam as ref point.
- left_y -= me->relative_coordinate (common[Y_AXIS], Y_AXIS);
-
- disallowed[yd] = left_y;
- }
- while (flip (&yd) != DOWN);
-
- forbidden_intervals.push_back (disallowed);
- }
- while (flip (&d) != LEFT);
- }
-
- Grob_array *arr
- = Pointer_group_interface::get_grob_array (me,
- ly_symbol2scm ("covered-grobs"));
- arr->set_array (filtered);
-
- vector_sort (forbidden_intervals, Interval::left_less);
- Real epsilon = 1.0e-10;
- Interval feasible_beam_placements (beam_left_y, beam_left_y);
-
- /*
- forbidden_intervals contains a vector of intervals in which
- the beam cannot start. it iterates through these intervals,
- pushing feasible_beam_placements epsilon over or epsilon under a
- collision. when this type of change happens, the loop is marked
- as "dirty" and re-iterated.
-
- TODO: figure out a faster ways that this loop can happen via
- a better search algorithm and/or OOP.
- */
-
- bool dirty = false;
- do
- {
- dirty = false;
- for (vsize i = 0; i < forbidden_intervals.size (); i++)
- {
- Direction d = DOWN;
- do
- {
- if (forbidden_intervals[i][d] == d * infinity_f)
- feasible_beam_placements[d] = d * infinity_f;
- else if (forbidden_intervals[i].contains (feasible_beam_placements[d]))
- {
- feasible_beam_placements[d] = d * epsilon + forbidden_intervals[i][d];
- dirty = true;
- }
- }
- while (flip (&d) != DOWN);
- }
- }
- while (dirty);
-
- // if the beam placement falls out of the feasible region, we push it
- // to infinity so that it can never be a feasible candidate below
- Direction d = DOWN;
- do
- {
- if (!feasible_left_point.contains (feasible_beam_placements[d]))
- feasible_beam_placements[d] = d * infinity_f;
- }
- while (flip (&d) != DOWN);
-
- if ((feasible_beam_placements[UP] == infinity_f && feasible_beam_placements[DOWN] == -infinity_f) && !feasible_left_point.is_empty ())
- {
- // We are somewhat screwed: we have a collision, but at least
- // there is a way to satisfy stem length constraints.
- beam_left_y = point_in_interval (feasible_left_point, 2.0);
- }
- else if (!feasible_left_point.is_empty ())
- {
- // Only one of them offers is feasible solution. Pick that one.
- if (abs (beam_left_y - feasible_beam_placements[DOWN]) > abs (beam_left_y - feasible_beam_placements[UP]))
- beam_left_y = feasible_beam_placements[UP];
- else
- beam_left_y = feasible_beam_placements[DOWN];
- }
- else
- {
- // We are completely screwed.
- me->warning (_ ("no viable initial configuration found: may not find good beam slope"));
- }
-
- pos = Drul_array<Real> (beam_left_y, (beam_left_y + beam_dy));
- scale_drul (&pos, 1 / Staff_symbol_referencer::staff_space (me));
-
- return ly_interval2scm (pos);
-}
-
-/* This neat trick is by Werner Lemberg,
- damped = tanh (slope)
- corresponds with some tables in [Wanske] CHECKME */
-MAKE_SCHEME_CALLBACK (Beam, slope_damping, 2);
-SCM
-Beam::slope_damping (SCM smob, SCM posns)
-{
- Grob *me = unsmob_grob (smob);
- Drul_array<Real> pos = ly_scm2interval (posns);
-
- if (normal_stem_count (me) <= 1)
- return posns;
-
- SCM s = me->get_property ("damping");
- Real damping = scm_to_double (s);
- Real concaveness = robust_scm2double (me->get_property ("concaveness"), 0.0);
- if (concaveness >= 10000)
- {
- pos[LEFT] = pos[RIGHT];
- me->set_property ("least-squares-dy", scm_from_double (0));
- damping = 0;
- }
-
- if (damping)
- {
- scale_drul (&pos, Staff_symbol_referencer::staff_space (me));
-
- Real dy = pos[RIGHT] - pos[LEFT];
-
- Grob *fvs = first_normal_stem (me);
- Grob *lvs = last_normal_stem (me);
-
- Grob *commonx = fvs->common_refpoint (lvs, X_AXIS);
-
- Real dx = last_normal_stem (me)->relative_coordinate (commonx, X_AXIS)
- - first_normal_stem (me)->relative_coordinate (commonx, X_AXIS);
-
- Real slope = dy && dx ? dy / dx : 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));
- }
-
- return ly_interval2scm (pos);
-}
-
-MAKE_SCHEME_CALLBACK (Beam, quanting, 2);