source file of the GNU LilyPond music typesetter
- (c) 1998--1999 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2000 Jan Nieuwenhuizen <janneke@gnu.org>
*/
#include <math.h>
#include "bezier.hh"
#include "dimensions.hh"
#include "direction.hh"
-#include "paper-def.hh"
#include "debug.hh"
#include "main.hh"
+#include "lily-guile.hh"
void
flipy (Array<Offset> &c)
}
-Bezier_bow::Bezier_bow (Paper_def* paper_l)
+Bezier_bow::Bezier_bow (Array<Offset> points, Direction dir)
{
- paper_l_ = paper_l;
+ dir_ = dir;
+ encompass_ = points;
+ to_canonic_form ();
+
+ rc_factor_ = 1.0;
+ height_limit_ = 1.0;
+ ratio_ = 1.0;
+}
+
+static Real
+default_height (Real len)
+{
+ // assume 20pt staff
+ // see fonts.doc
+ Real staff_space = 5.0;
+ Real h_inf = 2.0* staff_space;
+ Real r_0 = 0.33;
+ return h_inf * 2.0 / M_PI * atan ( M_PI * r_0 / (2.0 * h_inf) * len);
}
void
Bezier_bow::blow_fit ()
{
- Real x1 = encompass_[0][X_AXIS];
- Real x2 = encompass_.top ()[X_AXIS];
+ Real len = curve_.control_[3][X_AXIS];
+ Real h = curve_.control_[1][Y_AXIS] * fit_factor () / len;
+ curve_.control_[1][Y_AXIS] = h * len;
+ curve_.control_[2][Y_AXIS] = h * len;
+ curve_.check_sanity ();
+}
- Real factor = 1.0;
- for (int i=1; i < encompass_.size ()-1; i++)
+void
+Bezier_bow::de_uglyfy ()
+{
+ Real len = curve_.control_[3][X_AXIS] ;
+ Real ff = fit_factor ();
+ for (int i = 1; i < 3; i++)
{
- if (encompass_[i][X_AXIS] > x1 && encompass_[i][X_AXIS] < x2)
+ Real ind = abs (curve_.control_[(i-1)*3][X_AXIS]
+ - curve_.control_[i][X_AXIS]) / len;
+ Real h = curve_.control_[i][Y_AXIS] * ff / len;
+
+ // ugh. Unhardcode this
+#if 0
+ // Too crude.
+ if (h > 4 * ind)
{
- Real y = curve_.get_other_coordinate (X_AXIS, encompass_[i][X_AXIS]);
- if (y>0)
- {
- Real f = encompass_[i][Y_AXIS] / y;
- factor = factor >? f;
- }
+ h = 4* ind;
}
- }
-
- curve_.control_[1][Y_AXIS] *= factor;
- curve_.control_[2][Y_AXIS] *= factor;
- return_.control_[1][Y_AXIS] *= factor;
- return_.control_[2][Y_AXIS] *= factor;
+#else
+ Real f = default_height (len) / len;
+ if (h > 2.0 * f)
+ {
+ h = 2.0 * f;
+ }
+#endif
+
+ if (h > 0.8 + -2 * ind)
+ {
+ h = 0.8 - 2 *ind;
+ }
+
+ curve_.control_[i][Y_AXIS] = h * len;
+ }
curve_.check_sanity ();
}
Real
-Bezier_bow::calc_f (Real height)
+Bezier_bow::calc_enclosed_area_f () const
{
- transform ();
- calc_default (height);
-
- Real dy = check_fit_f ();
- calc_return (0, 0);
+ Real a = 0;
+ for (int i=0; i < encompass_.size (); i++)
+ {
+ Interval x;
+ Interval y;
+ if (i == 0)
+ {
+ x = Interval (0, encompass_[1][X_AXIS] / 2);
+ y = Interval (0,
+ curve_.get_other_coordinate (X_AXIS,
+ encompass_[1][X_AXIS]
+ / 2));
+ }
+ else if (i == encompass_.size () - 1)
+ {
+ x = Interval ((encompass_[i-1][X_AXIS] + encompass_[i][X_AXIS])/2,
+ encompass_[i][X_AXIS]);
+ y = Interval (0,
+ (curve_.get_other_coordinate (X_AXIS,
+ (x[MIN] + x[MAX]) / 2)));
+ }
+ else
+ {
+ x = Interval ((encompass_[i-1][X_AXIS] + encompass_[i][X_AXIS]) / 2,
+ (encompass_[i][X_AXIS] + encompass_[i+1][X_AXIS]) / 2);
+ y = Interval (encompass_[i][Y_AXIS],
+ (curve_.get_other_coordinate (X_AXIS, x[MIN])
+ + curve_.get_other_coordinate (X_AXIS,
+ (x[MIN] + x[MAX]) / 2)
+ + curve_.get_other_coordinate (X_AXIS, x[MAX])) / 3);
+ }
+
+ Real da = x.length () * y.length ();
+ a += da;
+ }
+ return a;
+}
- transform_back ();
- return dy;
+Array<Offset>
+Bezier_bow::area_gradient_offset_arr ()
+{
+ Real len = curve_.control_[3][X_AXIS];
+ Real area = calc_enclosed_area_f ();
+
+ Real grow = len / 10.0;
+ Array<Offset> da (2);
+ for (int i=1; i < 3; i++)
+ {
+ for (Axis a=X_AXIS; a < NO_AXES; incr (a))
+ {
+ Real r = curve_.control_[i][a];
+ curve_.control_[i][a] += grow;
+ da[i-1][a] = (calc_enclosed_area_f () - area) / grow;
+
+ curve_.control_[i][a] = r;
+ }
+ }
+ return da;
}
void
-Bezier_bow::calc ()
+Bezier_bow::minimise_enclosed_area ()
{
- transform ();
- calc_controls ();
- transform_back ();
-}
+ Real len = curve_.control_[3][X_AXIS];
+ Real beautiful = len * default_height (len) / 2.0;
+ DEBUG_OUT << to_str ("Beautiful: %f\n", beautiful);
+ DEBUG_OUT << to_str ("Length: %f\n", len);
+ int steps=2;
+ for (int i=0; i < steps; i++)
+ {
+ Real ff = fit_factor ();
+ if (!ff)
+ break;
+ DEBUG_OUT << to_str ("FitFac: %f\n", ff);
-/*
- [TODO]
- * see if it works
- * document in Documentation/fonts.tex
- */
+ // slur must be higher at every point
+ if (ff > 1.01)
+ {
+ blow_fit ();
+ DEBUG_OUT << to_str ("Blown area: %f\n", calc_enclosed_area_f ());
+ }
+ else
+ DEBUG_OUT << to_str ("Init area: %f\n", calc_enclosed_area_f ());
-/*
- Clipping
+ Real area = calc_enclosed_area_f ();
+
- This function tries to address two issues:
- * the tangents of the slur should always point inwards
- in the actual slur, i.e. *after rotating back*.
+ if (area <= beautiful)
+ break;
- * slurs shouldn't be too high
- let's try : h <= 1.2 b && h <= 3 staffheight?
+ Array<Offset> da = area_gradient_offset_arr ();
- We could calculate the tangent of the bezier curve from
- both ends going inward, and clip the slur at the point
- where the tangent (after rotation) points up (or inward
- with a certain maximum angle).
-
- However, we assume that real clipping is not the best
- answer. We expect that moving the outer control point up
- if the slur becomes too high will result in a nicer slur
- after recalculation.
-
- Knowing that the tangent is the line through the first
- two control points, we'll clip (move the outer control
- point upwards) too if the tangent points outwards.
- */
+ /*
+ Urg: empiric cs
+ Small slurs are easily too asymmetric,
+ while big slurs are too symmetric
-bool
-Bezier_bow::calc_clipping ()
-{
- Real clip_height = paper_l_->get_var ("slur_clip_height");
- Real clip_ratio = paper_l_->get_var ("slur_clip_ratio");
- Real clip_angle = paper_l_->get_var ("slur_clip_angle");
-
- Real b = curve_.control_[3][X_AXIS] - curve_.control_[0][X_AXIS];
- Real clip_h = clip_ratio * b <? clip_height;
- Real begin_h = curve_.control_[1][Y_AXIS] - curve_.control_[0][Y_AXIS];
- Real end_h = curve_.control_[2][Y_AXIS] - curve_.control_[3][Y_AXIS];
- Real begin_dy = 0 >? begin_h - clip_h;
- Real end_dy = 0 >? end_h - clip_h;
+ This makes short slurs strictly x-bound,
+ long slurs become y-bound.
+ */
+ Real ypct = 0.50;
+ //Real xpct = (0.07 * len * len / 1000.0) <? 0.80;
+ Real xpct = (0.1 * len * len * len / 100000.0) <? 0.80;
+
+ Real yu = (abs (curve_.control_[1][Y_AXIS] / da[0][Y_AXIS])
+ <? abs (curve_.control_[2][Y_AXIS] / da[1][Y_AXIS]))
+ * ypct;
+ Real xu = (abs (curve_.control_[1][X_AXIS] / da[0][X_AXIS])
+ <? abs ((curve_.control_[3][X_AXIS]
+ - curve_.control_[2][X_AXIS]) / da[1][X_AXIS]))
+ * xpct;
+ Real u = yu <? xu;
+ DEBUG_OUT << to_str ("u (xu, yu): %f (%f, %f)\n", u, xu, yu);
+ DEBUG_OUT << to_str ("pct (x, y): (%f, %f)\n", xpct, ypct);
+
+ DEBUG_OUT << to_str ("da1: (%f, %f)\n", da[0][X_AXIS], da[0][Y_AXIS]);
+ DEBUG_OUT << to_str ("da2: (%f, %f)\n", da[1][X_AXIS], da[1][Y_AXIS]);
+
+ curve_.control_[1] -= da[0] * u;
+ curve_.control_[2] -= da[1] * u;
+ }
- Real pi = M_PI;
- Real begin_alpha = (curve_.control_[1] - curve_.control_[0]).arg () + dir_ * alpha_;
- Real end_alpha = pi - (curve_.control_[2] - curve_.control_[3]).arg () - dir_ * alpha_;
-
- Real max_alpha = clip_angle / 90 * pi / 2;
- if ((begin_dy < 0) && (end_dy < 0)
- && (begin_alpha < max_alpha) && (end_alpha < max_alpha))
- return false;
-
- transform_back ();
- bool again = true;
+ if (fit_factor () > 1.5)
+ blow_fit ();
- if ((begin_dy > 0) || (end_dy > 0))
- {
- Real dy = (begin_dy + end_dy) / 4;
- dy *= cos (alpha_);
- encompass_[0][Y_AXIS] += dir_ * dy;
- encompass_.top ()[Y_AXIS] += dir_ * dy;
- }
- else
+ DEBUG_OUT << to_str ("Exarea: %f\n", calc_enclosed_area_f ());
+ Real area = calc_enclosed_area_f ();
+ /*
+ Slurs that fit beautifully are not ugly
+ */
+ if (area > beautiful)
{
- //ugh
- Real c = 0.4;
- if (begin_alpha >= max_alpha)
- begin_dy = 0 >? c * begin_alpha / max_alpha * begin_h;
- if (end_alpha >= max_alpha)
- end_dy = 0 >? c * end_alpha / max_alpha * end_h;
-
- encompass_[0][Y_AXIS] += dir_ * begin_dy;
- encompass_.top ()[Y_AXIS] += dir_ * end_dy;
-
- Offset delta = encompass_.top () - encompass_[0];
- alpha_ = delta.arg ();
+ DEBUG_OUT << "DE-UGLYFY\n";
+ de_uglyfy ();
}
- transform ();
-
- return again;
}
void
-Bezier_bow::calc_controls ()
+Bezier_bow::calculate ()
{
- for (int i = 0; i < 3; i++)
+ calc_default ();
+ if (fit_factor () > 1.0)
{
-
- if (i && !calc_clipping ())
- return;
-
- /*
- why do we always recalc from 0?
- shouldn't calc_f () be used (too), rather than blow_fit () (only)?
- */
- calc_default (0);
- curve_.check_sanity ();
- if (check_fit_f () > 0)
- {
- calc_tangent_controls ();
- blow_fit ();
- }
- else
- {
- calc_return (0, 0);
- return;
- }
+ // calc_tangent_controls ();
+ // blow_fit ();
+ minimise_enclosed_area ();
}
}
-void
-Bezier_bow::calc_return (Real begin_alpha, Real end_alpha)
-{
- Real thick = paper_l_->get_var ("slur_thickness");
- return_.control_[0] = curve_.control_[3];
- return_.control_[3] = curve_.control_[0];
+
+Bezier
+Bezier_bow::get_curve ()const
+{
+ Bezier rv = curve_;
+ if (dir_ == DOWN)
+ {
+ rv.flip (Y_AXIS);
+ }
- return_.control_[1] = curve_.control_[2] - thick * complex_exp (Offset (0, 90 + end_alpha));
- return_.control_[2] = curve_.control_[1] - thick * complex_exp (Offset (0, 90 - begin_alpha));
+ rv.rotate (alpha_);
+ rv.translate (origin_);
+
+ return rv;
}
static Real const FUDGE = 1e-8;
The curve will always be under line between curve_.control_0 -> curve_.control_1, so
make it extra steep by slur_rc_factor
*/
- Real rc_correct = paper_l_->get_var ("slur_rc_factor");
-
+
+
Drul_array<Real> angles;
Direction d = LEFT;
do
{
- maxtan[d] *= -d * rc_correct;
+ maxtan[d] *= -d * rc_factor_;
angles[d] = atan (maxtan[d]);
}
while (flip(&d) != LEFT);
// ugh: be less steep
- rc3 /= 2*rc_correct;
+ rc3 /= 2*rc_factor_;
Real c2 = -maxtan[RIGHT] * curve_.control_[3][X_AXIS];
curve_.check_sanity();
-
- calc_return (angles[LEFT], angles[RIGHT]);
}
/*
- The maximum amount that the encompass points stick out above the bezier curve.
+ max ( encompass.y / curve.y )
+
*/
Real
-Bezier_bow::check_fit_f () const
+Bezier_bow::fit_factor () const
{
- Real dy = 0;
Real x1 = encompass_[0][X_AXIS];
Real x2 = encompass_.top ()[X_AXIS];
- for (int i = 1; i < encompass_.size () - 1; i++)
+
+ Real factor = 0.0;
+ for (int i=1; i < encompass_.size ()-1; i++)
{
- Real x = encompass_[i][X_AXIS];
- if (x1< x&& x < x2)
- dy = dy >? (encompass_[i][Y_AXIS] - curve_.get_other_coordinate (X_AXIS, x));
+ if (encompass_[i][X_AXIS] > x1 && encompass_[i][X_AXIS] < x2)
+ {
+ Real y = curve_.get_other_coordinate (X_AXIS, encompass_[i][X_AXIS]);
+ if (y>0)
+ {
+ Real f = encompass_[i][Y_AXIS] / y;
+ factor = factor >? f;
+ }
+ }
}
- return dy;
-}
-void
-Bezier_bow::set (Array<Offset> points, Direction dir)
-{
- dir_ = dir;
- encompass_ = points;
+ return factor;
}
+
+
+
void
-Bezier_bow::transform ()
+Bezier_bow::to_canonic_form ()
{
origin_ = encompass_[0];
translate (encompass_,-origin_);
alpha_ = delta.arg ();
rotate (encompass_, -alpha_);
-
- if (dir_ == DOWN)
- flipy (encompass_);
-}
-
-void
-Bezier_bow::transform_back ()
-{
if (dir_ == DOWN)
{
- curve_.flip (Y_AXIS);
- return_.flip (Y_AXIS);
flipy (encompass_);
}
- curve_.rotate (alpha_);
- curve_.translate (origin_);
-
- return_.rotate (alpha_);
- return_.translate (origin_);
-
- rotate (encompass_,alpha_);
- translate (encompass_,origin_);
+ while (encompass_.size () > 1 && encompass_[1][X_AXIS] <= 0.0)
+ {
+ programming_error ("Degenerate slur: infinite steepness reqd");
+ encompass_.del (1);
+ }
+
+ Real l = encompass_.top ()[X_AXIS];
+ while (encompass_.size () > 1 && encompass_.top (1)[X_AXIS] >= l)
+ {
+ programming_error ("Degenerate slur: infinite steepness reqd");
+ encompass_.del (encompass_.size ()-2);
+ }
}
+
+
/*
See Documentation/fonts.tex
*/
void
-Bezier_bow::calc_default (Real h)
+Bezier_bow::calc_default ()
{
Real pi = M_PI;
- Real height_limit = paper_l_->get_var ("slur_height_limit");
- Real ratio = paper_l_->get_var ("slur_ratio");
-
- Real alpha = height_limit * 2.0 / pi;
- Real beta = pi * ratio / (2.0 * height_limit);
+ Real alpha = height_limit_ * 2.0 / pi;
+ Real beta = pi * ratio_ / (2.0 * height_limit_);
Offset delta (encompass_.top ()[X_AXIS]
- encompass_[0][X_AXIS], 0);
Real b = delta.length ();
Real indent = alpha * atan (beta * b);
- Real height = indent + h;
+ Real height = indent;
curve_.control_ [0] = Offset (0, 0);
curve_.control_ [1] = Offset (indent, height);
}
+
+
projects / lilypond.git / blobdiff