/*
- bezier.cc -- implement Bezier and Bezier_bow
+ This file is part of LilyPond, the GNU music typesetter.
- source file of the GNU LilyPond music typesetter
+ Copyright (C) 1998--2014 Jan Nieuwenhuizen <janneke@gnu.org>
- (c) 1998--2000 Jan Nieuwenhuizen <janneke@gnu.org>
+ LilyPond is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ LilyPond is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with LilyPond. If not, see <http://www.gnu.org/licenses/>.
*/
-#include <math.h>
-#include "bezier-bow.hh"
#include "misc.hh"
#include "bezier.hh"
-#include "dimensions.hh"
-#include "direction.hh"
-#include "debug.hh"
-#include "main.hh"
-#include "lily-guile.hh"
-void
-flipy (Array<Offset> &c)
+static Real
+F0_1 (Real x)
{
- for (int i = c.size (); i--;)
- c[i][Y_AXIS] = - c[i][Y_AXIS];
+ return 2 / M_PI * atan (M_PI * x / 2);
}
-void
-rotate (Array<Offset> &c, Real phi)
+Real
+slur_height (Real width, Real h_inf, Real r_0)
{
- Offset rot (complex_exp (Offset (0, phi)));
- for (int i = 0; i < c.size (); i++)
- c[i] = complex_multiply (rot, c[i]);
+ return F0_1 (width * r_0 / h_inf) * h_inf;
}
-void
-translate (Array<Offset> &c, Offset o)
-{
- for (int i = 0; i < c.size (); i++)
- c[i] += o;
-}
+/*
+ ^ x x
+ |
+ height <indent>
+ |
+ v x x
-Bezier_bow::Bezier_bow (Array<Offset> points, Direction dir)
-{
- dir_ = dir;
- encompass_ = points;
- to_canonic_form ();
- rc_factor_ = 1.0;
- height_limit_ = 1.0;
- ratio_ = 1.0;
-}
+ For small w, the height should be proportional to w, for w ->
+ infinity, the height should rise to a limit asymptotically.
-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);
-}
+ Hence we take F (x) such that
+ F (0) = 0 , F' (0) = 1, and F (infty) = 1
-void
-Bezier_bow::blow_fit ()
-{
- 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 ();
-}
+ and use
-void
-Bezier_bow::de_uglyfy ()
-{
- Real len = curve_.control_[3][X_AXIS] ;
- Real ff = fit_factor ();
- for (int i = 1; i < 3; i++)
- {
- 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
- Real f = default_height (len) / len;
- if (h > 2.0 * f)
- {
- h = 2.0 * f;
- }
- else if (h > 0.8 + -2 * ind)
- {
- h = 0.8 - 2 *ind;
- }
-
- curve_.control_[i][Y_AXIS] = h * len;
- }
-
- curve_.check_sanity ();
-}
+ h = h_infinity * F (x * r_0 / h_infinity)
-Real
-Bezier_bow::calc_enclosed_area_f () const
-{
- 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;
-}
-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;
-}
+ Examples:
-void
-Bezier_bow::minimise_enclosed_area ()
-{
- 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);
-
- // 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 ());
-
- Real area = calc_enclosed_area_f ();
-
-
- if (area <= beautiful)
- break;
-
- Array<Offset> da = area_gradient_offset_arr ();
-
- /*
- Urg: empiric cs
- Small slurs are easily too asymmetric,
- while big slurs are too symmetric
-
- 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;
- }
-
-
- if (fit_factor () > 1.5)
- blow_fit ();
-
- 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)
- {
- DEBUG_OUT << "DE-UGLYFY\n";
- de_uglyfy ();
- }
+ * F (x) = 2/pi * atan (pi x/2)
-}
+ * F (x) = 1/alpha * x^alpha / (1 + x^alpha)
-void
-Bezier_bow::calculate ()
-{
- calc_default ();
- if (fit_factor () > 1.0)
- {
- // calc_tangent_controls ();
- // blow_fit ();
- minimise_enclosed_area ();
- }
-}
+ * (etc.)
+ [with the 2nd recipe you can determine how quickly the conversion from
+ `small' slurs to `big' slurs occurs.]
-
-Bezier
-Bezier_bow::get_curve ()const
-{
- Bezier rv = curve_;
- if (dir_ == DOWN)
- {
- rv.flip (Y_AXIS);
- }
-
- rv.rotate (alpha_);
- rv.translate (origin_);
-
- return rv;
-}
+ Although this might seem cand_idates to SCM-ify, it is not all clear
+ which parameters (ie. h_inf, r_0, F (.)) should be candidates for
+ this. At present h_inf and r_0 come from layout settings, but we did
+ no experiments for determining the best combinations of F, h_inf and
+ r_0.
-static Real const FUDGE = 1e-8;
-/*
- This function calculates 2 center control points,
- based on lines through c_0 --> left disturbing
- and c_3--> right disturbing encompass points.
-
- See Documentation/fonts.tex
- */
-void
-Bezier_bow::calc_tangent_controls ()
-{
- Real b = curve_.control_[3][X_AXIS];
- Real h = curve_.control_[1][Y_AXIS];
-
-
- Drul_array<Offset> disturb;
- Drul_array<Real> maxtan;
- maxtan[LEFT] = maxtan[RIGHT] = h/(b/2);
- disturb[LEFT] = disturb[RIGHT] = Offset (b / 2, h);
-
- for (int i = 1; i < encompass_.size () -1; i++)
- {
- Real y= encompass_[i][Y_AXIS];
- if (y> 0)
- {
- Real x = encompass_[i][X_AXIS];
-
- Direction d = LEFT;
- do
- {
- // 1 if d == LEFT
- int k = (1 - d)/2;
- Real tan = y / ((1-k)* b - d * x);
-
- if (tan > maxtan[d])
- {
- maxtan[d] = tan;
- disturb[d] = Offset (x,y);
- }
- }
- while (flip (&d)!=LEFT);
- }
- }
-
- for (int i = 0; i < encompass_.size (); i++ )
- h = h >? encompass_[i][Y_AXIS];
-
- /*
- The curve will always be under line between curve_.control_0 -> curve_.control_1, so
- make it extra steep by slur_rc_factor
- */
-
-
- Drul_array<Real> angles;
- Direction d = LEFT;
- do
- {
- maxtan[d] *= -d * rc_factor_;
- angles[d] = atan (maxtan[d]);
- }
- while (flip(&d) != LEFT);
-
- Real rc3 = 0.0;
-
- /*
- if we have two disturbing points, have line through those...
- in order to get a sane line, make sure points are reasonably far apart
- X distance must be reasonably(!) big (division)
- */
- if (abs (disturb[LEFT][X_AXIS] - disturb[RIGHT][X_AXIS]) > FUDGE)
- rc3 = (disturb[RIGHT][Y_AXIS] - disturb[LEFT][Y_AXIS]) / (disturb[RIGHT][X_AXIS] - disturb[LEFT][X_AXIS]);
-
- else
- rc3 = tan ((angles[LEFT] - angles[RIGHT]) / 2);
-
-
- // ugh: be less steep
- rc3 /= 2*rc_factor_;
-
-
- Real c2 = -maxtan[RIGHT] * curve_.control_[3][X_AXIS];
-
- // use highest because rc3 is damped.
- Real maxy = disturb[LEFT][Y_AXIS] >? disturb[RIGHT][Y_AXIS];
- Real c3 = disturb[LEFT][Y_AXIS] > disturb[RIGHT][Y_AXIS] ?
- maxy - rc3 * disturb[LEFT][X_AXIS] :
- maxy - rc3 * disturb[RIGHT][X_AXIS];
-
- curve_.control_[1][X_AXIS] = c3 / (maxtan[LEFT] - rc3);
- curve_.control_[1][Y_AXIS] = maxtan[LEFT] * curve_.control_[1][X_AXIS];
-
- curve_.control_[2][X_AXIS] = (c3 - c2) / (maxtan[RIGHT] - rc3);
- curve_.control_[2][Y_AXIS] = maxtan[RIGHT] * curve_.control_[2][X_AXIS] + c2;
-
-
- curve_.check_sanity();
-}
+ The indent is proportional to the height of the slur for small
+ slurs. For large slurs, this gives a certain hookiness at the end,
+ so we increase the indent.
-/*
- max ( encompass.y / curve.y )
-
- */
-Real
-Bezier_bow::fit_factor () const
-{
- Real x1 = encompass_[0][X_AXIS];
- Real x2 = encompass_.top ()[X_AXIS];
-
- Real factor = 0.0;
- for (int i=1; i < encompass_.size ()-1; i++)
- {
- 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 factor;
-}
+ indent = G (w)
+ w -> 0, G (w) -> .33 w
+ (due to derivative constraints, we cannot have indent > len/3)
-void
-Bezier_bow::to_canonic_form ()
-{
- origin_ = encompass_[0];
- translate (encompass_,-origin_);
-
- Offset delta = encompass_.top () - encompass_[0];
- alpha_ = delta.arg ();
-
- rotate (encompass_, -alpha_);
- if (dir_ == DOWN)
- {
- flipy (encompass_);
- }
-
- 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);
- }
-}
+ w -> inf, G (w) -> 2*h_inf
+ i.e.
-/*
- See Documentation/fonts.tex
- */
+ G (0) = 0 , G'(0) 1/3, G (infty) = 2h_inf
+
+ solve from
+
+ G (w) = r + p/(w+q)
+
+ yields
+
+ G (w) = 2 h_inf - max_fraction * q^2/ (w + q)
+
+ with q = 2 h_inf
+*/
+
void
-Bezier_bow::calc_default ()
+get_slur_indent_height (Real *indent, Real *height,
+ Real width, Real h_inf, Real r_0)
{
- Real pi = M_PI;
-
- 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;
-
- curve_.control_ [0] = Offset (0, 0);
- curve_.control_ [1] = Offset (indent, height);
- curve_.control_ [2] = Offset (b - indent, height);
- curve_.control_ [3] = Offset (b, 0);
-}
+ Real max_fraction = 1.0 / 3.1;
+ *height = slur_height (width, h_inf, r_0);
+ Real q = 2 * h_inf / max_fraction;
+ *indent = 2 * h_inf - sqr (q) * max_fraction / (width + q);
+}
+Bezier
+slur_shape (Real width, Real h_inf, Real r_0)
+{
+ Real indent;
+ Real height;
+ get_slur_indent_height (&indent, &height,
+ width, h_inf, r_0);
+ Bezier curve;
+ curve.control_[0] = Offset (0, 0);
+ curve.control_[1] = Offset (indent, height);
+ curve.control_[2] = Offset (width - indent, height);
+ curve.control_[3] = Offset (width, 0);
+ return curve;
+}
projects / lilypond.git / blobdiff