/*
- 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--2012 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.
-#include <math.h>
+ You should have received a copy of the GNU General Public License
+ along with LilyPond. If not, see <http://www.gnu.org/licenses/>.
+*/
-#include "bezier-bow.hh"
#include "misc.hh"
#include "bezier.hh"
-static Real F0_1 (Real x)
+static Real
+F0_1 (Real x)
{
- return M_PI /2 * atan(2 * x / M_PI);
+ return 2 / M_PI * atan (M_PI * x / 2);
}
Real
return F0_1 (width * r_0 / h_inf) * h_inf;
}
- /*
+/*
+ ^ x x
+ |
+ height <indent>
+ |
+ v x x
+
+
+
For small w, the height should be proportional to w, for w ->
infinity, the height should rise to a limit asymptotically.
- Hence we take F(x) such that
- F(0) = 0 , F'(0) = 1, and F(infty) = 1
+ Hence we take F (x) such that
+ F (0) = 0 , F' (0) = 1, and F (infty) = 1
and use
- h = h_infinity * F(x * r_0 / h_infinity)
+ h = h_infinity * F (x * r_0 / h_infinity)
+
-
Examples:
- * F(x) = pi/2 * atan (2x/pi)
+ * F (x) = 2/pi * atan (pi x/2)
- * F(x) 1/alpha * x^alpha / (1 + x^alpha)
+ * F (x) = 1/alpha * x^alpha / (1 + x^alpha)
* (etc.)
`small' slurs to `big' slurs occurs.]
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 paper settings, but we did
+ 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.
- */
+
+ 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.
+
+ indent = G (w)
+
+ w -> 0, G (w) -> .33 w
+
+
+ (due to derivative constraints, we cannot have indent > len/3)
+
+ w -> inf, G (w) -> 2*h_inf
+
+ i.e.
+
+
+ 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
+get_slur_indent_height (Real *indent, Real *height,
+ Real width, Real h_inf, Real r_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)
{
- Bezier curve;
- Real height = slur_height (width, h_inf, r_0);
- Real indent = height;
+ 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;
}
-