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/*
This file is part of LilyPond, the GNU music typesetter.
Copyright (C) 1998--2015 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 "misc.hh"
#include "bezier.hh"
static Real
F0_1 (Real x)
{
return 2 / M_PI * atan (M_PI * x / 2);
}
Real
slur_height (Real width, Real h_inf, Real r_0)
{
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
and use
h = h_infinity * F (x * r_0 / h_infinity)
Examples:
* F (x) = 2/pi * atan (pi x/2)
* F (x) = 1/alpha * x^alpha / (1 + x^alpha)
* (etc.)
[with the 2nd recipe you can determine how quickly the conversion from
`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 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)
{
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;
}
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