2 bezier.cc -- implement Bezier and Bezier_bow
4 source file of the GNU LilyPond music typesetter
6 (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
11 #include "bezier-bow.hh"
19 return 2 / M_PI
* atan (M_PI
* x
/ 2);
23 slur_height (Real width
, Real h_inf
, Real r_0
)
25 return F0_1 (width
* r_0
/ h_inf
) * h_inf
;
39 For small w, the height should be proportional to w, for w ->
40 infinity, the height should rise to a limit asymptotically.
42 Hence we take F (x) such that
43 F (0) = 0 , F' (0) = 1, and F (infty) = 1
47 h = h_infinity * F (x * r_0 / h_infinity)
52 * F (x) = 2/pi * atan (pi x/2)
54 * F (x) = 1/alpha * x^alpha / (1 + x^alpha)
58 [with the 2nd recipe you can determine how quickly the conversion from
59 `small' slurs to `big' slurs occurs.]
61 Although this might seem cand_idates to SCM-ify, it is not all clear
62 which parameters (ie. h_inf, r_0, F (.)) should be candidates for
63 this. At present h_inf and r_0 come from paper settings, but we did
64 no experiments for determining the best combinations of F, h_inf and
68 The indent is proportional to the height of the slur for small
69 slurs. For large slurs, this gives a certain hookiness at the end,
70 so we increase the indent.
81 G(w) = h (w/(w+h_inf) 1.5 + .5 h
87 slur_shape (Real width
, Real h_inf
, Real r_0
)
90 Real height
= slur_height (width
, h_inf
, r_0
);
91 Real indent
= (width
/(h_inf
+ width
)*1.5 + 0.5) * height
;
93 curve
.control_
[0] = Offset (0, 0);
94 curve
.control_
[1] = Offset (indent
, height
);
95 curve
.control_
[2] = Offset (width
- indent
, height
);
96 curve
.control_
[3] = Offset (width
, 0);