source file of the GNU LilyPond music typesetter
- (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
+ (c) 1998--2009 Jan Nieuwenhuizen <janneke@gnu.org>
*/
-#include <math.h>
-
#include "misc.hh"
#include "bezier.hh"
-
static Real
F0_1 (Real x)
{
- return 2 / M_PI * atan (M_PI * x / 2);
+ return 2 / M_PI *atan (M_PI *x / 2);
}
Real
return F0_1 (width * r_0 / h_inf) * h_inf;
}
- /*
-
-
- ^ x x
+/*
+ ^ x x
|
-height <indent>
+ height <indent>
|
- v x x
+ v x x
+
+
-
-
For small w, the height should be proportional to w, for w ->
infinity, the height should rise to a limit asymptotically.
h = h_infinity * F (x * r_0 / h_infinity)
-
+
Examples:
* F (x) = 2/pi * atan (pi x/2)
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
+ 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.
slurs. For large slurs, this gives a certain hookiness at the end,
so we increase the indent.
- ind = G(w)
+ indent = G (w)
+
+ w -> 0, G (w) -> .33 w
- w -> 0, G(w) -> .5 h
- w -> inf, G(w) -> 2*h
+ (due to derivative constraints, we cannot have indent > len/3)
- eg.
+ w -> inf, G (w) -> 2*h_inf
+ i.e.
- G(w) = h (w/(w+h_inf) 1.5 + .5 h
-
-
- */
+
+ 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)
{
- *height = slur_height (width, h_inf, r_0);
- *indent = (width / (h_inf + width) * 1.5 + 0.5) * (*height);
+ 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
{
Real indent;
Real height;
-
+
get_slur_indent_height (&indent, &height,
- width, h_inf, r_0);
+ width, h_inf, r_0);
Bezier curve;
curve.control_[0] = Offset (0, 0);