X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;ds=sidebyside;f=lily%2Fbezier-bow.cc;h=e3707c13909d7b64a9efbd1a186ce14b92d7ddf5;hb=8984edadec97616a1c98c0027a809f960dea6e4b;hp=b98b613c1edaaba7a79463001960884c50e90118;hpb=fc3e875d6bf06f0680e897faffdcab36ad975a03;p=lilypond.git

diff --git a/lily/bezier-bow.cc b/lily/bezier-bow.cc
index b98b613c1e..e3707c1390 100644
--- a/lily/bezier-bow.cc
+++ b/lily/bezier-bow.cc
@@ -3,20 +3,16 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--2001 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2009 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
-#include <math.h>
-
-#include "bezier-bow.hh"
 #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
@@ -25,7 +21,15 @@ 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.
 
@@ -36,12 +40,12 @@ slur_height (Real width, Real h_inf, Real r_0)
 
   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)
+  * F (x) = 1/alpha * x^alpha / (1 + x^alpha)
 
   * (etc.)
 
@@ -50,23 +54,64 @@ slur_height (Real width, Real h_inf, Real r_0)
 
   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.
 
-  */
+
+  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;
 }
-