Uniformize, internalize.

[lilypond.git] / lily / bezier-bow.cc

diff --git a/lily/bezier-bow.cc b/lily/bezier-bow.cc
index 06f6cc211846bed34a8be22e211197b00a100f77..c7a26d9424a9fb4f01cc815d0a6984db3f01d862 100644 (file)
--- a/lily/bezier-bow.cc
+++ b/lily/bezier-bow.cc
@@ -3,7 +3,7 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2005 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
 #include <math.h>
@@ -59,7 +59,7 @@ height   <indent>
 
   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.
 
@@ -68,30 +68,44 @@ height   <indent>
   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) -> .5 h
+  w -> 0,  G(w) -> .33 w
 
-  w -> inf, G(w) -> 2*h
+  
+  (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
 
-  eg.
+   G(w) = r  + p/(w+q)
 
+  yields
 
-  G(w) = h (w/(w+h_inf) 1.5 + .5 h 
+   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,
+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);
-  *indent = (width/(h_inf+ width)*1.5 + 0.5) * (*height);
-}
-
-
 
+  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)