X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier-bow.cc;h=d9510704eef33f1955c9b79934bb1a1f26d9d369;hb=d445cda01e4d86896f55fd1cf2ccbaba8cb7917a;hp=06f6cc211846bed34a8be22e211197b00a100f77;hpb=054aaa1ccfdcb8d9a8fbf4d8d7376767e4f7b7d7;p=lilypond.git

diff --git a/lily/bezier-bow.cc b/lily/bezier-bow.cc
index 06f6cc2118..d9510704ee 100644
--- a/lily/bezier-bow.cc
+++ b/lily/bezier-bow.cc
@@ -3,19 +3,16 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2006 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
@@ -24,17 +21,15 @@ slur_height (Real width, Real h_inf, Real r_0)
   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.
 
@@ -45,7 +40,7 @@ height   <indent>
 
   h = h_infinity * F (x * r_0 / h_infinity)
 
-  
+
   Examples:
 
   * F (x) = 2/pi * atan (pi x/2)
@@ -59,7 +54,7 @@ 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.
 
@@ -68,39 +63,50 @@ 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) -> .33 w
+
+
+  (due to derivative constraints, we cannot have indent > len/3)
 
-  w -> 0,  G(w) -> .5 h
+  w -> inf, G(w) -> 2*h_inf
 
-  w -> inf, G(w) -> 2*h
+  i.e.
 
-  eg.
 
+  G(0) = 0 , G'(0) 1/3, G(infty) = 2h_inf
 
-  G(w) = h (w/(w+h_inf) 1.5 + .5 h 
-  
-  
-  */
+  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,
+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
 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);
+			  width, h_inf, r_0);
 
   Bezier curve;
   curve.control_[0] = Offset (0, 0);