* configure.in: Test for and accept lmodern if EC fonts not found.

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

diff --git a/lily/bezier-bow.cc b/lily/bezier-bow.cc
index c0a87c155299c18a269de75da7e94e8eef9f48c0..70072356edab1bc5f421909fad2d69e878b8f7dc 100644 (file)
--- a/lily/bezier-bow.cc
+++ b/lily/bezier-bow.cc
@@ -3,12 +3,11 @@
 
   source file of the GNU LilyPond music typesetter
 
-  (c) 1998--2002 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
-#include <math.h>
+#include <cmath>
 
-#include "bezier-bow.hh"
 #include "misc.hh"
 #include "bezier.hh"
 
@@ -26,6 +25,16 @@ slur_height (Real width, Real h_inf, Real r_0)
 }
 
   /*
+
+
+  ^              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.
 
@@ -41,7 +50,7 @@ slur_height (Real width, Real h_inf, Real r_0)
 
   * 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 +59,67 @@ 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;
 }
-