* python/lilylib.py (make_ps_images): only compute bbox when needed.

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

diff --git a/lily/bezier-bow.cc b/lily/bezier-bow.cc
index 6861f61fc4d1e3e2f8861b9ca70831595a393b0f..85d116e78c0725671c357363340009a619806803 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--2000 Jan Nieuwenhuizen <janneke@gnu.org>
+  (c) 1998--2004 Jan Nieuwenhuizen <janneke@gnu.org>
 */
 
 #include <math.h>
@@ -12,9 +12,11 @@
 #include "misc.hh"
 #include "bezier.hh"
 
-static Real F0_1 (Real x)
+
+static Real
+F0_1 (Real x)
 {
-  return M_PI /2 *  atan(2 * x / M_PI);
+  return 2 / M_PI * atan (M_PI * x / 2);
 }
 
 Real
@@ -24,22 +26,32 @@ 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.
 
-  Hence we take F(x) such that
-  F(0) = 0 , F'(0) = 1, and F(infty) = 1
+  Hence we take F (x) such that
+  F (0) = 0 , F' (0) = 1, and F (infty) = 1
 
   and use
 
-  h = h_infinity * F(x * r_0 / h_infinity)
+  h = h_infinity * F (x * r_0 / h_infinity)
 
   
   Examples:
 
-  * F(x) = pi/2 * atan (2x/pi)
+  * 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.)
 
@@ -47,11 +59,28 @@ slur_height (Real width, Real h_inf, Real r_0)
   `small' slurs to `big' slurs occurs.]
 
   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
+  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
   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.
+
+  ind = G(w)
+
+  w -> 0,  G(w) -> .5 h
+
+  w -> inf, G(w) -> 2*h
+
+  eg.
+
+
+  G(w) = h (w/(w+h_inf) 1.5 + .5 h 
+  
+  
   */
 
 Bezier
@@ -59,7 +88,7 @@ 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 = (width/(h_inf+ width)*1.5 + 0.5) * height;
 
   curve.control_[0] = Offset (0, 0);
   curve.control_[1] = Offset (indent, height);