lily/bezier-bow.cc

   1 /*
   2   bezier.cc -- implement Bezier and Bezier_bow
   3
   4   source file of the GNU LilyPond music typesetter
   5
   6   (c) 1998--2002 Jan Nieuwenhuizen <janneke@gnu.org>
   7 */
   8
   9 #include <math.h>
  10
  11 #include "bezier-bow.hh"
  12 #include "misc.hh"
  13 #include "bezier.hh"
  14
  15
  16 static Real
  17 F0_1 (Real x)
  18 {
  19   return 2 / M_PI * atan (M_PI * x / 2);
  20 }
  21
  22 Real
  23 slur_height (Real width, Real h_inf, Real r_0)
  24 {
  25   return F0_1 (width * r_0 / h_inf) * h_inf;
  26 }
  27
  28   /*
  29   For small w, the height should be proportional to w, for w ->
  30   infinity, the height should rise to a limit asymptotically.
  31
  32   Hence we take F (x) such that
  33   F (0) = 0 , F' (0) = 1, and F (infty) = 1
  34
  35   and use
  36
  37   h = h_infinity * F (x * r_0 / h_infinity)
  38
  39
  40   Examples:
  41
  42   * F (x) = 2/pi * atan (pi x/2)
  43
  44   * F (x) 1/alpha * x^alpha / (1 + x^alpha)
  45
  46   * (etc.)
  47
  48   [with the 2nd recipe you can determine how quickly the conversion from
  49   `small' slurs to `big' slurs occurs.]
  50
  51   Although this might seem cand_idates to SCM-ify, it is not all clear
  52   which parameters (ie. h_inf, r_0, F (.)) should be candidates for
  53   this.  At present h_inf and r_0 come from paper settings, but we did
  54   no experiments for determining the best combinations of F, h_inf and
  55   r_0.
  56
  57   */
  58
  59 Bezier
  60 slur_shape (Real width, Real h_inf, Real r_0)
  61 {
  62   Bezier curve;
  63   Real height =  slur_height (width, h_inf, r_0);
  64   Real indent = height;
  65
  66   curve.control_[0] = Offset (0, 0);
  67   curve.control_[1] = Offset (indent, height);
  68   curve.control_[2] = Offset (width - indent, height);
  69   curve.control_[3] = Offset (width, 0);
  70   return curve;
  71 }
  72