lily/bezier.cc

   1 /*
   2   bezier.cc -- implement Bezier and Bezier_bow
   3
   4   source file of the GNU LilyPond music typesetter
   5
   6   (c) 1998 Jan Nieuwenhuizen <jan@digicash.com>
   7 */
   8
   9 #include <math.h>
  10 #include "offset.hh"
  11 #include "bezier.hh"
  12 #include "dimen.hh"
  13 #include "paper-def.hh"
  14
  15 Bezier::Bezier (int steps_i)
  16 {
  17   steps_i_ = steps_i;
  18   curve_ = new Offset [steps_i_ + 1];
  19 }
  20
  21 Bezier::~Bezier ()
  22 {
  23   delete[] curve_;
  24 }
  25
  26 //from GNU gs3.33: ega.c
  27 void
  28 Bezier::calc (Offset control[4])
  29 {
  30   Real dt = 1.0 / steps_i_;
  31   Real cx = 3.0 * (control[1].x() - control[0].x());
  32   Real bx = 3.0 * (control[2].x() - control[1].x()) - cx;
  33   Real ax = control[3].x() - (control[0].x() + cx + bx);
  34   Real cy = 3.0 * (control[1].y () - control[0].y ());
  35   Real by = 3.0 * (control[2].y () - control[1].y ()) - cy;
  36   Real ay = control[3].y () - (control[0].y () + cy + by);
  37   Real t = 0.0;
  38   int i = 0;
  39   while ( t <= 1.0 )
  40     {
  41       curve_[i].x() = ((ax * t + bx) * t + cx) * t + control[0].x();
  42       curve_[i++].y () = ((ay * t + by) * t + cy) * t + control[0].y ();
  43       t += dt;
  44     }
  45 }
  46
  47 Real
  48 Bezier::y (Real x)
  49 {
  50   if (x <= curve_[0].x())
  51     return curve_[0].y ();
  52   for (int i = 1; i < steps_i_; i++ )
  53     {
  54       if (x < curve_[i].x())
  55         {
  56           Real lin = (x - curve_[i-1].x()) / (curve_[i].x() - curve_[i-1].x());
  57           return curve_[i-1].y () + lin * (curve_[i].y () - curve_[i-1].y ());
  58         }
  59     }
  60   return curve_[steps_i_-1].y ();
  61 }
  62
  63
  64 Bezier_bow::Bezier_bow (Paper_def* paper_l)
  65   : Bezier(10)
  66 {
  67   paper_l_ = paper_l;
  68 }
  69
  70
  71 /*
  72   from feta-sleur.ly
  73
  74         slurheightlimit#:=staffsize#/2;
  75         sluralpha:=slurheightlimit#*pi/2;
  76         % slurratio:=1/3;
  77         slurratio:=0.3333;
  78         slurbeta:=3/4*pi*slurratio/sluralpha;
  79
  80         b#:=length(dx#,dy#);
  81         % ugh: huh? 2/5
  82         indent#:=2/5*sluralpha*atan(slurbeta*b#);
  83         height:=(indent+h)*d;
  84         z1=(0,0);
  85         z2=(b,0);
  86         z3=(indent,height);
  87         z4=(b-indent,height);
  88
  89         boogje:=boogje rotated angle(dxs,dys);
  90 */
  91
  92 void
  93 Bezier_bow::calc (Real dx, Real dy, Real h, Real d)
  94 {
  95   // ugh
  96   Real pi = M_PI;
  97   // ugh
  98   Real staffsize_f = paper_l_->get_var ("barsize");
  99   Real height_limit = staffsize_f;
 100   Real alpha = height_limit * pi / 2.0;
 101   Real ratio = 1.0/3.0;
 102   Real beta = 3.0/4.0 * pi * ratio/alpha;
 103
 104   Real b = sqrt (dx * dx + dy * dy);
 105   Real indent = 2.0/5.0 * alpha * atan (beta * b);
 106   // ugh, ugly height hack, see lily-ps-defs.tex
 107   Real height = (indent + h) * d;
 108
 109   Offset control[4];
 110   control[0] = Offset(0, 0);
 111   control[1] = Offset(indent, height);
 112   control[2] = Offset(b - indent, height);
 113   control[3] = Offset( b, 0 );
 114
 115   Real phi = dx ? atan (dy/dx) : sign (dy) * pi / 2.0;
 116   Real sphi = sin (phi);
 117   Real cphi = cos (phi);
 118   for (int i = 1; i < 4; i++)
 119     {
 120       control[i].x() = cphi * control[i].x() - sphi * control[i].y ();
 121       control[i].y () = sphi * control[i].x() + cphi * control[i].y ();
 122     }
 123   Bezier::calc (control);
 124 }
 125