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