lily/slur-bezier-bow.cc

   1 /*
   2   slur-bezier-bow.cc -- implement Slur_bezier_bow
   3
   4   source file of the GNU LilyPond music typesetter
   5
   6   (c) 2000--2001  Jan Nieuwenhuizen <janneke@gnu.org>
   7 */
   8
   9 #include "debug.hh"
  10 #include "paper-def.hh"
  11 #include "slur-bezier-bow.hh"
  12 #include "main.hh"
  13
  14 Slur_bezier_bow::Slur_bezier_bow (Array<Offset> encompass, Direction dir,
  15                                   Real h_inf, Real r_0)
  16 {
  17   h_inf_ = h_inf;
  18   r_0_ = r_0;
  19   alpha_ = 0;
  20   dir_ = dir;
  21   encompass_ = encompass;
  22   to_canonical_form ();
  23
  24   Real w = encompass_.top ()[X_AXIS] - encompass_[0][X_AXIS];
  25   curve_ = slur_shape (w, h_inf, r_0);
  26 }
  27
  28 Bezier
  29 Slur_bezier_bow::get_bezier () const
  30 {
  31   Bezier rv = curve_;
  32   if (dir_ == DOWN)
  33     {
  34       rv.scale (1, -1);
  35     }
  36
  37   rv.rotate (alpha_);
  38   rv.translate (origin_);
  39
  40   return rv;
  41 }
  42
  43 void
  44 Slur_bezier_bow::to_canonical_form ()
  45 {
  46   origin_ = encompass_[0];
  47   translate (&encompass_, -origin_);
  48
  49   Offset delta = encompass_.top () - encompass_[0];
  50   alpha_ = delta.arg ();
  51
  52   rotate (&encompass_, -alpha_);
  53   if (dir_ == DOWN)
  54     {
  55       scale (&encompass_, 1, -1);
  56     }
  57
  58   while (encompass_.size () > 1 && encompass_[1][X_AXIS] <= 0.0)
  59     {
  60       programming_error ("Degenerate bow: infinite steepness reqd");
  61       encompass_.del (1);
  62     }
  63
  64   Real l = encompass_.top ()[X_AXIS];
  65   while (encompass_.size () > 1 && encompass_.top (1)[X_AXIS] >= l)
  66     {
  67       programming_error ("Degenerate bow: infinite steepness reqd");
  68       encompass_.del (encompass_.size ()-2);
  69     }
  70 }
  71
  72
  73
  74 void
  75 Slur_bezier_bow::blow_fit ()
  76 {
  77   Real len = curve_.control_[3][X_AXIS];
  78   Real h = curve_.control_[1][Y_AXIS] * fit_factor () / len;
  79   curve_.control_[1][Y_AXIS] = h * len;
  80   curve_.control_[2][Y_AXIS] = h * len;
  81   curve_.assert_sanity ();
  82 }
  83
  84
  85 Real
  86 Slur_bezier_bow::enclosed_area_f () const
  87 {
  88   Real a = 0;
  89   for (int i=0; i < encompass_.size (); i++)
  90     {
  91       Interval x;
  92       Interval y;
  93       if (i == 0)
  94         {
  95           x = Interval (0, encompass_[1][X_AXIS] / 2);
  96           y = Interval (0,
  97                         curve_.get_other_coordinate (X_AXIS,
  98                                                      encompass_[1][X_AXIS]
  99                                                      / 2));
 100         }
 101       else if (i == encompass_.size () - 1)
 102         {
 103           x = Interval ((encompass_[i-1][X_AXIS] + encompass_[i][X_AXIS])/2,
 104                         encompass_[i][X_AXIS]);
 105           y = Interval (0,
 106  (curve_.get_other_coordinate (X_AXIS,
 107  (x[MIN] + x[MAX]) / 2)));
 108         }
 109       else
 110         {
 111           x = Interval ((encompass_[i-1][X_AXIS] + encompass_[i][X_AXIS]) / 2,
 112  (encompass_[i][X_AXIS] + encompass_[i+1][X_AXIS]) / 2);
 113           y = Interval (encompass_[i][Y_AXIS],
 114  (curve_.get_other_coordinate (X_AXIS, x[MIN])
 115                          + curve_.get_other_coordinate (X_AXIS,
 116  (x[MIN] + x[MAX]) / 2)
 117                          + curve_.get_other_coordinate (X_AXIS, x[MAX])) / 3);
 118         }
 119
 120       Real da = x.length () * y.length ();
 121       a += da;
 122     }
 123   return a;
 124 }
 125
 126 Array<Real>
 127 Slur_bezier_bow::area_x_gradients_array (Real area)
 128 {
 129   Real len = curve_.control_[3][X_AXIS];
 130   Real grow = len / 10.0;
 131   Array<Real> da (2);
 132   for (int i=0; i < 2; i++)
 133     {
 134       Real r = curve_.control_[i+1][X_AXIS];
 135       curve_.control_[i+1][X_AXIS] += grow;
 136       da[i] = (enclosed_area_f () - area) / grow;
 137       curve_.control_[i+1][X_AXIS] = r;
 138     }
 139   return da;
 140 }
 141
 142 /*
 143   ugh, should have another look, and use a regular optimization
 144   algorithm, instead of this homebrew.
 145 */
 146 void
 147 Slur_bezier_bow::minimise_enclosed_area (Real beauty,
 148                                          SCM bezier_props)
 149 {
 150   Real length = curve_.control_[3][X_AXIS];
 151   Real beautiful = beauty * length * slur_height (length, h_inf_, r_0_);
 152
 153
 154   if (fit_factor () > 1.0)
 155     blow_fit ();
 156
 157   Real pct_c0 = gh_scm2double (gh_cdr (scm_assoc (ly_symbol2scm ("bezier-pct-c0"), bezier_props)));
 158   Real pct_c3 = gh_scm2double (gh_cdr (scm_assoc (ly_symbol2scm ("bezier-pct-c3"), bezier_props)));
 159   Real pct_in_max =  gh_scm2double (gh_cdr (scm_assoc (ly_symbol2scm ("bezier-pct-in-max"), bezier_props)));
 160   Real pct_out_max = gh_scm2double (gh_cdr (scm_assoc (ly_symbol2scm ("bezier-pct-out-max"), bezier_props)));
 161   Real steps =  gh_scm2double (gh_cdr (scm_assoc (ly_symbol2scm ("bezier-area-steps"),bezier_props)));
 162
 163   for (int i=0; i < steps; i++)
 164     {
 165       Real area = enclosed_area_f ();
 166       if (area <= beautiful)
 167         break;
 168
 169       Array<Real> da = area_x_gradients_array (area);
 170
 171       // urg
 172       Real pct = pct_c0 + pct_c3 * length * length * length;
 173       pct *= (steps - i) / steps;
 174       if (da[0] > 0 || da[1] < 0)
 175         pct = pct <? pct_out_max;
 176       else
 177         pct = pct <? pct_in_max;
 178
 179       Real u = (abs (curve_.control_[1][X_AXIS] / da[0])
 180                 <? abs ((curve_.control_[3][X_AXIS]
 181                          - curve_.control_[2][X_AXIS]) / da[1]));
 182
 183       curve_.control_[1][X_AXIS] -= da[0] * u * pct;
 184       curve_.control_[2][X_AXIS] -= da[1] * u * pct;
 185     }
 186 }
 187
 188
 189
 190 /*
 191   max (encompass.y / curve.y)
 192
 193  */
 194 Real
 195 Slur_bezier_bow::fit_factor () const
 196 {
 197   Real x1 = encompass_[0][X_AXIS];
 198   Real x2 = encompass_.top ()[X_AXIS];
 199
 200   Real factor = 0.0;
 201   for (int i=1; i < encompass_.size ()-1; i++)
 202     {
 203       if (encompass_[i][X_AXIS] > x1 && encompass_[i][X_AXIS] < x2)
 204         {
 205          Real y = curve_.get_other_coordinate (X_AXIS, encompass_[i][X_AXIS]);
 206          if (y>0)
 207            {
 208              Real f = encompass_[i][Y_AXIS] / y;
 209              factor = factor >? f;
 210            }
 211         }
 212     }
 213
 214
 215   return factor;
 216 }
 217
 218
 219
 220