Gets vertical skylines from grob stencils

lily/bezier.cc

 /*
   This file is part of LilyPond, the GNU music typesetter.
 
   Copyright (C) 1998--2012 Jan Nieuwenhuizen <janneke@gnu.org>
 
   LilyPond is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation, either version 3 of the License, or
   (at your option) any later version.
 
@@ skipping 120 matching lines @@
 
       tj *= t;
     }
 
 #ifdef PARANOID
   assert (fabs (o[X_AXIS] - polynomial (X_AXIS).eval (t)) < 1e-8);
   assert (fabs (o[Y_AXIS] - polynomial (Y_AXIS).eval (t)) < 1e-8);
 #endif
 
   return o;
+}
+
+Real
+Bezier::slope_at_point (Real t) const
+{
+  Offset second_order[3];
+  Offset third_order[2];
+
+  for (vsize i = 0; i < 3; i++)
+    second_order[i] = ((control_[i + 1] - control_[i]) * t) + control_[i];
+
+  for (vsize i = 0; i < 2; i++)
+    third_order[i] = ((second_order[i + 1] - second_order[i]) * t) + second_order[i];
+
+  if (third_order[1][X_AXIS] - third_order[0][X_AXIS] == 0)
+    return infinity_f;
+
+  return (third_order[1][Y_AXIS] - third_order[0][Y_AXIS]) / (third_order[1][X_AXIS] - third_order[0][X_AXIS]);
 }
 
 /*
   Cache binom (3, j) t^j (1-t)^{3-j}
 */
 struct Polynomial_cache
 {
   Polynomial terms_[4];
   Polynomial_cache ()
   {
@@ skipping 226 matching lines @@
   else
     subdivide (t_min, &bez1, &bez2);
   if (t_max == 1.0)
     return bez2;
   else
     {
       bez2.subdivide ((t_max - t_min) / (1 - t_min), &bez3, &bez4);
       return bez3;
     }
 }