/*
This file is part of LilyPond, the GNU music typesetter.
- Copyright (C) 1998--2011 Jan Nieuwenhuizen <janneke@gnu.org>
+ Copyright (C) 1998--2015 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
#include "warn.hh"
#include "libc-extension.hh"
-Real binomial_coefficient_3[] =
+Real binomial_coefficient_3[]
+=
{
1, 3, 3, 1
};
return o;
}
+// The return value is normalized unless zero or indefinite.
+Offset
+Bezier::dir_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];
+
+ return (third_order[1] - third_order[0]).direction ();
+}
+
/*
Cache binom (3, j) t^j (1-t)^{3-j}
*/
// or intersections of the curve with the bounding lines at L and R.
Interval lr (l, r);
- Direction dir = LEFT;
- do
+ for (LEFT_and_RIGHT (dir))
{
vector<Real> v = get_other_coordinates (ax, lr[dir]);
for (vsize i = v.size (); i--;)
iv.add_point (v[i]);
}
- while (flip (&dir) != LEFT);
if (iv.is_empty ())
{