X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=eacd4fe6a44e95f224d6a9f4894455198167710a;hb=97a0169312a260933246ab224e4f8b0969871dd5;hp=f0197fc0e2ffbd390aee8c3b0a1587a76f4bca6e;hpb=49fbcc8b526edcad8a0650e9d7870b647c43d698;p=lilypond.git

diff --git a/lily/bezier.cc b/lily/bezier.cc
index f0197fc0e2..eacd4fe6a4 100644
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -1,7 +1,7 @@
 /*
   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
@@ -38,9 +38,9 @@ scale (vector<Offset> *array, Real x, Real y)
 }
 
 void
-rotate (vector<Offset> *array, Real phi)
+rotate (vector<Offset> *array, Real deg)
 {
-  Offset rot (complex_exp (Offset (0, phi)));
+  Offset rot (offset_directed (deg));
   for (vsize i = 0; i < array->size (); i++)
     (*array)[i] = complex_multiply (rot, (*array)[i]);
 }
@@ -140,6 +140,22 @@ Bezier::curve_point (Real t) const
   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}
 */
@@ -245,14 +261,12 @@ Bezier::minmax (Axis ax, Real l, Real r, Direction d) const
 
   //  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 ())
     {
@@ -308,9 +322,9 @@ Bezier::scale (Real x, Real y)
 }
 
 void
-Bezier::rotate (Real phi)
+Bezier::rotate (Real deg)
 {
-  Offset rot (complex_exp (Offset (0, phi)));
+  Offset rot (offset_directed (deg));
   for (int i = 0; i < CONTROL_COUNT; i++)
     control_[i] = complex_multiply (rot, control_[i]);
 }