Web-ja: update introduction

[lilypond.git] / lily / bezier.cc

diff --git a/lily/bezier.cc b/lily/bezier.cc
index c4cdbb1c7b6c07d41bb338767994eef1bccc2ae4..eacd4fe6a44e95f224d6a9f4894455198167710a 100644 (file)
--- 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--2012 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}
 */
@@ -306,9 +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]);
 }