X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=lily%2Fbezier.cc;h=d9267124037f329b37c6a9d2c7a5e68ad521fcfe;hb=21f6ea846dc1930cb41f185485ce6e1c8d9b30bd;hp=56e14943f8d75c235c4af6abc589c5c129b19bb9;hpb=d61cf3bbdb1c6670a127ba3baddf2f04d3e34fd3;p=lilypond.git

diff --git a/lily/bezier.cc b/lily/bezier.cc
index 56e14943f8..d926712403 100644
--- a/lily/bezier.cc
+++ b/lily/bezier.cc
@@ -140,6 +140,24 @@ Bezier::curve_point (Real t) const
   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}
 */
@@ -245,14 +263,12 @@ 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 ())
     {