Imported Upstream version 2.18.0

[lilypond.git] / lily / bezier.cc

diff --git a/lily/bezier.cc b/lily/bezier.cc
index c4cdbb1c7b6c07d41bb338767994eef1bccc2ae4..d9267124037f329b37c6a9d2c7a5e68ad521fcfe 100644 (file)
--- 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}
 */