Frenet reference

Let g=g(u) be a 3D curve. The trihedron known as Frenet frame (or reference) is the one identified by (t(u), n(u), b(u)) where:


        is the unit tangent



        is the unit normal



  is the unit binormal.

These definitions do not depend on the specific parameterization. The three vectors identify three planes at each point of the curve:

• The osculating plane is the plane spanned by t and n
• The normal plane is the plane spanned by n and b
• The rectifying plane is the plane spanned by t and b.