Definition:Frenet-Serret Frame

Definition
Let $\alpha : I \to \R^3$ be a smooth curve parameterized by arc length.

Let $s \in I$ be such that the curvature $\map \kappa s \ne 0$.

The Frenet-Serret frame of $\alpha$ at $s$ is the triple:
 * $\struct {\map t s, \map n s, \map b s}$

where:
 * $\map t s$ is the unit tangent vector
 * $\map n s$ is the normal vector
 * $\map b s$ is the binormal vector

Also known as
Also called:
 * Frenet trihedron
 * TNB frame
 * moving trihedron