If $c$ is a regular path in space with non-vanishing acceleration, we define the unit tangent $\mathbf{T}$ to be the normalized velocity; we define the principal normal $\mathbf{N}$ to be the unique unit vector orthogonal to $\mathbf{T}$ such that $c'' = v\mathbf{T} + \kappa\mathbf{N}$ with $\kappa > 0$; and we define the binormal $\mathbf{B}$ to be the cross product $\mathbf{T} \times \mathbf{N}$.
The ordered triple $(\mathbf{T}, \mathbf{N}, \mathbf{B})$ is the Frenet-Serret frame of $c$. Each demo shows a space curve with its Frenet-Serret frame. The tangent is blue, the principal normal is light blue, and the binormal is light green.
The left and right arrow keys “pan” the view point; the up and down arrow keys “tilt” the view point; comma (less-than) and period (greater-than) move the frame backward and forward along the curve.