Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^. N^. B^.] = [0 | κ | 0 -κ | 0 | τ 0 | -τ | 0][T N B], where T is the unit tangent vector, N is the unit normal vector, B is the unit binormal vector, τ is the torsion, κ is the curvature, and x^. denotes d x/d s.
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