Chapter 2: Space Curves
Section 2.7: Frenet-Serret Formalism
If s is arc length, establish the Frenet equation T′s=κ N.
By definition, the curvature is κ=T′s. Since T is a unit vector, T·T=1, and T·T′=2 T·T′=0, so T′ is orthogonal to T. The direction of T′ defines the direction of the principal normal, the unit vector N. Hence, T′/κ=N, or T′=κ N.
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