2007/09/18 by Anthony A. Ruffa, Ruffa, Anthony A.
Engineering · Mathematics · Computer Science · #Advanced Numerical Analysis Techniques #Mathematics and Applications #Computer Graphics and Visualization Techniques
paper · pdf · doi:10.48550/arxiv.0709.2855
A set of equations is developed to describe a curve in space given the curvature κ and the angle of rotation θ of the osculating plane. The set of equations has a solution (in terms of κ and θ) that indirectly solves the Frenet-Serret equations, with a unique value of θ for each specified value of τ. Explicit solutions can be generated for constant θ. The equations break down when the tangent vector aligns to one of the unit coordinate vectors, requiring a reorientation of the local coordinate system.