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Third order surface analysis is an important aspect of shape interrogation and design. We present a novel parameterization-independent exposition of the geometric behavior of a surface point up to third order. Unlike existing algebraic expositions, our work produces an intuitive explanation of the third order surface behavior, analogous to the principal curvatures and directions that describe second order behavior. We extract four parameters that provide a quick and concise understanding of the third order surface behavior at any given point. Our shape parameters can be used to characterize different third order surface shapes without having to use tensor algebra.

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