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An intuitive explanation of third-order surface behavior

Pushkar Joshi - No affiliation found

2010/02/01 Full-length article DOI: 10.1016/j.cagd.2009.11.003 Journal: Computer Aided Geometric Design

Abstract:

AbstractWe present a novel parameterization-independent exposition of the third-order geometric behavior of a surface point. Unlike existing algebraic expositions, our work produces an intuitive explanation of third-order shape, analogous to the principal curvatures and directions that describe second-order shape. We extract four parameters that provide a quick and concise understanding of the third-order surface behavior at any given point. Our shape parameters are useful for easily characterizing different third-order surface shapes without having to use tensor algebra. Our approach generalizes to higher orders, allowing us to extract similarly intuitive parameters that fully describe fourth- and higher-order surface behavior.