Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
Ridges, crests and sub-parabolic lines of evolving surfaces
International Journal of Computer Vision
The Sub-Parabolic Lines of a Surface
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Suggestive contours for conveying shape
ACM SIGGRAPH 2003 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
G2 surface modeling using minimal mean-curvature-variation flow
Computer-Aided Design
Constrained surface interpolation by means of a genetic algorithm
Computer-Aided Design
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We 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.