
Title  Curvature Approximation of 3D Manifolds in 4D Space
(Article) 
in  Computer Aided Geometric Design 
Author(s) 
Bernd Hamann 
Keyword(s)  Approximation; Curvature, Differentiable manifold; GaussWeingarten map; Least square approximation; Scattered data; Triangulation 
Year 
1994

Volume  11 
Number  6 
Pages  621633 
Download  
BibTeX  
Abstract 
A method for the approximation of the three principal curvatures at points on a discretized, triangulated 3D manifold in 4D space (referred to as 3surface) is presented. The approximation scheme is based on the fact that a parametric 3surface can locally be approximated by the graph of a trivariate function. Using a local coordinate system, at lest square polynomial approximation is constructed for the estimation of the principal curvature at each 3surface point. Curvature is extremely useful for the analysis of qualitative characteristics of surfaces. The technique presented is an example of extending existing surface interrogation methods to multivariate data. Such a generalization is valuble for scientific visualization.
