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TitleCurvature Approximation of 3D Manifolds in 4D Space (Article)
inComputer Aided Geometric Design
Author(s) Bernd Hamann
Keyword(s)Approximation; Curvature, Differentiable manifold; Gauss-Weingarten map; Least square approximation; Scattered data; Triangulation
Year 1994
Volume11
Number6
Pages621--633
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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 3-surface) is presented. The approximation scheme is based on the fact that a parametric 3-surface 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 3-surface 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.