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| Title | Curvature Approximation of 3D Manifolds in 4D Space
(Article) |
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| in | Computer Aided Geometric Design |
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| Author(s) |
Bernd Hamann |
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| Keyword(s) | Approximation; Curvature, Differentiable manifold; Gauss-Weingarten map; Least square approximation; Scattered data; Triangulation |
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| Year |
1994
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| Volume | 11 |
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| Number | 6 |
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| Pages | 621--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.
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