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Curvature Approximation of 3D Manifolds in 4D Space

@article{Hamann:1994:CAO,
title="Curvature Approximation of 3D Manifolds in 4D Space",
journal="Computer Aided Geometric Design",
author="Bernd Hamann ",
year="1994",
keywords="Approximation; Curvature, Differentiable manifold; Gauss-Weingarten map; Least square approximation; Scattered data; Triangulation",
pages="621--633",
volume="11",
number="6",
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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