### 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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