CURVATURE APPROXIMATION OF 3D MANIFOLDS IN 4D SPACE

A method for the approximation of the three principal curvatures at po ints on a discretized, triangulated 3D manifold in 4D space (referred to as 3-surface) is presented. The approximation scheme is based on th e fact that a parametric 3-surface can locally be approximated by the graph of a trivariate function. Using a local coordinate system, a lea st square polynomial approximation is constructed for the estimation o f the principal curvatures at each 3-surface point. Curvature is extre mely useful for the analysis of qualitative characteristics of surface s. The technique presented is an example of extending existing surface interrogation methods to multivariate data. Such a generalization is valuable for scientific visualization.