Discrete Distortion in Triangulated 3-Manifolds
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Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
Abstract
We introduce a novel notion, that we call discrete distortion, for a triangulated 3-manifold. Discrete distortion naturally generalizes the notion of concentrated curvature defined for triangulated surfaces and provides a powerful tool to understand the local geometry and topology of 3-manifolds. Discrete distortion can be viewed as a discrete approach to Ricci curvature for singular flat manifolds. We distinguish between two kinds of distortion, namely, vertex distortion, which is associated with the vertices of the tetrahedral mesh decomposing the 3-manifold, and bond distortion, which is associated with the edges of the tetrahedral mesh. We investigate properties of vertex and bond distortions. As an example, we visualize vertex distortion on manifold hypersurfaces in R4 defined by a scalar field on a 3D mesh. distance fields.
Description
@article{10.1111:j.1467-8659.2008.01272.x,
journal = {Computer Graphics Forum},
title = {{Discrete Distortion in Triangulated 3-Manifolds}},
author = {Mesmoudi, Mohammed Mostefa and De Floriani, Leila and Port, Umberto},
year = {2008},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2008.01272.x}
}