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arXiv · 1502.07782

Distributed mean curvature on a discrete manifold for Regge calculus

Rory Conboye·Warner A. Miller·Shannon Ray
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Abstract

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as a fractional rate of change of the normal vector.

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Rory Conboye, Warner A. Miller, Shannon Ray. 2015-02-26. Distributed mean curvature on a discrete manifold for Regge calculus. https://doi.org/10.1088/0264-9381/32/18/185009

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