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A discrete diagonal Hodge star operator for pairwise Delaunay triangulations was described in Hirani et al. (2013). This note fixes errors in two figures and some indexing mistakes in the original paper. One consequence of this fix is that discrete exterior calculus may be applicable to a wider class of meshes.
There are several classes of operators on graphs to consider in deciding on a collection of building blocks for graph algorithms. One class involves traditional graph operations such as breadth first or depth first search, finding connected components, spanning trees, cliques and other sub graphs, operations for editing graphs and so on. Another class consists of linear algebra operators where the...
We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for DEC...
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