A geometric convection approach of 3-D reconstruction
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete exterior calculus
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
The flow complex: A data structure for geometric modeling
Computational Geometry: Theory and Applications
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
Computational Geometry: Theory and Applications
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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 and is a diagonal matrix with the ratio of primal and dual volumes along the diagonal. A correct definition requires that all entries be positive. DEC is a framework for numerically solving differential equations on meshes and for geometry processing tasks and has had considerable impact in computer graphics and scientific computing. Our result allows the use of DEC with a much larger class of meshes than was previously considered possible.