Delaunay Hodge star

Anil N. Hirani, Kaushik Kalyanaraman, Evan B. Vanderzee

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)540-544
Number of pages5
JournalCAD Computer Aided Design
Issue number2
StatePublished - Feb 2013


  • Circumcentric dual
  • Discrete exterior calculus
  • Primal mesh

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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