Parametrization of Generalized Primal-Dual Triangulations

  • Pooran Memari
  • Patrick Mullen
  • Mathieu Desbrun


Motivated by practical numerical issues in a number of modeling and simulation problems, we introduce the notion of a compatible dual complex to a primal triangulation, such that a simplicial mesh and its compatible dual complex (made out of convex cells) form what we call a primal-dual triangulation. Using algebraic and computational geometry results, we show that compatible dual complexes exist only for a particular type of triangulation known as weakly regular. We also demonstrate that the entire space of primal-dual triangulations, which extends the well known (weighted) Delaunay/Voronoi duality, has a convenient, geometric parametrization. We finally discuss how this parametrization may play an important role in discrete optimization problems such as optimal mesh generation, as it allows us to easily explore the space of primal-dual structures along with some important subspaces.


Voronoi Diagram Delaunay Triangulation Convex Polytopes Lower Envelope Dual Complex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pooran Memari
    • 1
    • 2
  • Patrick Mullen
    • 1
  • Mathieu Desbrun
    • 1
  1. 1.California Institute of TechnologyUS
  2. 2.CNRS - LTCI, Télécom ParisTechFrance

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