Declarative Mesh Subdivision Using Topological Rewriting in MGS

  • Antoine Spicher
  • Olivier Michel
  • Jean-Louis Giavitto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6372)


Mesh subdivision algorithms are usually specified informally using graphical schemes defining local mesh refinements. These algorithms are then implemented efficiently in an imperative framework. The implementation is cumbersome and implies some tricky indices management. Smith et al. (2004) asks the question of the declarative programming of such algorithms in an index-free way. In this paper, we positively answer this question by presenting a rewriting framework where mesh refinements are described by simple rules. This framework is based on a notion of topological chain rewriting. Topological chains generalize the notion of labeled graph to higher dimensional objects. This framework has been implemented in the domain specific language MGS. The same generic approach has been used to implement Loop as well as Butterfly, Catmull-Clark and Kobbelt subdivision schemes.


Graph Transformation Membrane Computing Subdivision Algorithm Cellular Complex Topological Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Antoine Spicher
    • 1
  • Olivier Michel
    • 1
  • Jean-Louis Giavitto
    • 2
  1. 1.LACLUniversité Paris-Est CréteilCréteilFrance
  2. 2.Laboratoire IBISCCNRS - Université d’ÉvryÉvryFrance

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