Using hierarchical simplicial sets for surface intersection

Matthieu Dazy and Bruno Levy and Bruno Mallet. ( 2000 )
in: 20th gOcad Meeting, ASGA

Abstract

We propose a data structure to represent the transient state of geometrical algorithms on triangulated surfaces, with the problem of surface intersection as a particular interest. The structure is based on simplicial sets and uses a hierarchy of simplicial complexes to store the history of the computations. We introduce a relationship of combinatorial embedding to represent intersection relationships. Barycentric coordinates are computed for newly created points in order to allow for local computations when necessary. A set of operations is defined to allow for simple design of the algorithm.

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    BibTeX Reference

    @inproceedings{DazyRM2000,
     abstract = { We propose a data structure to represent the transient state of geometrical algorithms on triangulated surfaces, with the problem of surface intersection as a particular interest. The structure is based on simplicial sets and uses a hierarchy of simplicial complexes to store the history of the computations. We introduce a relationship of combinatorial embedding to represent intersection relationships. Barycentric coordinates are computed for newly created points in order to allow for local computations when necessary. A set of operations is defined to allow for simple design of the algorithm. },
     author = { Dazy, Matthieu AND Levy, Bruno AND Mallet, Bruno },
     booktitle = { 20th gOcad Meeting },
     month = { "june" },
     publisher = { ASGA },
     title = { Using hierarchical simplicial sets for surface intersection },
     year = { 2000 }
    }