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Link Conditions for Simplifying Meshes with Embedded Structures
July 2011 (vol. 17 no. 7)
pp. 1007-1019
Dilip Mathew Thomas, Indian Institute of Science, Bengaluru
Vijay Natarajan, Indian Institute of Science, Bengaluru
Georges-Pierre Bonneau, LJK, INRIA Grenoble and and the University of Grenoble, Rhone-Alpes, Montbonnot
Interactive visualization applications benefit from simplification techniques that generate good-quality coarse meshes from high-resolution meshes that represent the domain. These meshes often contain interesting substructures, called embedded structures, and it is desirable to preserve the topology of the embedded structures during simplification, in addition to preserving the topology of the domain. This paper describes a proof that link conditions, proposed earlier, are sufficient to ensure that edge contractions preserve the topology of the embedded structures and the domain. Excluding two specific configurations, the link conditions are also shown to be necessary for topology preservation. Repeated application of edge contraction on an extended complex produces a coarser representation of the domain and the embedded structures. An extension of the quadric error metric is used to schedule edge contractions, resulting in a good-quality coarse mesh that closely approximates the input domain and the embedded structures.

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Index Terms:
Embedded structures, extended complex, link conditions, mesh simplification, topology preservation, quadric error metric.
Citation:
Dilip Mathew Thomas, Vijay Natarajan, Georges-Pierre Bonneau, "Link Conditions for Simplifying Meshes with Embedded Structures," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 7, pp. 1007-1019, July 2011, doi:10.1109/TVCG.2010.90
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