N-dimensional Data-Dependent Reconstruction Using Topological Changes

Zsolt Toth, Ivan Viola, Andrej Ferko, Meister Eduard Gröller
N-dimensional Data-Dependent Reconstruction Using Topological Changes
In Proceedings of TopoInVis 2005, Topology-based Methods in Visualization, pages 183-198. September 2007.
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Also available in TR-186-2-05-08.

Abstract

We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson‘s optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

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@inproceedings{toth-2007-ndd,
  title =      "N-dimensional Data-Dependent Reconstruction Using
               Topological Changes",
  author =     "Zsolt Toth and Ivan Viola and Andrej Ferko and Meister
               Eduard Gr{\"o}ller",
  year =       "2007",
  abstract =   "We introduce a new concept for a geometrically based feature
               preserving reconstruction technique of n-dimensional
               scattered data. Our goal is to generate an n-dimensional
               triangulation, which preserves the high frequency regions
               via local topology changes. It is the generalization of a 2D
               reconstruction approach based on data-dependent
               triangulation and Lawson‘s optimization procedure. The
               definition of the mathematic optimum of the reconstruction
               is given. We discuss an original cost function and a
               generalization of known functions for the n-dimensional
               case.",
  pages =      "183--198",
  month =      sep,
  note =       "Konferenz hat 2005 stattgefunden, Proceeding ist allerdings
               erst 2007 erschienen",
  booktitle =  "Proceedings of TopoInVis 2005, Topology-based Methods in
               Visualization",
  editor =     "H. Hauser, H. Hagen, H. Theisel",
  publisher =  "Springer",
  location =   "Budmerice, Slovakia",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/2007/toth-2007-ndd/",
}