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Representing Interpolant Topology for Contour Tree Computation

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Topology-Based Methods in Visualization II

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Summary

Algorithms for computing contour trees for visualization commonly assume that the input is defined by barycentric interpolation on simplicial meshes or by trilinear interpolation on cubic meshes. In this paper, we describe a general framework for computing contour trees from a graph that captures all significant topological features. We show how to construct these graphs from any mesh-based interpolant by using cell-by-cell “widgets,” and also how to avoid constructing the entire graphs by making finite state machines that capture their traversals.

Our framework eases algorithm development and implementation, and can be used to establish relationships between interpolants. For example, we use it to demonstrate a formal equivalence between the topology defined by implicitly dis-ambiguated marching cubes cases and the topology induced by 8-/18- digital image connectivity.

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Authors
  1. Hamish Carr
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  2. Jack Snoeyink
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Editor information

Editors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin Devision Scientific Computing, Department Visualization and Data Analysis, Takustraβe 7, Berlin, 14195, Germany

    Hans-Christian Hege

  2. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Germany

    Konrad Polthier

  3. Fakultät für Mathematik und Informatik Institut für Informatik, Universität Leipzig, Postfach 100920, Leipzig, 04009, Germany

    Gerik Scheuermann

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© 2009 Springer-Verlag Berlin Heidelberg

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Carr, H., Snoeyink, J. (2009). Representing Interpolant Topology for Contour Tree Computation. In: Hege, HC., Polthier, K., Scheuermann, G. (eds) Topology-Based Methods in Visualization II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88606-8_5

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