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Interpolation and parallel adjustment of center-sampled trees with new balancing constraints

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Abstract

We present a novel tree balancing constraint that is slightly stronger than the well-known 2-to-1 balancing constraint used in octree data structures (Tu and O’hallaron, Balanced refinement of massive linear octrees. Tech. Rep. CMU-CS-04-129. Carnegie Mellon School of Computer Science, Pennsylvania, 2004). The new balancing produces a limited number of local cell connectivity types (stencils): 5 for a quadtree and 21 for an octree. Using this constraint, we interpolate the data sampled at cell centers using weights pre-computed by interpolation or by generating interpolation codes for each stencil. In addition, we develop a parallel tree adjustment algorithm, and show that the imposed balancing constraint is satisfied even when the tree is adjusted in parallel. We also show that the adjustment has high parallelization performance. We finally apply the new balancing scheme to level set image segmentation and smoke simulation problems.

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Notes

  1. Whereas the term “node” means a corner of a cell in the previous paper [16], we use the term as a tree node in a quadtree/octree structure. In addition, the term is equivalent to “cell” in our cell-centered tree.

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Acknowledgments

The second author was supported by the US National Science Foundation, award CMMI-0856565. The third author was supported by National Research Foundation of Korea (NRF) (Grant NRF-2011-0023134).

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Authors and Affiliations

  1. Adobe Systems, San Jose, USA

    Byungmoon Kim

  2. Georgia Institute of Technology, Atlanta, USA

    Panagiotis Tsiotras

  3. Dongguk University, Seoul Campus, Seoul, South Korea

    Jeong-Mo Hong

  4. Sejong University, Seoul, South Korea

    Oh-young Song

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  1. Byungmoon Kim
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  2. Panagiotis Tsiotras
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Correspondence to Oh-young Song.

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Kim, B., Tsiotras, P., Hong, JM. et al. Interpolation and parallel adjustment of center-sampled trees with new balancing constraints. Vis Comput 31, 1351–1363 (2015). https://doi.org/10.1007/s00371-014-1018-2

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