@article{Lu2021Curve-54294,
  year={2021},
  doi={10.1111/cgf.142647},
  title={Curve Complexity Heuristic KD-trees for Neighborhood-based Exploration of 3D Curves},
  number={2},
  volume={40},
  issn={0167-7055},
  journal={Computer Graphics Forum},
  pages={461--474},
  author={Lu, Yucheng and Cheng, Luyu and Isenberg, Tobias and Fu, Chi-Wing and Chen, Guoning and Liu, Hui and Deussen, Oliver and Wang, Yunhai}
}

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    <dcterms:title>Curve Complexity Heuristic KD-trees for Neighborhood-based Exploration of 3D Curves</dcterms:title>
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    <dc:creator>Chen, Guoning</dc:creator>
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    <dcterms:abstract xml:lang="eng">We introduce the curve complexity heuristic (CCH), a KD-tree construction strategy for 3D curves, which enables interactive exploration of neighborhoods in dense and large line datasets. It can be applied to searches of k-nearest curves (KNC) as well as radius-nearest curves (RNC). The CCH KD-tree construction consists of two steps: (i) 3D curve decomposition that takes into account curve complexity and (ii) KD-tree construction, which involves a novel splitting and early termination strategy. The obtained KD-tree allows us to improve the speed of existing neighborhood search approaches by at least an order of magnitude (i. e., 28×for KNC and 12×for RNC with 98% accuracy) by considering local curve complexity. We validate this performance with a quantitative evaluation of the quality of search results and computation time. Also, we demonstrate the usefulness of our approach for supporting various applications such as interactive line queries, line opacity optimization, and line abstraction.</dcterms:abstract>
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    <dc:creator>Liu, Hui</dc:creator>
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