Visual Computing

University of Konstanz
Computer Graphics Forum

Curve Complexity Heuristic KD-trees for Neighborhood-based Exploration of 3D Curves

Y. Lu, L. Cheng, T. Isenberg, C. Fu, G. Chen, H. Liu, O. Deussen, Y. Wang


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.


  author    = {Y. Lu, L. Cheng, T. Isenberg, C. Fu, G. Chen, H. Liu, O. Deussen, Y. Wang},
  journal   = {Computer Graphics Forum},
  title     = {Curve Complexity Heuristic {KD}-trees for Neighborhood-based Exploration of 3D Curves},
  year      = {2021},
  month     = {may},
  number    = {2},
  pages     = {461--474},
  volume    = {40},
  doi       = {10.1111/cgf.142647},
  publisher = {Wiley},
    url        = {},