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Curve Complexity Heuristic KD‐trees for Neighborhood‐based Exploration of 3D Curves
Author(s) -
Lu Yucheng,
Cheng Luyu,
Isenberg Tobias,
Fu Chi-Wing,
Chen Guoning,
Liu Hui,
Deussen Oliver,
Wang Yunhai
Publication year - 2021
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.142647
Subject(s) - heuristic , computer science , line (geometry) , computation , tree (set theory) , abstraction , k d tree , radius , line segment , algorithm , computational complexity theory , theoretical computer science , mathematics , artificial intelligence , combinatorics , geometry , philosophy , computer security , epistemology , tree traversal
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.