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Computing Voronoi Treemaps: Faster, Simpler, and Resolution‐independent
Author(s) -
Nocaj Arlind,
Brandes Ulrik
Publication year - 2012
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/j.1467-8659.2012.03078.x
Subject(s) - voronoi diagram , centroidal voronoi tessellation , computer science , graphics , weighted voronoi diagram , theoretical computer science , power diagram , algorithm , resolution (logic) , mathematics , computer graphics (images) , geometry , artificial intelligence
Voronoi treemaps represent hierarchies as nested polygons. We here show that, contrary to the apparent popular belief, utilization of an algorithm for weighted Voronoi diagrams is not only feasible, but also more efficient than previous low‐resolution approximations, even when the latter are implemented on graphics hardware. More precisely, we propose an instantiation of Lloyd's method for centroidal Voronoi diagrams with Aurenhammer's algorithm for power diagrams that yields an algorithm running in (n log n) rather than Ω(n 2 ) time per iteration, with n the number of sites. We describe its implementation and present evidence that it is faster also in practice.