Computing Voronoi Treemaps: Faster, Simpler, and Resolution-independent

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 impleme...

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Bibliographic Details
Published in:Computer graphics forum Vol. 31; no. 3pt1; pp. 855 - 864
Main Authors: Nocaj, Arlind, Brandes, Ulrik
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.06.2012
Subjects:
Algorithms
Approximation
H.5.2 [Information Interfaces and Presentation]: User Interfaces
Hardware
Hierarchies
I.3.6 [Computer Graphics]: Methodology and Techniques
I.3.8 [Computer Graphics]: Applications
Iterative methods
Polygons
Running in
Utilization
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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 𝒪(n log n) rather than Ω(n2) time per iteration, with n the number of sites. We describe its implementation and present evidence that it is faster also in practice.
Bibliography:istex:97AB1903B0842A6CDB5E44C660C19E2EA5616840
ArticleID:CGF3078
ark:/67375/WNG-MNN3BNDF-1
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2012.03078.x