Approximating the Generalized Voronoi Diagram of Closely Spaced Objects

We present an algorithm to compute an approximation of the generalized Voronoi diagram (GVD) on arbitrary collections of 2D or 3D geometric objects. In particular, we focus on datasets with closely spaced objects; GVD approximation is expensive and sometimes intractable on these datasets using previ...

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Vydáno v:	Computer graphics forum Ročník 34; číslo 2; s. 299 - 309
Hlavní autoři:	Edwards, John, Daniel, Eric, Pascucci, Valerio, Bajaj, Chandrajit
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	England Blackwell Publishing Ltd 01.05.2015 Wiley
Témata:	[I.3.6]: Methodology and Techniques-Graphics data structures and data types Algorithms Analysis Approximation Categories and Subject Descriptors (according to ACM CCS) Computation Computer Graphics [I.3.5]: Computational Geometry and Object Modeling-Boundary representations Computer Graphics Computer Graphics, Computational Geometry and Object Modeling Datasets Hardware Image processing systems Mathematical analysis MATHEMATICS AND COMPUTING Octrees Studies Three dimensional Two dimensional
ISSN:	0167-7055, 1467-8659
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Popis
Shrnutí:	We present an algorithm to compute an approximation of the generalized Voronoi diagram (GVD) on arbitrary collections of 2D or 3D geometric objects. In particular, we focus on datasets with closely spaced objects; GVD approximation is expensive and sometimes intractable on these datasets using previous algorithms. With our approach, the GVD can be computed using commodity hardware even on datasets with many, extremely tightly packed objects. Our approach is to subdivide the space with an octree that is represented with an adjacency structure. We then use a novel adaptive distance transform to compute the distance function on octree vertices. The computed distance field is sampled more densely in areas of close object spacing, enabling robust and parallelizable GVD surface generation. We demonstrate our method on a variety of data and show example applications of the GVD in 2D and 3D.
Bibliografie:	Supporting Information ArticleID:CGF12561 istex:D7C74B3FCC952449C1C277C9E21ED1723FE27503 ark:/67375/WNG-2RPMVJ4M-Z SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 DOE-UTAH-PASCUCCI-0010 NA0002375 USDOE National Nuclear Security Administration (NNSA)
ISSN:	0167-7055 1467-8659
DOI:	10.1111/cgf.12561