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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Bibliographic Details
Published in:Computer graphics forum Vol. 34; no. 2; pp. 299 - 309
Main Authors: Edwards, John, Daniel, Eric, Pascucci, Valerio, Bajaj, Chandrajit
Format: Journal Article
Language:English
Published: England Blackwell Publishing Ltd 01.05.2015
Wiley
Subjects:
[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
Online Access:Get full text
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Description
Summary: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.
Bibliography:Supporting Information
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DOE-UTAH-PASCUCCI-0010
NA0002375
USDOE National Nuclear Security Administration (NNSA)
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12561