Improved initialisation for centroidal Voronoi tessellation and optimal Delaunay triangulation

Quinn, Jonathan; Sun, Feng; Langbein, Frank C.; Lai, Yu‐Kun; Wang, Wenping; Martin, Ralph R.

doi:10.1016/j.cad.2012.05.002

Cited by 5 publications

(9 citation statements)

References 30 publications

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“…As pointed out by Quinn et al . [QSL*12], this method can be time‐consuming, and the sites may not be regularly positioned if the object is not described by a regular mesh. Consequently, the quality of the resulting CVT can be even worse than using random sampling.…”

Section: Background and Related Workmentioning

confidence: 99%

“…Quinn et al . suggest to use Hammersley sequences to generate the initial site locations [QSL*12]. Hammersley sequences have correlated positions, which means that the probability of a site being at some position depends on the positions of its neighbours.…”

Section: Background and Related Workmentioning

confidence: 99%

“…Hammersley sequences have correlated positions, which means that the probability of a site being at some position depends on the positions of its neighbours. Unfortunately, the Hammersley sequence generation algorithm as described in [QSL*12] can only place the sites in a square in 2D or a cube in 3D. As a result, the number of sites in the region tessellation is difficult to control.…”

Section: Background and Related Workmentioning

confidence: 99%

“…The density of the lattice should be chosen so that there are k 0 sites inside the object. As stated by [QSL*12], it is very hard to control the number of sites inside the object because the density depends on both the size and the shape of the input object. However, tuning the density of the lattice to reach the proper number of sites inside the object is easier with a small number k 0 of sites than with a large number n sites.…”

Section: Hierarchical Cvtmentioning

confidence: 99%

“…Inspired by a recent work from Quinn et al . [QSL*12], we study CVT optimality with respect to the spatial regularity of the cells.…”

Section: Introductionmentioning

confidence: 99%

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A Hierarchical Approach for Regular Centroidal Voronoi Tessellations

Wang

Hétroy-Wheeler

Boyer

2015

Computer Graphics Forum

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International audienceIn this paper we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modeling and analysis. While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers. This criterion allows us to compare CVTs on a common basis. It builds on earlier theoretical work showing that second moments of cells converge to a lower bound when optimising CVTs. In addition to proposing a regularity criterion, this paper also considers computational strategies to determine regular CVTs. We introduce a hierarchical framework that propagates regularity over decomposition levels and hence provides CVTs with provably better regularities than existing methods. We illustrate these principles with a wide range of experiments on synthetic and real models

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Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Section: Hierarchical Cvtmentioning

confidence: 99%

“…Inspired by a recent work from Quinn et al . [QSL*12], we study CVT optimality with respect to the spatial regularity of the cells.…”

Section: Introductionmentioning

confidence: 99%