A Review of Properties and Variations of Voronoi Diagrams

A REVIEW OF PROPERTIES AND VARIATIONS OF VORONOI DIAGRAMS39(a)(b)(c)(d)Figure 17. 256-Point CVT’s Using a Probability DensityFunction of ρ(x, y) = e −10x2 y 2 on [−1, 1] × [−1, 1]with Limits of: (a) i = 10 3 , (b) i = 10 5 , (c) ɛ = 10 −4 ,and (d) ɛ = 10 −8 .using these methods close enough to true CVT’s because the differencesbetween them are minimal. The only way to guarantee that the Voronoidiagram of P that we get using Lloyd or MacQueen’s method is truly acentroidal Voronoi diagram is by carrying the method out indefinitely.This cannot be done for all practical purposes. Thus, we accept theapproximation that we make.