By Bahman Kalantari (auth.), Marina L. Gavrilova, C. J. Kenneth Tan, Bahman Kalantari (eds.)
ISBN-10: 3642419046
ISBN-13: 9783642419041
ISBN-10: 3642419054
ISBN-13: 9783642419058
This, the 20 th factor of the Transactions on Computational technology magazine, edited via Bahman Kalantari, is dedicated to the subject of Voronoi Diagrams and their purposes. the ten complete papers integrated within the quantity are revised and prolonged models of a variety of papers offered on the foreign Symposium on Voronoi Diagrams 2012, held in Rutgers, NJ, united states, in June 2012. they supply an in-depth review of present study on topological facts constructions and a accomplished overview in their purposes within the fields of cartography, physics, fabric modeling, chemistry, GIS, movement making plans and machine graphics.
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Extra resources for Transactions on Computational Science XX: Special Issue on Voronoi Diagrams and Their Applications
Sample text
Let the three rectangles be of widths w1 , w2 , and w3 respectively such that (a) w1 < w2 , (b), w3 < w2 , (c) (w2 /2 < w1 ) and (d ) (w2 /2 < w3 ). Observe that placing one site in each rectangle is necessary and sufficient if all the above conditions hold simultaneously. Suppose, all the above conditions do not hold simultaneously; in this case, placing two sites in the rectangle of width w2 and one site in each of the rectangles corresponding to w1 and w3 , is necessary and sufficient (Fig. 2(b)).
The existence of GVI for any rectangular tessellation follows from the following theorem: Theorem 1. For any rectangular tessellation T , there exists a point set S of size O(n2 ) such that any cell V (s)(⊆ V (S), s ∈ S) lies in exactly one cell of T , where n is the number of cells in T . On the Construction of Generalized Voronoi Inverse of a Rectangular Tessellation (a) (b) 25 (c) Fig. 1. Proof of Theorem 1. (a) Original tessellation (b) site placement on Hanan tessellation and (c) site placement in original tessellation.
Algorithms 2 shows the pseudo-code for the incremental update of P and Q. In Algorithm 2, m + 1 and j − 1 are computed modulus length(P ). For the algorithm to have good performance, we need a data structure that supports efficient disk range queries on a set of points. We use the standard cell/bucket data structure proposed by Bentley et al. [7] and Maus [8]: the domain, the bounding box of the point set, is partitioned into boxes of the same size, and an index array is used to store the indices of the points inside each box.
Transactions on Computational Science XX: Special Issue on Voronoi Diagrams and Their Applications by Bahman Kalantari (auth.), Marina L. Gavrilova, C. J. Kenneth Tan, Bahman Kalantari (eds.)
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