We introduce a new concept of constructing a generalized Voronoi inverse (GVI) of a given tessellation τ of the plane. Our objective is to place a set S i of one or more sites in each convex region (cell) t i ∈ τ , such that all the edges of τ coincide with the edges of Voronoi diagram V (S), where S = ∪ i S i, and Ai, j, i= j, S i ∩S j = θ. In this paper, we study the properties of GVI for the special case when T is a rectangular tessellation and propose an algorithm that finds a minimal set of sites S. We also show that for a general tessellation, a solution of GVI always exists.

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Persistent URL dx.doi.org/10.1109/ISVD.2012.24
Conference 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012
Citation
Banerjee, S. (Sandip), Bhattacharya, B.B. (Bhargab B.), Das, S. (Sandip), Karmakar, A. (Arindam), Maheshwari, A, & Roy, S. (Sasanka). (2012). On the construction of a generalized Voronoi inverse of a rectangular tessellation. Presented at the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012. doi:10.1109/ISVD.2012.24