Abstract
Given an orthogonal polygon P, let |Π(P)| be the number of rectangles that result when we partition P by extending the edges incident to reflex vertices towards INT(P). In [4] we have shown that |Π(P)| ≤ 1+r+r 2, where r is the number of reflex vertices of P. We shall now give sharper bounds both for max p |Π(P)| and min p |Π(P)|. Moreover, we characterize the structure of orthogonal polygons in general position for which these new bounds are exact. We also present bounds on the area of grid n-ogons and characterize those having the largest and the smallest area.
Partially funded by LIACC through Programa de Financiamento Plurianual, Fundaçã o para a Ciência e Tecnologia (FCT) and Programa POSI, and by CEOC (Univ. of Aveiro) through Programa POCTI, FCT, co-financed by EC fund FEDER.
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Bajuelos, A.L., Tomás, A.P., Marques, F. (2004). Partitioning Orthogonal Polygons by Extension of All Edges Incident to Reflex Vertices: Lower and Upper Bounds on the Number of Pieces. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_14
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DOI: https://doi.org/10.1007/978-3-540-24767-8_14
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