Partitioning orthogonal polygons by extension of all edges incident to reflex vertices: Lower and upper bounds on the number of pieces Article

Bajuelos, AL, Tomás, AP, Marques, F. (2004). Partitioning orthogonal polygons by extension of all edges incident to reflex vertices: Lower and upper bounds on the number of pieces . 3045 127-136. 10.1007/978-3-540-24767-8_14

cited authors

  • Bajuelos, AL; Tomás, AP; Marques, F

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 + r2, where r is the number of reflex vertices of P. We shall now give sharper bounds both for maxP |Π(P)| and minP |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. © Springer-Verlag Berlin Heidelberg 2004.

publication date

  • January 1, 2004

Digital Object Identifier (DOI)

start page

  • 127

end page

  • 136

volume

  • 3045