On \(d\)-convex partitions of polygonal regions (Q2731381)

This paper considers subdivisions of a polygon \(D\) with holes into pieces that are generalized convex, subject to a number of side constraints.NEWLINENEWLINENEWLINE(a) A finite set of points \(P\) is given. These points must be vertices of the resulting subpolygons. NEWLINENEWLINENEWLINE(b) For each point \(p\in P\), the number of pieces incident to \(p\) is given. NEWLINENEWLINENEWLINE(c) Any edge of the subdivision must be parallel to one of the directions \(d\) that are given by the edges of \(D\).NEWLINENEWLINENEWLINE(d) Any piece is \(d\)-convex. NEWLINENEWLINENEWLINEThe paper gives a worst-case bound on the number of pieces necessary, depending on the subdivision structure in an \(\varepsilon\)-neighborhood of each point in \(P\). NEWLINENEWLINENEWLINEA potential reader should be warned that this paper is basically a technical report that has not been edited carefully. This results in suboptimal presentation, and obfuscating problems with English grammar.