DETERMINING A SET OF MAXIMUM INSCRIBED RECTANGLES FOR LABEL PLACEMENT IN A REGION
Marina L. Gavrilova · International Journal of Computational Geometry & Applications · 2009
Driven by the industrial challenge of labeling maps for GIS applications, we investigate the problem of computing a map region P such that a rectangular axis-parallel label L of a given size can be placed in it. The map region to be labeled is in general a non-convex n-gon which may contain holes. We first derive a new practical algorithm based on the sweep-line technique that determines the com set of Maximum Inscribed Rectangles (MIRs) in P in O(nk), where k is the size of the output, for the case when the polygon sides have an axis-parallel orientation. After the set of MIRs has been found, any subsequent query on label L placement runs in only O(logn) time. We then provide an algorithm to convert the general case to the axis-parallel case. Extensive experimentation in both laboratory and industrial settings confirms that the developed method is practical and highly efficient for processing large GIS data sets.