2 Abstract. We present a new method that allows to enumerate various classes of column-convex polygons, according to their perimeter and their area. The rst step of this method leads to a functional equation which deenes implicitly the generating function of the class under consideration. The second step consists in solving this equation. We apply systematically our method to all the usual clas...

We aim at splitting a given multiply connected polygon into a set of convex quadrilaterals. Our approach consists in repeatedly removing quadrilaterals from the given polygon. We will first derive theoretical results pertaining to quadrangulation of simple polygons from the usual 2-ear theorem. Unfortunately, that theorem holds only for simply connected polygons while we are interested in quadr...

Given two points p and q and a finite number of simple polygons in a plane. The basic version of a touring-a-sequence-of-polygons problem (in brief: a touring polygons problem, TPP) is how to find a shortest path such that it starts at p, then it visits these polygons in the given order, and finally it ends at q. This paper describes approximate algorithms for different versions of touring poly...

Existing methods of spatial data clustering have focused on point data, whose similarity can be easily defined. Due to the complex shapes and alignments of polygons, the similarity between non-overlapping polygons is important to cluster polygons. This study attempts to present an efficient method to discover clustering patterns of polygons by incorporating spatial cognition principles and mult...