Refolding Planar Polygons

Counting Convex Polygons in Planar

Partitions of planar point sets into polygons

In this paper, we characterize planar point sets that can be partitioned into disjoint polygons of arbitrarily specified sizes. We provide an algorithm to construct such a partition, if it exists, in polynomial time. We show that this problem is equivalent to finding a specified 2-factor in the visibility graph of the point set. The characterization for the case where all cycles have length 3 a...

Boolean representation of general planar polygons

There are many applications of the geometric modelling in which it is necessary to accomplish decompositions of the geometric objects that intervene in the model, to facilitate the analysis and design of the algorithms implicated in the resolution of particular problems. Triangulations, trapezoidations, convex decompositions and BSP (binary space partitioning trees) are some of the methods used...

Counting Convex Polygons in Planar Point Sets

Given a set S of n points in the plane, we compute in time O(n) the total number of convex polygons whose vertices are a subset of S. We give an O(m n) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3; : : : ;m; previously known bounds were exponential (O(ndk=2e)). We also compute the number of empty convex polygons (resp., k-gons, k m) with vertices ...

A fast trapezoidation technique for planar polygons

Triangulation is one of the most popular methods for decomposing a planar polygon into primitive cells. Often trapezoidation is performed as a first step in triangulation. That is, a polygon is decomposed into a set of trapezoids; a trapezoid being a four sided polygon with two parallel sides. Although much work has gone into fast triangulation methods, there has been little work on trapezoidat...