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 trapezoidation. A generalized trapezoidation algorithm for decomposing a polygon, as well as decomposing holes within that polygon, did not exist until recently. Recently, an algorithm [4] has been proposed for trapezoidation of a planar polygon in O(n2 logn) time. We present a new approach for trapezoidation in this paper. Our algorithm can decompose a planar polygon with holes inside it in O(n logn) time where n is the total number of vertices in the polygon and holes. We also present a brief history of trapezoidation and some of its applications.