An Extension to Hain’s Trapezoidation Algorithm to Handle Polygons with Holes

Hain’s trapezoidation algorithm is a fast, practical algorithm for the reduction of simple polygons into horizontally aligned trapezoids partitioned into a minimal collection of trapezoid sequences. An extension to this algorithm is described which allows trapezoidation of simple polygons with an arbitrary number of non-intersecting holes. The minimal computational cost per hole is a traversal on the current polygon contour of all vertices that join the vertical monotone chains making up the contour. Keywords—trapezoidation, trapezoidalization, triangulation, decomposition, simple polygon with holes, trapezoid sequence.