A Fast, Practical Algorithm for the Trapezoidation of Simple Polygons

A fast, practical, deterministic algorithm for the horizontal trapezoidation of simple polygons is presented. The polygon is decomposed into a minimal collection of trapezoid sequences, such that two trapezoids adjacent within a sequence always share a common horizontal border. Such trapezoid sequences are a convenient data structure in a display list for a collection of polygonal objects to be filled/rendered. A linear traversal of the polygon outline identifies a subset of critical vertices, which are then processed in sweep order. Horizontal as well as vertical edges—very common in practical polygons—are handled explicitly. Complexity is linear for most ‘practical’ polygons, with non-linear running times being required only for much less frequently occurring geometries. A straightforward extension allows trapezoidation of simple polygons with holes.