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.