POLYGONS Joseph O ’ Rourke , Subhash Suri , and Csaba

Polygons are one of the fundamental building blocks in geometric modeling, and they are used to represent a wide variety of shapes and figures in computer graphics, vision, pattern recognition, robotics, and other computational fields. By a polygon we mean a region of the plane enclosed by a simple cycle of straight line segments; a simple cycle means that nonadjacent segments do not intersect and two adjacent segments intersect only at their common endpoint. This chapter describes a collection of results on polygons with both combinatorial and algorithmic flavors. After classifying polygons in the opening section, Section 30.2 looks at simple polygonizations, Section 30.3 covers polygon decomposition, and Section 30.4 polygon intersection. Sections 30.5 addresses polygon containment problems and Section 30.6 touches upon a few miscellaneous problems and results.