Robust Point Location in Approximate Polygons

This paper presents a framework for reasoning about robust geoemtric algorithms. Robustness is formally deened and a data structure called an approximate polygon is introduced and used to reason about polygons constructed of edges whose positions are uncertain. A robust algorithm for point location in an approximate polygon is presented. The algorithm uses only the signature of the point (not its location) to determine whether the point is inside or outside the polygon. An approximate polygon could, by shifting its edges back and forth within their error bounds, induce a large number of diierent line arrangements. The cell C with signature in one such arrangment will be diierent than the cell C 0 with signature in another arrangement. This paper proves that, regardless of their positions and shapes, the cells C and C 0 are always to the same side of the polygons which induce their respective arrangements.