Topologically Correct Subdivision Simplification Using the Bandwidth Criterion

Abstract

The line simplification problem is an old and well studied problem in cartography. Although there are several algorithms to compute a simplification there seem to be no algorithms that perform line simplification in the context of other geographical objects. This paper presents a nearly quadratic time algorithm for the following line simplification problem: Given a polygonal line, a set of extra points, and a real e> 0, compute a simplification that guarantees (i) a maximum error e (ii) that the extra points remain on the same side of the simplified chain as of the original chain; and (iii) that the simplified chain has no self-intersections. The algorithm is applied as the main subroutine for subdivision simplification and guarantees that the resulting subdivision is topologically correct.