Asymptotically Optimal and Linear-time Algorithm for Polygonal Curve Simplification

Abstract

In many application domains involving shapes and curves, polygonal curve simplification is an important part of the computer analysis processes. In this work, we have developed asymptotically optimal and linear-time algorithms to approximate a polygonal curve by another polygonal curve whose vertices are a subset of the vertices of the original one. The algorithm developed in this paper can be applied to a vector map data reduction in geographical information system especially for large-scale data. The error of the approximation is measured by the area of the domain bounded by the two polygonal curves. Based on the equidistribution principle and local refinement/coarsening strategy, an efficient