Asymptotically Optimal and Liner-time Algorithm for Polygonal Curve Simplification

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 This work is supported by the US National Science Foundation (NSF) under Grant Nos. IIS-0219272 and IIS-0347148, The Pennsylvania State University, the PNC Foundation, and SUN Microsystems. Long Chen is with Department of Mathematics, University of California at San Diego, . The work was done when he was with the Department of Mathematics and the School of Information Sciences and Technology, The Pennsylvania State University, University Park, PA 16802 USA. Email: [email protected] James Z. Wang is with the School of Information Sciences and Technology and Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA 16802 USA. Email: [email protected] Jinchao Xu is with the Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 USA. Email: [email protected] November 18, 2005 DRAFT