Data Reduction of Piecewise Linear Curves

Abstract

We present and study two new algorithms for data reduction or simplification of piecewise linear plane curves. Given a curve P and a tolerance ε ≥ 0, both methods determine a new curve Q, with few vertices, which is at most e in Hausdorff distance from P. The methods differ from most existing methods in that they do not require a vertex in Q to be a vertex in P. Several examples are given where we show that the methods presented here compare favorably to other methods found in the literature. We also show how the vertices of a curve can be reordered so that the first, say n, vertices of the reordered sequence form an approximation to the curve itself.