# Data Reduction of Piecewise Linear Curves

Chapter

## 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.

## Keywords

Data Reduction Local Algorithm Hausdorff Distance General Step Point Sequence
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## Copyright information

© Springer Science+Business Media New York 1997