A natural metric for curves — Computing the distance for polygonal chains and approximation algorithms

Abstract

The often explored problem to approximate a given polygonal chain has been considered from a computational geometric point of view only for a short time. To model it reasonably we give a natural definition of the distance between curves. Furthermore we give algorithms to calculate this distance between two polygonal chains in the d-dimensional space for arbitrary d. With known methods this yields polynomial time algorithms to approximate polygonal chains. These algorithms find an optimal solution under some constraints. We will show that this solution is only by a constant factor worse than the global optimum.

This research was supported by the DFG under Grant Al 253,1–3; SPP “Datenstrukturen und effiziente Algorithmen”