Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs

An algorithm for approximating a given open polygonal curve with a minimum number of circular arcs is introduced. In computer-aided manufacturing environments the paths of cutting tools are usually described with circular arcs and straight line segments. Greedy algorithms for approximating a polygonal curve with curves of higher order can be found in the literature. Without theoretical bounds it is difficult to prove anything about the quality of these algorithms. We present an algorithm which allows us to build a directed graph of all possible arcs and look for the shortest path from the start point to the end point of the polygonal curve. We can prove a runtime of O(n 2 logn), for n the number of vertices of the original polygonal chain.

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