Numerical methods for approximating digitized curves by piecewise circular arcs

Two-dimensional digitized curves are often approximated by some piecewise linear or high-order curves. The approximation usually results in a compact and effective representation for further applications. In this paper, we propose new algorithms to approximate digitized curves by piecewise circular arcs with geometric continuity G0 or G1. First, iterative methods are proposed to solve the best single arc and biarc approximation problems of a digitized curve with respect to the maximum norm. The basic notion of our methods is to show that the error functions of two approximations are unimodal functions, so techniques developed in optimization theory can be used to search for the best approximation. Then the piecewise arcs approximation problems can be solved by applying these approximation algorithms to construct an arcwise curve such that each join point between two arcs is G0 or G1 continuity and its maximum approximation error is no more than a given tolerance ε > 0. Some experimental results are given to demonstrate the quality and the performance of the proposed algorithms.