Numerical methods for approximating digitized curves by piecewise circular arcs (Q1919404)

The authors measure the deviation of a circular arc from a given digitized curve between points \(\{V_i\}\) by the maximum of the minum distance of any \(V_i\) form the curve. They show that under very weak conditions the distance function so defined has a unique maximum and transform this result into a search algorithm. Next, they study biarcs (unions of two circular arcs with a common tangent at the point of contact) and prove a similar uniqueness property for approximation of \(C'\) arcs under restrictive conditions on the nature of the turning angle of the tangents and turn this also into a search algorithm for best \(G^1\) approximation. In their procedure, corners have to be identified before computing starts since the procedures work only for \(G^1\) curves. A practical example is given.