Approximating NURBS curves by arc splines

It is desirable to approximate a smooth curve by arc splines with the fewest segments within a prescribed tolerance. We present an efficient algorithm for fitting planar smooth curves by arc splines. The main idea is that we construct the optimal arc spline by optimizing the interpolating biarc curve. The scheme consists of three steps: sampling the curve based on consecutive tangent deviation; construct the interpolating arc spline; and reduce the arc number to the minimum within a prescribed tolerance. The algorithm can control the approximating error efficiently and results in the fewest number of arc segments.