Fast Discretization Algorithm of Densely Subdivided NURBS Curves

Abstract

This paper develops a discretization algorithm for non-uniform rational B-spline (NURBS) curves. The algorithm is used for CAM software which is developed for HNC-3000 five-axis woodworking NC milling machine. Functions from the CAM software divide the NURBS into dense segments with equal arc length by vertex set p1, p2pn. The algorithm simultaneously considers chord error δ and curvature of the NURBS curve to maximize the arc length of the segments to get vertex set p'1, p'2 pm'. The algorithm can be described as f (p1, p2pn, δ) = (p1', p2'pm'). The complexity of the algorithm is O (n).