Comparison of discretization algorithms for nurbs surfaces with application to numerically controlled machining

Sculptured surfaces used in automotive, aerospace and naval design are usually mathematically defined by parametric forms such as the well-known Bézier, B-Spline and nurbs representations. Although widely used in many applications, they are not ideal for NC tool path generation, primarily because of the difficulty in calculating gouge free contact points between the tool and the surface. Discrete representations of the parametric surfaces can be used to simplify the contact point calculation. Algorithms for surface discretization may be broadly classified as local, global or subdivision methods. Implementations of each of these classes were compared for five nurbs surfaces. An algorithm based on parametric rectangular subdivision produced the best overall performance.