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.

In the automotive industry, it is highly important that the exterior body panels be esthetically pleasing. One aspect of creating esthetically pleasing surfaces is to require that they be fair. A system that has proven useful for diagnosis of surface fairness problems is presented. How to choose a set of colors with perceptually uniform spacing is described, and the usefulness of a logarithmic scale for relating curvature to colors is shown.>

We describe a method for simulating and verifying the correctness of Numerical Control (NC) programs. NC programs contain the sequence of cutting tool movements which machine raw stock into a finished object. Our method is based on a discrete approximation of the object by a set of points. A vector is passed through each of the points and machining is simulated by finding the intersections of tool movements with these vectors. We present a point-selection method and an analysis that shows that the error introduced by the approximation can be made as small as desired. The run time is inversely proportional to the allowable error and the size of the cutting tool, and directly proportional to the distance that the cutting tool moves.