The machining of sculptured surfaces with Numerical Control (NC) is a common practice in many industries. Sculptured surfaces arise in the design of car bodies, ship hulls, aircraft, and other applications. The problem that the principal investigators want to solve is: given a mathematically defined sculptured surface and a set of NC tool movements, does the shape cut by the tool match the mathematical shape within a given tolerance? Previously, the principal investigators have developed algorithms and data structures for rapidly simulating the actions of a three-axis mill on a carefully chosen sample of points on the surface. This method can guarantee tolerances at every point on the surface both for areas where excess material remains and for areas that have been gouged. The concept of surface discretization is a new one and poses a series of research questions which the principal investigators intend to address: 1) Can the simulation method, currently limited to three-axis NC machining, be extended to five-axis NC machining without marked decrease in efficiency? 2) Would a discretization of the surface into a triangle-based boundary representation be more efficient or reliable than the current point-based method? 3) Can the error information generated by the simulation be used to make corrections to the NC program and could the discretized surface be used as a basis for algorithms to generate NC tool paths? 4) What is the trade-off between the spacing between points and the accuracy of the method? and 5) Can the simulation speed be improved through parallel algorithms?
