In order to detect potential problems of a cutter path, geometric verification of the NC milling result is necessary prior to actual machining. Result shape of the workpiece can be computed by subtracting the swept volume of a cutter moving along the path from a solid model representing the stock shape. In this paper, the authors propose an acceleration method of the subtracting operation using the hidden surface elimination mechanism of the 3 dimensional graphics hardware. Before the operation, component surfaces of the cutter swept volume must be tessellated. Computation time of the proposed method is proportional to the total number of polygons approximating the component surfaces. Some portions of the surfaces do not contribute the result shape of the workpiece. Our algorithm reduces the polygons by properly excluding such surface portions from the tessellation. An experimental program is implemented and computations of some sculptured surface milling results are demonstrated.

In the sheet metal part manufacturing, bending is the most commonly used to realize sufficient rigidity and to obtain a part of desired shape to perform a certain function. Feasible bending sequences of a sheet metal part can be determined by successively applying bending simulations to the geometric model of a blank. Unfortunately, this simulation based method is computationally expensive because enormous search-space must be explored if complex parts with many bending lines are given. Complex parts usually have rather small number of feasible bending sequences because other sequences cause self interferences or interferences with tools in the bending operations. Based on this characteristic of the sheet metal part, we develop a new method to accelerate the simulation based bending sequence planning. This method reduces the computation cost by efficiently detecting the interferences in the early stage of the search process. In the bending sequence planning, the same geometric computations for the interference detection are repeated many times. This redundancy is eliminated by saving and reusing the previous computation results. The proposed method is implemented and an experimental bending sequencing program is demonstrated.