Molds and dies with sculptured surfaces are usually fabricated using numerically controlled 3-axis milling tools. Machining simulations are used prior to actual milling to detect potential problems of a tool path, for example excess milling of a workpiece. A simulation method based on the dexel representation of the workpiece is widely used. In this method, a milling process is geometrically evaluated by subtracting successive tool swept volumes along the path from a collection of dexels representing the workpiece shape. Two technologies for accelerating the dexel based machining simulation are proposed in this paper. Most computation time in the simulation is elapsed in detecting such dexels intersecting the tool swept volumes. Our method defines a tight bounding box to each surface element of the volumes, which efficiently limits the range of potential intersecting dexels. A critical milling process must be checked repeatedly from various viewing directions. The simulation method is further improved by integrating a history mechanism which records the computation results obtained in the first simulation process. By using the record, the computation time of repeated simulations can be substantially reduced. The method is implemented and simulations of some sculptured surface milling are demonstrated.
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