An algorithm to extract machining volumes

Presented in this paper is an algorithm to compute machining volumes from a rough part model by comparing it with the corresponding final part model. In regard to the comparison, the most intuitive idea is to use a 3D BOOLEANING operation, but it is not desirable because of heavy computation costs and potential degeneracy cases. To cope with the difficulties, we transformed the machining volume computation problem into a simpler one by using the inherent attributes of the problem. The transforming procedure consists of two steps: 1) transforming the machining volume computation problem into a 2D BOOLEANING problem on the 2D domain of a parent surface, and 2) transforming the 2D BOOLEANING problem into a 1D BOOLEANING problem on the 1D domain of a parent curve. Since the proposed algorithm is based on a 1D BOOLEANING operation instead of a 3D BOOLEANING operation, it is very efficient and robust.