A flexible quantitative method for NC machining verification using a space-division based solid model

A geometric-modeling method called Graftree and a system design of an NC (numerical control) machining verifier based on Graftree are proposed. Graftree is constructed by combining Oct-tree and constructive solid geometry (CSG) so as to simulate machining processes precisely in three-dimensional space. Using Graftree, the Boolean operation produces no risk of yielding topological conflicts, which often cause the simulation to stop abnormally. Based on the properties of Graftree, an NC machining verifier is designed to consist of three individual subsystems: data-input operations, geometric simulation, and interactive verification, i.e., visuluatzation of machining scenes and evaluation of the machined product using models of the measuring instruments. This design lets the users watch selectively only the machining steps they want to check precisely, and verify the machining according to dimensional tolerance.