Realizing Swept Volume Modeling of General Cutter Based on Gauss Map on GPU

A method is proposed to rapidly generate the swept volume of a general cutter through parallel computing according to the requirement of NC process simulation. The method is based on Gauss map theory and GPU. Combining general cutter mathematical model and Gauss map theory, the fundamental of the swept volume modeling for a translational cutter is analyzed. And by analyzing the surface points and related normal vectors of a spatial motion cutter, the formula of solving swept volume envelope boundary is derived. According to computing method and graphics rendering pipeline of GPU, the specific process flow is devised to realize spatial swept volume modeling of a cutter on GPU. The method has been implemented with C++, Open GL and Open GL Shading Language. Some examples of cutter swept volume modeling are presented to demonstrate the validity and instantaneity of the method.