在GPU上实现基于高斯映射的通用刀具扫描体建模

摘要

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 the-ory 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 de-vised to realize spatial swept volume modeling of a cutter on GPU. The method has been implemented with C++, OpenGL and OpenGL Shading Language. Some examples of cutter swept volume modeling are pre-sented to demonstrate the validity and instantaneity of the method.%以针对数控加工仿真的需要，以高斯映射理论为基础、GPU为主要硬件平台，提出一种基于并行计算的快速通用刀具空间扫描体建模方法。首先结合通用刀具的数学模型，利用高斯映射理论分析刀具平动时的扫描体建模原理；然后分析刀具做任意空间运动时的刀具表面点法向量和对应的接触映射，推导求解扫描体包络边界的表达式；再根据GPU上的通用计算方法和GPU图形绘制管线设计基于GPU实现刀具空间扫描体建模的算法流程，并利用C++、OpenGL和OpenGL着色语言GLSL实现了该方法。通过刀具扫描体建模实例，验证了文中方法的正确性与实时性。