This paper presents how freeform surface properties can be estimated through bounding, rather than sampling. Bounding surface positions using the control mesh, and bounding surface normals using normal cones, are both well known procedures. In this paper, we add to these, a procedure to bound the normal curvature values of a surface.

We then show how collision free 5-axis tool-paths for CNC machining, using any convex shaped tool, can be generated using the normal curvature bounds of a surface, without calculating surface offsets. As the tool-paths are generated using conservative bounds on the surface, and not sampled points, the tool-paths can be both globally optimized and globally guaranteed to be collision free. Simulation results validating our approach are also presented.

本文介绍了如何通过边界而不是采样来估计自由曲面的特性。使用控制网格的边界表面位置和使用法线圆锥的边界表面法线都是众所周知的过程。在本文中，我们添加了一个方法来约束曲面的法线曲率值。

然后，我们展示了如何使用曲面的法向曲率边界生成使用任何凸形刀具进行CNC加工的无冲突5轴刀具路径，而无需计算曲面偏移。由于刀具路径是使用曲面上的保守边界（而不是采样点）生成的，因此可以全局优化刀具路径，并且可以全局保证刀具路径无碰撞。仿真结果也验证了我们的方法。