From Event: SPIE Astronomical Telescopes + Instrumentation, 2018
We present two methods for generating novel hyper-crossing tool paths for use with CNC and robotic sub-aperture polishing techniques. One generation method utilizes an optimization based on a Voronoi diagram. The second method is seeded by a unicursal pseudo-random pattern to generate a hyper-crossing tool path which features many self-crossings over the entire part surface. Each instance of generation for a given surface for either algorithm will result in a new hyper-crossing pattern. Tool paths can be generated for any surface area including those with interior holes. We also present results of an experiment using a hyper-crossing tool path to remove diamond turning marks.
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Christina Reynolds, David Walker, Guoyu Yu, and Hongyu Li, "A novel hyper-crossing tool path generation algorithm for sub-aperture polishing," Proc. SPIE 10706, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation III, 107060F (Presented at SPIE Astronomical Telescopes + Instrumentation: June 10, 2018; Published: 10 July 2018); https://doi.org/10.1117/12.2312827.