Boundary-Conformed Tool Path Generation Based on Global Reparametrization

In this paper, a boundary-conformed tool path generation method for either compound or trimmed surfaces are proposed, based on two powerful reparametrization schemes- the discretized harmonic mapping and the convex combination mapping. By globally mapping a 3D surface onto a 2D unit square and then planning an iso-parametric curve in the 2D domain, the corresponding Cutter Contact (CC) curve on the original 3D surface is easily generated which conforms with the boundary of the surface. Based on this CC curve generation strategy, a CC curve expansion algorithm for covering the entire surface is designed which takes into account the machining accuracy requirement, i.e., The specified maximum cusp height. Tool paths generated in this way for compound or trimmed surfaces are boundary-conformed, smooth, and guarantee the required machining accuracy.