Trimming offset surface self-intersections around near-singular regions

Abstract

We present a new method for offset surface trimming that eliminates redundant parts of an offset surface that are closer than the offset distance to the original surface. The proposed approach deals with numerical instability around near-singular regions of an offset surface using the concept of offset trimming regions in the parameter space and carrying out numerical computations based on the regularity and intrinsic properties of the given input surface. In particular, we replace the self-intersection of an offset surface (which can be unstable around near-singular regions) by computation on the original input surface (and its derivatives) only, and also by the intersection of osculating tori that can be constructed in a highly stable way by offsetting the osculating tori of the given input regular surface. We demonstrate the effectiveness of our approach using non-trivial test examples of offset surface trimming, including some examples from the previous publications for the purpose of comparison. © 2019 Elsevier Ltd