An Optimization Process for p-Curves in Surface-to-Surface Intersection to Improve Accuracy and Reduce Redundancy

Abstract

The problem of surface-to-surface intersection (SSI) is among the most fundamental challenges encountered in computer-aided geometric design. In industrial applications, the execution of an SSI operation usually demands a high degree of precision while maintaining a concise representation of the intersection curve. We present a post-processing scheme for refining the intersection curve in the parameter domain (p-curves), achieving an improvement in accuracy without additional control points inserted. Moreover, by adjusting the parameterization, a one-to-one correspondence is created between a pair of p-curves. The proposed methodology is grounded on the minimization of an objective function that describes both accuracy and parameterization. The effectiveness of our method is illustrated through examples in comparison with the open-source NURBS library SISL and commercial software ACIS.