An Efficient Algorithm for Approximate Polyline-Sourced Offset Computation on Triangulated Surfaces

Abstract

The computation of polyline-sourced geodesic offset holds significant importance in a variety of applications, including but not limited to solid modeling, tool path generation for computer numerical control (CNC) machining, and parametrization. The traditional approaches for geodesic offsets have typically relied on the availability of an exact geodesic metric. Nevertheless, the computation of exact geodesics is characterized by its time-consuming nature and substantial memory usage. To tackle the limitation, our study puts forward a novel approach that seeks to circumvent the reliance on exact geodesic metrics. The proposed method entails a reformulated graph method that incorporates Steiner point insertion, serving as an effective solution for obtaining geodesic distances. By leveraging the aforementioned strategies, we present an efficient and robust algorithm designed for the computation of polyline-sourced geodesic offsets. The experimental evaluation, conducted on a diverse set of three-dimensional models, demonstrates significant improvements in computational speed and memory requirements compared to established state-of-the-art methods.