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.

We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as developable as possible. Specifically, the terminal ruling lines are treated as hard constraints. Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control, our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings. We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications. The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for the path planning in 5-axis computer numerical control (CNC) flank milling.