A Precision Controlled Surface-Surface Intersection Algorithm for NURBS

Abstract

Precision control is a challenging problem in surface-surface intersections. It has a direct impact on the watertight issue, rendering, mesh generation, Computer-Aided Engineering (CAE) numerical computation, and Computer-Aided Manufacturing (CAM). In this paper, we propose a priori precision control method for the most widely used NURBS. We leverage Lipschitz continuity and convex hulls to control the Hausdorff distance between the polyline and actual intersection curves, and a novel curve fitting method to control the Hausdorff distance between the fitted curve and the polyline. In addition, we propose a fast OBB computation method and use normal range analysis to determine the existence and type of intersection, enabling categorized processing. We present some examples to demonstrate the algorithm’s correctness and precision control ability. Our algorithm demonstrates superior precision, efficiency, and robustness compared to several commercial and open-source kernels.