In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection topologies persists. While subdivision algorithms have demonstrated strong robustness in computing surface/surface intersection and are capable of addressing singular cases, determining the topology of the intersection obtained through these methods is a key factor for calculating correct intersection, and remains a difficult issue. To address this challenge, we propose a Mapper-based method for determining the topology of the intersection between two B-spline surfaces. Our algorithm is designed to efficiently handle various common and complex intersection topologies. Experimental results verify the robustness and topological correctness of this method.

翻译：在计算机辅助设计（CAD）软件领域，B样条曲面的相交是一项基础操作。尽管曲面求交算法历史悠久，但处理复杂相交拓扑的挑战依然存在。细分算法在计算曲面/曲面交点时展现出强大的鲁棒性，能够处理奇异情况，但通过此类方法获取的交点拓扑是计算正确交点的关键因素，且仍是一个难点问题。为应对这一挑战，我们提出了一种基于Mapper的方法，用于确定两片B样条曲面间交点的拓扑结构。该算法旨在高效处理各种常见及复杂的相交拓扑。实验结果验证了该方法的鲁棒性与拓扑正确性。