Topology Understanding of B-Spline Surface/Surface Intersection with Mapper
Abstract
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.
Cite
@article{arxiv.2604.12631,
title = {Topology Understanding of B-Spline Surface/Surface Intersection with Mapper},
author = {Chenming Gao and Hongwei Lin and Gengchen Li},
journal= {arXiv preprint arXiv:2604.12631},
year = {2026}
}