Topology Understanding of B-Spline Surface/Surface Intersection with Mapper
For CAD software users and developers, this method improves the reliability of surface intersection computations, though it is an incremental improvement over existing subdivision algorithms.
The paper tackles the challenge of determining the topology of B-spline surface/surface intersections, a fundamental operation in CAD. The proposed Mapper-based method efficiently handles various complex intersection topologies, demonstrating robustness and topological correctness in experiments.
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.