Topology Understanding of B-Spline Surface/Surface Intersection with Mapper

TL;DR

This paper introduces a Mapper-based method for accurately determining the complex intersection topology of B-spline surfaces in CAD, addressing a longstanding challenge in surface intersection algorithms.

Contribution

The paper presents a novel Mapper-based approach that effectively handles complex intersection topologies of B-spline surfaces, improving robustness and correctness.

Findings

The method accurately identifies intersection topologies in complex cases.

Experimental results confirm the robustness and topological correctness of the approach.

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.