Error-Bounded Adaptive Generalized Winding Number Evaluation for B-Reps

The generalized winding number (GWN) offers a robust solution for point membership classification (PMC), tolerating geometric imperfections such as non-watertight boundaries. While GWN evaluation on discrete representations (e.g., meshes) has demonstrated its efficiency, its computation on B-Reps with trimmed surfaces remains computationally expensive, hindering practical use. We present a fast GWN evaluation framework for B-Reps with bounded error. The key idea is to adaptively discretize boundary curves with explicit analysis on deviation bounds. With the consistent discrete representations, queries inside and outside the surface bounding boxes are distinguished, and errors on the shared curves of adjacent surfaces are canceled out. Queries outside surface bounding boxes are reduced to efficient mesh-based evaluations with bounded error, which further enables efficient spatial acceleration. In addition, an optimized spherical projection that is both fast and accurate is designed for the remaining queries in boxes. Numerical experiments demonstrate the approach's superior efficiency while avoiding misclassification, compared with SOTA GWN approaches, and classic open-source CAD kernel Open CASCADE.