Topology-First B-Rep Meshing

2026-04-02

AI Summary

This work addresses the common failure of geometric approximation during mesh generation from parametric boundary representation (B-Rep) models, which often corrupts the original topological structure and leads to incorrect adjacency relationships. The paper proposes a topology-first meshing approach that, for the first time, enforces B-Rep topology as a hard constraint at the algorithmic level, rigorously preserving topological invariance throughout the discretization process. Geometric deviation is controlled solely through user-defined tolerances, thereby decoupling topological correctness from geometric approximation. The method produces robust, topologically consistent meshes without requiring post-processing and has been validated on thousands of real-world CAD models—including cases where conventional tools fail—demonstrating significantly improved reliability for downstream applications.

Abstract

Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order surface and curve intersections to low-order primitives: the resulting geometric realization often fails to respect the exact topology encoded in the B-Rep, producing meshes with incorrect or missing adjacencies. Existing meshing pipelines address these inconsistencies through heuristic feature-merging and repair strategies that offer no topological guarantees and frequently fail on complex models. We propose a fundamentally different approach: the B-Rep topology is treated as an invariant of the meshing process. Our algorithm enforces the exact B-Rep topology while allowing a single user-defined tolerance to control the deviation of the mesh from the underlying parametric surfaces. Consequently, for any admissible tolerance, the output mesh is topologically correct; only its geometric fidelity degrades as the tolerance increases. This decoupling eliminates the need for post-hoc repairs and yields robust meshes even when the underlying geometry is inconsistent or highly approximated. We evaluate our method on thousands of real-world CAD models from the ABC and Fusion 360 repositories, including instances that fail with standard meshing tools. The results demonstrate that topological guarantees at the algorithmic level enable reliable mesh generation suitable for downstream applications.

Problem

• B-Rep meshing
• topology preservation
• geometric approximation
• mesh validity
• CAD models

Innovation

• topology-preserving
• B-Rep meshing
• parametric CAD
• robust mesh generation
• geometric approximation