Topology-First B-Rep Meshing

TL;DR

This paper introduces a topology-first meshing algorithm for B-Rep models that guarantees topological correctness at any user-defined tolerance, improving robustness over existing heuristic methods.

Contribution

The proposed method enforces exact B-Rep topology during meshing, decoupling topology from geometry and eliminating the need for post-processing repairs.

Findings

Successfully meshes thousands of CAD models, including those failing with standard tools.

Provides topologically correct meshes with controllable geometric deviation.

Yields robust meshes suitable 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.