Topology-First B-Rep Meshing

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.

Figures (22)

• Figure 1: Inconsistency between curves (black) and the 2D trimming curves lifted with the parameterization (red). Since our method relies only on the 3D curves (black), it successfully generates a mesh despite these inconsistencies.
• Figure 2: Parametric domain of a patch with its 2D trimming curves. Although all curves are intended to form simple loops, approximation errors cause unintended intersections and artifacts.
• Figure 3: A B-Rep contains topology, a combinatorial structure in which faces are bounded by loops of edges and edges by vertices, and geometry, which embeds these entities as 3D surfaces, curves, and points.
• Figure 4: Overview of the topological entities and their relationships.
• Figure 5: B-Rep topology of a cube. The same b-vertices and b-edges are shown with the same color, highlighting the correspondence between b-vertices, b-edges, b-loops, and b-faces.