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.

翻译：参数化边界表示模型（B-Reps）是CAD、图形学与机器人领域的实际标准，但将其转换为有效网格仍存在脆弱性。其困难源于高阶曲面与曲线交点不可避免地被低阶基元近似化：由此产生的几何实现往往无法满足B-Rep中编码的精确拓扑结构，导致生成的网格存在邻接关系错误或缺失。现有网格生成管线通过启发式特征合并与修复策略处理这些不一致性，但此类方法既不提供拓扑保证，也常在复杂模型上失败。本文提出一种根本性不同的方法：将B-Rep拓扑视为网格生成过程中的不变量。我们的算法在强制执行精确B-Rep拓扑的同时，允许用户通过单一容差参数控制网格与底层参数化曲面之间的偏差。因此，对于任意可接受的容差，输出网格在拓扑上始终正确；仅几何保真度会随容差增大而退化。这种解耦机制消除了事后修复需求，即便在底层几何不一致或高度近似的情况下也能生成鲁棒网格。我们基于ABC和Fusion 360资源库中的数千个真实CAD模型（包括导致标准网格生成工具失败的实例）对方法进行评估。结果表明，算法层面的拓扑保证能够生成适合下游应用的可靠网格。