As the most essential part of CAD modeling operations, boolean operations on B-rep CAD models often suffer from errors. Errors caused by geometric precision or numerical uncertainty are hard to eliminate. They will reduce the reliability of boolean operations and damage the integrity of the resulting models. And it is difficult to repair false boolean resulting models damaged by errors. In practice, we find that the illegal boolean resulting models stem from the false intersection edges caused by errors. Therefore, this paper proposes an automatic method based on set reasoning to repair flawed structures of the boolean resulting models by correcting their topological intersection edges. We provide a local adaptive tolerance estimation method for each intersection edge based on its geometric features as well as its origin. Then, we propose a set of inference mechanisms based on set operations to infer whether a repair is needed based on the tolerance value and how to correct the inaccurate intersection edge. Our inference strategies are strictly proven, ensuring the reliability and robustness of the repair process. The inference process will transform the problem into a geometric equivalent form less susceptible to errors to get a more accurate intersection edge. Since our inference procedure focuses on topological features, our method can repair the flawed boolean resulting models, no matter what source of errors causes the problem.

翻译：作为CAD建模操作中最核心的部分，B-rep CAD模型的布尔运算常因几何精度或数值不确定性而导致误差。这些误差难以消除，会降低布尔运算的可靠性，破坏结果模型的完整性，且修复因误差损坏的虚假布尔结果模型十分困难。实践中发现，布尔结果模型非法源于误差导致的虚假相交边。为此，本文提出一种基于集合推理的自动方法，通过修正拓扑相交边来修复布尔结果模型的缺陷结构。我们针对每条相交边，基于其几何特征与来源提出局部自适应容差估计方法；进而设计一套基于集合运算的推理机制，依据容差值推断是否需要修复以及如何修正不精确的相交边。推理策略经过严格证明，确保了修复过程的可靠性与鲁棒性。该推理过程将问题转化为几何等价形式，从而降低误差敏感性，获得更精确的相交边。由于推理过程聚焦拓扑特征，无论误差源于何种因素，本方法均可修复存在缺陷的布尔结果模型。