We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward offsets. Compared to the existing approaches focusing on constant-radius offset, to the best of our knowledge, we propose the first-ever solution for mitered offset that can well preserve sharp features. Our method is designed based on several core principals: 1) explicitly generating the offset vertices and triangles with feature-capturing energy and constraints; 2) prioritizing the generation of the offset geometry before establishing its connectivity, 3) employing exact algorithms in critical pipeline steps for robustness, balancing the use of floating-point computations for efficiency, 4) applying various conservative speed up strategies including early reject non-contributing computations to the final output. Our approach further uniquely supports variable offset distances on input surface elements, offering a wider range practical applications compared to conventional methods. We have evaluated our method on a subset of Thinkgi10K, containing models with diverse topological and geometric complexities created by practitioners in various fields. Our results demonstrate the superiority of our approach over current state-of-the-art methods in terms of element count, feature preservation, and non-uniform offset distances of the resulting offset mesh surfaces, marking a significant advancement in the field.

翻译：本文提出一种新颖的偏移网格生成方法，能够鲁棒处理具有任意几何与拓扑构型的三维表面网格，并在内外偏移过程中精确捕捉原始输入的尖锐特征。相较于现有专注于恒定半径偏移的研究，据我们所知，我们首次提出了能够完整保持尖锐特征的斜接偏移解决方案。本方法基于以下核心原理设计：1）通过特征捕捉能量函数与约束条件显式生成偏移顶点与三角形；2）优先构建偏移几何结构再建立其连接关系；3）在关键流程步骤采用精确算法以保证鲁棒性，同时平衡浮点运算以提升效率；4）应用包括早期剔除无效计算在内的多种保守加速策略。本方法进一步独特地支持输入表面单元的可变偏移距离，相较于传统方法具有更广泛的实际应用价值。我们在Thinkgi10K数据集的子集上进行了方法评估，该数据集包含各领域从业者创建的具有不同拓扑与几何复杂度的模型。实验结果表明，本方法在生成偏移网格表面的单元数量、特征保持度及非均匀偏移距离方面均优于当前最先进方法，标志着该领域的重要进展。