Mesh reduction using quadric error metrics is the industry standard for producing level-of-detail (LOD) geometry for meshes. Although industry tools produce visually excellent LODs, mesh topology is often ruined during decimation. This is because tools focus on triangle simplification and preserving rendered appearance, whereas artists often produce quad dominant meshes with clean edge topology. Artist created manual LODs preserve both appearance and quad topology. Furthermore, most existing tools for quad decimation only accept pure quad meshes and cannot handle any triangles. The gap between quad and triangular mesh decimation is because they are built on fundamentally different operations, triangle simplification uses single edge collapses, whereas quad decimation requires that entire sets of edges be collapsed atomically. In this work, we demonstrate that single edge collapse can be used to preserve most input quads without degrading geometric quality. Single edge collapse quad preservation is made possible by introducing dihedral-angle weighted quadrics for every edges, allowing optimization to evenly space edges while preserving features. It is further enabled by explicitly ordering edge collapses with nearly equivalent quadric error that preserves quad topology. In addition to quad preservation, we demonstrate that by introducing weights for quadrics on certain edges, our framework can be used to preserve symmetry and joint influences. To demonstrate our approach is suitable for skinned mesh decimation (a key use case of quad meshes), we show that QEM with attributes can preserve joint influences better than prior work. On both static and animated meshes, our approach consistently outperforms prior work with lower Chamfer and Hausdorff distance, while preserving more quad topology.

翻译：使用二次误差度量的网格简化是生成网格多层次细节（LOD）几何的行业标准。尽管行业工具能生成视觉上优秀的LOD，但在简化过程中网格拓扑结构常遭破坏。这是因为工具侧重于三角形简化与渲染外观保持，而艺术家通常制作的是具有清晰边缘拓扑的四边形主导网格。艺术家创建的手动LOD能同时保持外观与四边形拓扑。此外，现有四边形简化工具大多仅接受纯四边形网格，无法处理任何三角形。四边形与三角形网格简化之间的鸿沟源于其基于根本不同的操作：三角形简化采用单边折叠，而四边形简化要求整组边被原子化折叠。本工作中，我们证明单边折叠可用于保持大部分输入四边形而不降低几何质量。通过为每条边引入二面角加权的二次误差度量，使优化过程能在保持特征的同时均匀分布边，从而实现单边折叠的四边形保持。进一步地，通过对具有近乎等效二次误差的边折叠进行显式排序，实现了四边形拓扑的保持。除四边形保持外，我们证明通过对特定边的二次误差度量引入权重，本框架可用于保持对称性与关节影响。为验证本方法适用于蒙皮网格简化（四边形网格的关键应用场景），我们展示了带属性的二次误差度量比先前工作能更好地保持关节影响。在静态与动态网格上，本方法始终以更低的倒角距离与豪斯多夫距离优于先前工作，同时保持了更多的四边形拓扑。