Single Edge Collapse Quad-Dominant Mesh Reduction

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 edge, allowing optimization to evenly space edges while preserving features. It is further enabled by explicitly ordering edge collapses with nearly equivalent quadric error in a way 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 on triangle meshes, we show that QEM with attributes can preserve joint influences better than prior work. We implement and test our approach on 67 static and 19 animated meshes from Sketchfab. On both static and animated meshes, our approach consistently outperforms prior work with lower Chamfer and Hausdorff distance, while preserving more quad topology when present.