Single Edge Collapse Quad-Dominant Mesh Reduction

TL;DR

It is demonstrated that single edge collapse can be used to preserve most input quads without degrading geometric quality and it is shown that QEM with attributes can preserve joint influences better than prior work.

Abstract

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.

Figures (20)

• Figure 1: Our approach is able to better preserve input topology and quads than QEM qemqem_hoppe for hybrid triangle/quad meshes, with comparable geometric similarity to the input mesh. In the zoomed inset, the input sphere becomes triangulated in QEM and the floor has many high valence vertices, whereas our approach preserves quads on the sphere and floor. We also compare to MeshLab meshlab, which requires that the input mesh be triangulated before decimation, making it unsuitable for quad preservation. Humesh Dilchund.
• Figure 2: A visualization of terminology for structure within quad meshes. Part of a quad chord is shown in teal, opposing quad edges are shown in red, and part of an edge loop is shown in green.
• Figure 3: To measure the symmetry of each edge, we compute a matching of all vertices across the plane that spans each manifold edge and the halfway vector between its two adjacent faces. Left: vertices with a matching are shown in green, and those without are shown in red. Each edge's weight is the fraction of all vertices with a matching. This weight is then used during edge collapse for each edge's quadric. In the middle figure, edges along the axes of symmetry (shown in red) are preserved with this weighting, but are lost when it is not explicitly included, shown on the right. Keenan Crane.
• Figure 4: Left: mesh in its rest pose, with edges marked with higher joint distances highlighted. Most distances are centered around anatomical joints, such as elbows and fingers. Right: frame of the animation of the mesh, visualizing range of motion after decimation. Animations tend to deform regions where joint influences vary heavily between vertices. Catholomew.
• Figure 5: Cube mesh simplified with our approach. All edges in the input cube have equivalent cost, but differ slightly when computed due to floating point error. We group these approximately equivalent edges and provide an explicit ordering based on the recency of collapsed opposing quad edges, which preserves topology. This is in contrast to ordering purely based on QEM, which is unable to preserve topology.