SDF-RVD: Restricted Voronoi Diagram on Signed Distance Field. (March 2022) - Hou, Wenjuan; Zong, Chen; Wang, Pengfei; Xin, Shiqing; Chen, Shuangmin; Liu, Guozhu; Tu, Changhe; Wang, Wenping
Abstract: Signed distance fields (SDFs), as a powerful surface representation, draw more and more attention in recent years, especially with the innovation of geometric deep learning techniques. In fact, many kinds of popular surface representations, whether explicit forms (point cloud, mesh, or S ( u, v ) = x ( u, v ), y ( u, v ), z ( u, v ) ) or implicit forms ( f ( x, y, z ) = 0 ), can be easily transformed into the SDF representation. It is an interesting research direction to accomplish some important operations directly on the SDF representation. Considering that restricted Voronoi diagrams (RVDs), as a fundamental geometric tool, are central to sampling, meshing and many other geometry processing tasks, we focus on how to define and compute RVDs based SDF, named SDF-RVD . Given a set of samples x i i = 1 m lying on the surface, the key idea is to define RVD based on analyzing how the 3D Voronoi diagram w.r.t. x i i = 1 m passes through the implicit surface, without rigorously decomposing the watertight surface into a set of curved surface patches. We further observe that SDF-RVD works well on an arbitrary surface representation as long as it is equipped with the projection operation. Even for the mesh input, the timing cost spent in computing SDF-RVD is nearly independent of the original mesh resolution, which distinguishes itself from the traditional RVD based meshing approaches. We further show that SDF-RVD is able to naturally work with centroidal Voronoi tessellation (CVT) and report a well triangulated mesh as the output. Finally, we link SDF-RVD plus CVT up with those continuous SDF based neural networks (e.g., DeepSDF) for directly transforming a point cloud into a high-quality triangle mesh, which does not include a step of extracting a poor-quality mesh using marching cubes. Highlights: We propose SDF-RVD to extend RVD from a polygonal mesh to SDF representation. SDF-RVD works well as long as the projection operation is equipped. We give a strategy to assign each site a single RVD patch. Our algorithm operates on SDF, yielding a good triangle mesh without marching cubes.