Low-Resolution Remeshing Using the Localized Restricted Voronoi Diagram

Abstract

A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation.

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

“…2) Within a fixed θ, when δ increases, the mesh complexity decreases slightly and smoothly, since the higher δ is set, the more edge collapse operators are triggered. We compare our results with those provided by Yan et al [9], [19], [22]. The best record of the approximation error is 0.10(%bb), which is generated by [8] with the Homer model as input.…”

“…We set δ = 0.2(%bb), and the Fandisk (Fig. 1(a) We compare our results with the state-of-the-art methods, and find only in a small portion of results presented in [19] and [9], the minimal angles exceed 35…”

“…However, the resulting mesh quality can be poor due to the inexact computation. Yan et al [8], [19], [20] avoid the parameterization by computing the 3D CVT restricted to the surface. Additionally, they proposed blue-noise remeshing techniques using adaptive maximal Poisson-disk sampling [9], [21], farthest point optimization [22], and push-pull operations [23], which improve the element quality as well as introducing blue-noise properties.…”

“…However, none of them works reliably for all kinds of meshes. Most remeshing algorithms avoid this problem by assuming that the features have been specified in advance [8], [9], [19], [21], [22], [33]. Some remeshing techniques try to preserve features implicitly [34], [35].…”

“…[8], [9], [19], [22], [33], our goal is to implicitly preserve features. This not only releases users from the time-consuming burden of manual tagging but moreover often enables the recovery of features that were lost, e.g.…”