A Simple Push-Pull Algorithm for Blue-Noise Sampling

Abstract

We describe a simple push-pull optimization (PPO) algorithm for blue-noise sampling by enforcing spatial constraints on given point sets. Constraints can be a minimum distance between samples, a maximum distance between an arbitrary point and the nearest sample, and a maximum deviation of a sample's capacity (area of Voronoi cell) from the mean capacity. All of these constraints are based on the topology emerging from Delaunay triangulation, and they can be combined for improved sampling quality and efficiency. In addition, our algorithm offers flexibility for trading-off between different targets, such as noise and aliasing. We present several applications of the proposed algorithm, including anti-aliasing, stippling, and non-obtuse remeshing. Our experimental results illustrate the efficiency and the robustness of the proposed approach. Moreover, we demonstrate that our remeshing quality is superior to the current state-of-the-art approaches.

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

“…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, these approaches still suffer from common limitations, e.g., geometric fidelity and the minimal angle cannot be explicitly bounded.…”

Surface remeshing with robust user-guided segmentation

“…For example, representative works include mesh simplification-based methods [8,9], advancingfront-based method [10], Delaunay insertion methods [11], field-based approaches [12][13][14], and mesh optimization with either local operations [15][16][17][18] or global energy minimization. Global optimization approaches can be further classified as parametrization-based methods [2,19,20], discrete clustering methods [4], and direct 3D optimization methods [3,[21][22][23][24][25][26][27]. In this section, we briefly review those remeshing methods most closely related to our proposed method, focusing on feature preservation.…”

Weighted linde-buzo-gray stippling

“…On surfaces, the socalled Restricted Voronoi Diagram (RVD) has to be computed. While early methods such as from Alliez et al [2005] and Valette et al [2008] compute only approximate RVDs for remeshing, more recent methods improve the quality by computing exact RVDs [Ahmed et al 2016;Yan et al 2009]. The RVDs are then used to perform Lloyd's 233:3 ... Fig.…”

“…Because our method ultimately distributes vertices similar to Lloyd's algorithm-at least if cells are no longer split or merged-we are not able to surpass the quality produced by the most recent works on remeshing (cf. Ahmed et al [2016]). Nevertheless, our method allows quick adaption to local geometric features such as curvature.…”