A Remeshing Method via Adaptive Multiple Original-Facet-Clipping and Centroidal Voronoi Tessellation

TL;DR

This work tackles the trade-off in CVT-based surface remeshing between high-quality, exact methods and efficient but potentially lower-quality approximations. It introduces curvature-adaptive, multi-clip Centroidal Voronoi Tessellation where adaptive clipping of CVT cells is guided by local surface curvature, implemented with GPU-accelerated clipping and an area-weighted centroid update, followed by RVD-based mesh extraction. Key contributions include the curvature-driven determination of clipping counts (1–3), a neighborhood-ring facet strategy for clipping decisions, an area-weighted centroid projection onto the original surface, and GPU-enabled parallelism, all validated against multiple baselines across diverse models. The results show improved average triangle quality ($Q_{avg}$) and robust geometric fidelity (low $d_H$ and $RMS$) while offering tunable performance from faster approximations to near-exact accuracy, making the method practical for complex geometries.

Abstract

CVT (Centroidal Voronoi Tessellation)-based remeshing optimizes mesh quality by leveraging the Voronoi-Delaunay framework to optimize vertex distribution and produce uniformly distributed vertices with regular triangles. Current CVT-based approaches can be classified into two categories: (1) exact methods (e.g., Geodesic CVT, Restricted Voronoi Diagrams) that ensure high quality but require significant computation; and (2) approximate methods that try to reduce computational complexity yet result in fair quality. To address this trade-off, we propose a CVT-based surface remeshing approach that achieves balanced optimization between quality and efficiency through multiple clipping times of 3D Centroidal Voronoi cells with curvature-adaptive original surface facets. The core idea of the method is that we adaptively adjust the number of clipping times according to local curvature, and use the angular relationship between the normal vectors of neighboring facets to represent the magnitude of local curvature. Experimental results demonstrate the effectiveness of our method.

Figures (11)

• Figure 1: Overall surface remeshing procedure with bunny by our method. (a) Original model with 35.292k vertices and 70.580k facets, the average quality of its triangles is 0.715; (b) Initial sample points on original model; (c) Clipped facets of model based on initial sample points; (d) Optimal clipped facets of model after multiple times with optimized sample points; (e) Output triangular mesh with 7k vertices and 13.996k facets, the average quality of its triangles is 0.917. The average quality of the output model has improved 28.252% compared to the original model. Notably, the geometric details (e.g., leg-body junctions) exhibit higher-quality triangulation.
• Figure 2: Illustration of Voronoi Diagram and CVT.
• Figure 3: (a) The blue point is the current site $\mathbf{s}_i$, where: The red dashed line encloses the first-layer neighborhood-ring of the original triangular facet $\mathbf{f}_t$ containing $\mathbf{s}_i$; The pink solid line encloses the second-layer neighborhood-ring of $\mathbf{f}_t$; The green circle defines a range with radius $2 \times d_{\max,i}$ (where $d_{\max,i} = \max_{\mathbf{s}_k \in N(\mathbf{s}_i)} \|\mathbf{s}_k - \mathbf{s}_i\|$, and $N(\mathbf{s}_i)$ denotes the neighboring sites of $\mathbf{s}_i$). The set of original triangular facets lying within both neighborhood-rings and not exceeding the green circle is defined as the neighboring facet set $F_{\text{near}}$ of $\mathbf{s}_i$. By traversing facets in $F_{\text{near}}$ and calculating the cosine values of angles between each facet and $\mathbf{f}_t$, it is determined that the current cell requires three clippings. The clipping facets $\mathbf{f}_u$ and $\mathbf{f}_v$ are identified using \ref{['eq:score nd clip']} and \ref{['eq:score th clip']}. (b) After performing three clippings on the cell, three sub-facets are generated: $F_{i1}$ (light green), $F_{i2}$ (dark green), and $F_{i3}$ (deepest green).
• Figure 4: Half-space clipping process: First, we identify the removal side containing vertices $a$, $b$, $c$ and eliminate them with connected edges; Second, computing intersections $e$, $f$, $g$, $h$ between the clipping plane and cell edges and generating new facet by connecting these intersections.
• Figure 5: The Voronoi cell undergoes three sequential clipping operations along the arrow direction, starting from the unclipped state at the top-left and terminating at the bottom-right. The algorithm retains only the facets $F_{i1}$, $F_{i2}$, $F_{i3}$ generated through these clips. The middle facet in the bottom row represents the final retained result, while the leftmost element provides an adjusted viewpoint for intuitive facet inspection.