VoroCrust

Abstract

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface, circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.

Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm

“…The triangular faces of the reconstruction have bounded angles and edge-length ratios, except perhaps in the presence of slivers. In a forthcoming paper [ 3 ], we describe the design and implementation of the complete VoroCrust algorithm, which generates conforming Voronoi meshes of realistic models, possibly containing sharp features, and produces samples that follow a natural sizing function and ensure output quality.…”

“…Ultimately, we seek a conforming Voronoi mesher that can handle realistic inputs possibly containing sharp features, can estimate a sizing function and generate samples, and can guarantee the quality of the output mesh. This is the subject of a forthcoming paper [ 3 ] which describes the design and implementation of the complete VoroCrust algorithm.…”

PowerRTF: Power Diagram based Restricted Tangent Face for Surface Remeshing

“…Auxiliary points based methods . One class of methods for computing CVT on these approximative polygonal facets is on the basis of auxiliary points, such as RPF [XXT19], VoroCrust [ABE*20], etc. They construct 3D Voronoi or power diagrams using sample points and auxiliary ones.…”

“…Recently, the idea of approximation has been used for surface remeshing [BLM17]. Several strategies [CZC*18, XXT19, ABE*20] that could be considered approximative CVT‐based methodologies have been put forth. Instead of calculating precise geodesic distances or intersections, they use a set of planar polygonal facets to approximate the surface and compute CVT on these planar facets [ZCHK13].…”

“…The primary challenge with this sort of method is computing the approximative polygonal facets. One idea is to construct a 3D Voronoi diagram using a series of auxiliary points, where these facets of adjacent Voronoi cells close to the surface boundary are considered as these desired approximative facets, such as the restricted power face (RPF) [XXT19] and Voro‐Crust [ABE*20], etc. They are simple and straightforward, but the facet extraction relies on the 3D Voronoi diagram construction.…”