Robust hex-dominant mesh generation using field-guided polyhedral agglomeration

Abstract

We propose a robust and eicient ield-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra. The latter are placed according to the singularities of two optimized guiding ields, which allow our method to generate meshes with an exceptionally high amount of isotropy. The ield design phase of our method relies on a compact quaternionic representation of volumetric octa-ields and a corresponding optimization that explicitly models the discrete matchings between neighboring elements. This optimization naturally supports alignment constraints and scales to very large datasets. We also propose a novel extraction technique that uses ield-guided mesh simplification to convert the optimized ields into a hexdominant output mesh. Each simplification operation maintains topological validity as an invariant, ensuring manifold output. These steps easily generalize to other dimensions or representations, and we show how they can be an asset in existing 2D surface meshing techniques. Our method can automatically and robustly convert any tetrahedral mesh into an isotropic hex-dominant mesh and (with minor modifications) can also convert any triangle mesh into a corresponding isotropic quad-dominant mesh, preserving its genus, number of holes, and manifoldness. We demonstrate the beneits of our algorithm on a large collection of shapes provided in the supplemental material along with all generated results

Design and Optimization of Conforming Lattice Structures

“…To efficiently and robustly extract consistent lattice structures, we extend the robust meshing approach that was proposed by Jacob et al [57] and further developed by Gao et al [50]. The per vertex local parameterization from [50] fits our purpose well since the local parameterization aligns exactly with the direction field by construction and permits fast and scalable computations. The extension proposed in this paper allows to incorporate anisotropy and heterogeneity.…”

“…The unit lengths are fixed through the entire process. Unlike the previous approaches [50], [57] that treat directions as a 4 rotational symmetric field in 2D or a 24 rotational symmetric field in 3D, since the unit length varies for different axis, our coordinate system is mutable only by flipping the signs of each axis while maintaining the right-hand rule. The origin with a random initialization, is the variable we need to optimize.…”

Finding hexahedrizations for small quadrangulations of the sphere

“…Hexahedral mesh generation is a thriving field of research, with a variety of proposed methods. These include multi-block decomposition methods using frame-field parametrizations [Kowalski et al 2014;Lyon et al 2016;Nieser et al 2011], hex-dominant meshing methods [Baudouin et al 2014Gao et al 2017;Sokolov et al 2017;Yamakawa and Shimada 2003], octreebased methods [Ito et al 2009;Maréchal 2009;Qian and Zhang 2010;Zhang et al 2012], and polycube-based methods [Fang et al 2016;Gregson et al 2011;Han et al 2011;Yu et al 2014].…”

Hex-dominant meshing: Mind the gap!

“…Global optimization produces impressive results, but it has failure cases of its own. For the sake of completeness, we also mention the alternative approach proposed in [8], that generates a hexahedral mesh by merging tetrahedra of an input mesh along the guidance direction field. All these methods (parameterizations and agglomeration) rely on frame fields [10,19], however, no existing frame-field method is guaranteed to produce an integrable 3D frame field.…”