Interactive all-hex meshing via cuboid decomposition

Abstract

Standard PolyCube-based hexahedral (hex) meshing methods aim to deform the input domain into an axis-aligned PolyCube volume with integer corners; if this deformation is bijective, then applying the inverse map to the voxelized PolyCube yields a valid hex mesh. A key challenge in these methods is to maintain the bijectivity of the PolyCube deformation, thus reducing the robustness of these algorithms. In this work, we present an interactive pipeline for hex meshing that sidesteps this challenge by using a new representation of PolyCubes as unions of cuboids. We begin by deforming the input tetrahedral mesh into a near-PolyCube domain whose faces are loosely aligned to the major axis directions. We then build a PolyCube by optimizing the layout of a set of cuboids with user guidance to closely fit the deformed domain. Finally, we construct an inversion-free pullback map from the voxelized PolyCube to the input domain while optimizing for mesh quality metrics. We allow extensive user control over each stage, such as editing the voxelized PolyCube, positioning surface vertices, and exploring the trade-off among competing quality metrics, while also providing automatic alternatives. We validate our method on over one hundred shapes, including models that are challenging for past PolyCube-based and frame-field-based methods. Our pipeline reliably produces hex meshes with quality on par with or better than state-of-the-art. We additionally conduct a user study with 21 participants in which the majority prefer hex meshes they make using our tool to the ones from automatic state-of-the-art methods. This demonstrates the need for intuitive interactive hex meshing tools where the user can dictate the priorities of their mesh.

Hex-Mesh Generation and Processing: a Survey

“…Also this method is not guaranteed to converge to a valid polycube structure. Interactive tools for user assisted polycube construction also exist [Li et al 2021;Yu et al 2021Yu et al , 2020.…”

“…Alternatively to volumetric deformation, one could in principle use a surface method to define a polycube-surface map (e.g., with [Yang et al 2019]) and then solve for a compatible volumetric mapping between the two shapes. Again, however, despite the high level of practical robustness showcased by recent approaches [Du et al 2020;Garanzha et al 2021], the fully reliable automatic generation of constrained volumetric maps without flips remains an open problem [Fu et al 2021] Motivated by this difficulty, an interactive polycube construction pipeline that puts the user in the loop has been recently proposed [Li et al 2021]. Users are allowed extensive control over each stage, such as editing the polycube structure, positioning vertices, and exploring the trade-off among competing quality metrics, while also providing automatic alternatives.…”

“…Since these tools follow a divide-and-conquer approach, direct hexmeshing techniques are preferred to indirect ones, because they ensure that the meshes of all sub components will be conforming. In recent years, academic literature has started to explore the possibility to couple user guidance with indirect approaches that operate on a supporting tetrahedral mesh [Li et al 2021;Takayama 2019;Yu et al 2021Yu et al , 2020. These methods are not based on the typical divide-and-conquer paradigm, and their ability to scale on complex shapes it yet to be demonstrated.…”

Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary

“…A parameterization is a deformation of a volume to a simpler domain, such as a topological ball Garanzha et al 2021;Paillé and Poulin 2012;Wang et al 2003;Yueh et al 2019] or a polycube [Aigerman and Lipman 2013;Li et al 2021;Paillé and Poulin 2012;Wang et al 2008b;Xia et al 2010]. The better-studied instance of parameterization in graphics maps two-dimensional surfaces (rather than volumes) into the plane; see [Floater and Hormann 2005;Fu et al 2021;Sheffer et al 2007] for discussion of this broad area of research.…”

“…We implement our method in MATLAB, using CUDA to optimize the projection step by extending the projection code in [Li et al 2021] to R 6 .…”