  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 close but
not perfectly 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 20 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.
