  We present a new fully automatic block-decomposition hexahedral meshing
algorithm capable of producing high quality meshes that strictly preserve
feature curve networks on the input surface and align with an input surface
cross-field. We produce all-hex meshes on the vast majority of inputs, and
introduce localized non-hex elements only when the surface feature network
necessitates those. The input to our framework is a closed surface with a
collection of geometric or user-demarcated feature curves and a feature-aligned
surface cross-field. Its output is a compact set of blocks whose edges
interpolate these features and are loosely aligned with this cross-field. We
obtain this block decomposition by cutting the input model using a collection
of simple cutting surfaces bounded by closed surface loops. The set of cutting
loops spans the input feature curves, ensuring feature preservation, and is
obtained using a field-space sampling process. The computed loops are uniformly
distributed across the surface, cross orthogonally, and are loosely aligned
with the cross-field directions, inducing the desired block decomposition. We
validate our method by applying it to a large range of complex inputs and
comparing our results to those produced by state-of-the-art alternatives.
Contrary to prior approaches, our framework consistently produces high-quality
field aligned meshes while strictly preserving geometric or user-specified
surface features.
