Feature-Aware Reconstruction of Volume Data via Trivariate Splines

In this paper, we propose a novel approach that transforms discrete volumetric data directly acquired from scanning devices into continuous spline representations with tensor-product regular structure. Our method is achieved through three major steps as follows. First, in order to capture fine features, we construct an as-smooth-as-possible frame field, satisfying a sparse set of directional constraints. Next, a globally smooth parametrization is computed, with iso-parameter curves following the frame field directions. We utilize the parametrization to remesh the data and construct a set of regular-structured volumetric patch layouts, consisting of a small number of patches while enforcing good feature alignment. Finally, we construct trivariate T-splines on all patches to model geometry and density functions simultaneously. Compared with conventional discrete data, our data-spline-conversion results are more efficient and compact, serving as a powerful toolkit with broader application appeal in shape modeling, GPC computing, data reduction, scientific visualization and finite element analysis.