A Survey of Spline-based Volumetric Data Modeling Framework and Its Applications

The strategic technical vision of this thesis proposal is to seek to systematically trailblaze a novel vol-umetric modeling framework/methdology to represent 3D solids. The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. The strong need to explore more efficient and robust 3D modeling techniques has become prominent. Although the traditional surface representation (e.g., triangle meshes) has many attractive properties, it is incapable of expressing the solid interior space and materials. Such a serious drawback overshadows many potential modeling and analysis applications. Consequently, volumetric modeling techniques become the well-known solution to this problem. Nevertheless, many unsolved research issues still remain outstanding when developing an efficient modeling paradigm for existing 3D models, including complex geometry (fine details and extreme concaveness), arbitrary topology, heterogenous materials, large-scale data storage and processing, etc. In this thesis proposal, we concentrate on the challenging research issue of developing a spline-based modeling framework, which aims to convert the conventional data (e.g., surface meshes) to tensor-product trivariate splines. This methodology can represent both boundary/volumetric geometry and real volumet-ric physical attributes in a compact and continuous matter. The regularly-defined tensor-product structure enables our newly-developed methods to be embedded into the CAD-design industry standards such as NURBS and B-splines seamlessly. These properties make our techniques highly preferable in many physically-based applications including mechanical analysis, shape deformation and editing, reverse engineering , hexahedral meshing, virtual surgery training, etc. Using tensor-product trivariate splines to reconstruct existing 3D objects is highly challenging, which always involves component-aware decomposition, volumetric parameterization, and trivariate spline approximation. This thesis proposal seeks accurate and efficient technical solutions to these fundamental and important problems, and demonstrates their efficiencies in modeling 3D objects of arbitrary topology. First, in order to achieve a " from surface model to trivariate splines " transformation, we define our new splines upon a novel parametric domain called generalized poly-cubes (GPCs), which comprise a set of regular cube-like domains topologically glued together. We then further improve our trivariate splines to support arbitrary topology by allowing the divide-and-conquer scheme, i.e., the user can decompose the model into components and represent them using trivariate spline volumetric patches. We design algorithms and prove valuable properties for our powerful merging strategy that can glue tensor-product spline solids together, while preserving many attractive modeling advantages. We also develop an effective method to reconstruct discrete volumetric datasets (e.g., volumetric …