  The rapid advances in 3D scanning and acquisition techniques have given rise
to the explosive increase of volumetric digital models in recent years. This
dissertation systematically trailblazes a novel volumetric modeling framework
to represent 3D solids. The need to explore more efficient and robust 3D
modeling framework has gained the prominence. Although the traditional surface
representation (e.g., triangle mesh) has many attractive properties, it is
incapable of expressing the 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 remain when
developing an efficient modeling paradigm for existing 3D models: complex
geometry (fine details and extreme concaveness), arbitrary topology,
heterogenous materials, large-scale data storage and processing, etc.
