  In this dissertation, we concentrate on the challenging research issue of
developing a spline-based modeling framework, which converts the conventional
data (e.g., surface meshes) to tensor-product trivariate splines. This
methodology can represent both boundary/volumetric geometry and real volumetric
physical attributes in a compact and continuous fashion. The regular
tensor-product structure enables our new developed methods to be embedded into
the industry standard seamlessly. These properties make our techniques highly
preferable in many physically-based applications including mechanical analysis,
shape deformation and editing, virtual surgery training, etc.
