Ph.D Thesis

Ph.D StudentSchein Sagi
SubjectTrivariate Functions in Solid Modeling, Medical Imaging
and Computer Graphics
DepartmentDepartment of Computer Science
Supervisor PROF. Gershon Elber


Over the past decade, volume graphics has been recognized as an important field of research. Most early research in volume graphics was focused on the problem of rendering of volumetric models. Only recently, volume modeling had been suggested. Volume modeling encompasses the tools, data representations and algorithms that are needed to describe and manipulate the inner parts of a model, as well as its outer shell. Volume modeling can be applied in wide range of fields such as material sciences, medical imaging, the movie-making industry, etc. As with surface-based geometric modeling, volume modeling seeks to supply the designer with a set of robust, fast and predictable manipulation tools for designing volumetric models. Since our aim is to develop tools for volumetric modeling, we should consider the state-of-the-art in surface-based modeling. In computer aided geometric design (CAGD), tensor product B-spline functions are, perhaps, the most commonly used surface representations. Therefore, we consider their extension into three-dimensional parametric space as a data representation for volume modeling.

This thesis focuses on tools and algorithms for modeling with trivariate tensor product B-spline functions. These functions are used to solve several geometric modeling and computer graphics problems. We present diverse and novel applications such as placement of deformable objects inside virtual scenes, incision simulation of surface and silhouette extraction from volume data. In an attempt to make trivariate tensor product B-spline functions a better deformation tool, we also supply bounds on the deformation error of polygonal models inside free-form deformation. Lastly, in order to reduce the computational burden of trivariate functions, we propose fast evaluation techniques that employ programmable graphics hardware. These evaluation techniques are used for real-time model deformation and for adding arbitrary surface details in real-time applications.