During my undergraduate work in the departments of both Mathematics and Computer Science at the University of Toronto, I became increasingly interested in the fields of Computer Graphics and Human Computer Interaction.
In May 1994 I joined the Collaborative Multimedia Research Group at DGP, and participated in the design and development of a multimedia authoring tool called MAD . The tool is designed to assist in the composure of multimedia documents, specifically movies, much in the same way word processing facilitates the creation of textual documents. The project involved solving problems of user interface design as well as resolving various models of data representation.
During the course of my graduate studies, I became interested in Computer Aided Geometric Design and Texture Mapping. I have undertaken research in this area with a specific focus upon modeling textured surfaces using triangularly shaped patches known as Bézier Triangles. From a topological standpoint, triangular patches are better suited for surface modeling than the more commonly used rectangular ones despite the fact that the latter are more commonly employed. I have developed this line of inquiry for my Master's Thesis, with the aim of amalgamating it with concepts of interface design. This involved two tasks. The first was the development and implementation of a three-dimensional textured surface modeler that represents surfaces using piecewise collections of Bézier triangles. The second was to provide this modeler with a workable user interface. To see my thesis click here; to get a copy of my modeling software click here.
For my doctoral studies, I intend to develop the research I have undertaken for my Master's thesis in order to further investigate this relatively unexplored area. I will pursue my research in three simultaneous directions. On the imaging side, I would like to determine the effects of this method on other image synthesis techniques such as texture mappings and illumination models. The geometric aspect would not be complete without considering the inverse problem, that of obtaining a piecewise patch-representation of surfaces from a given image. This would allow space-time optimization, as well as improve the user's control over the surface modeled. Finally, user interface issues must be resolved if there is any hope of applying the theoretical results obtained. These problems would require the mapping of three-dimensional virtual space to a collection of two-dimensional surfaces, or would require the development of ergonomic three-dimensional tools for user interaction.