Current collaborative shape modeling techniques could not utilize all our senses to achieve maximum immersion. Visual rendering alone is unable to convey object properties other than geometry and appearance, such as physical properties. This causes difficulties in practical modeling, and it could be solved by incorporating haptic rendering. On the other hand, traditional polygon-based modeling representation yields large files, which conflict with the limited network bandwidth in collaborative shape modeling. This deficiency could be overcome by employing memory-efficient function-based representations. A survey of the web visualization and shared virtual environments methods and tools leads to the conclusion on the active research niche for proposing new data models and frameworks suitable for visual and haptic rendering in shared virtual spaces. A novel uniform modeling paradigm of defining virtual objects' geometry, visual appearance and tangible physical properties is therefore proposed, in which these three entities are defined in their own coordinate domains and then merged into virtual objects in the application problem coordinate domain. To provide for a faster model exchange and any precision of the representation, mathematical functions and procedures are used for defining geometry, appearance and physical properties. An innovative visual and haptic collaborative framework for shared virtual spaces is also proposed, where the visual and haptic pipelines complement each other to provide a simple and efficient solution to problems requiring collaboration on the web. Mathematical functions and procedures are also adopted there to provide for rapid information transmission and flexible interactive modeling operations. First of all, I would like to thank my supervisor Associate Professor Alexei Sourin for his invaluable instructions. I am grateful for his help throughout my graduate study in Nanyang Technological University. He helps me to understand basic ideas, and to correct theoretical findings. Without his effects, ideas and comments, the project could not reach this point. I would also like to thank Nanyang Technological University and School of Computer Engineering for providing me the opportunity and financial support to further my study and research. Special thanks go to Centre for Advanced Media Technology for providing me the first class equipment and technical supports. Last but not least, I would like to thank my friends and colleagues, Dr. Qi Liu and Dr. Konstantin Levinski, for their precious support. Furthermore, I wish to thank my parents, their selfless concern and encouragement are the best support during my postgraduate study.