Efficient data structures for distributed and mobile geometry processing

3D geometry data is now establishing as a new digital multimedia data type after text and sound in 1980' and images and video in 1990'. One of the major advantages of 3D data is that it enables users to actually interact with the displayed contents, which has embraced more and enhanced interactive multimedia applications.On the other hand, the rapid evolution of the network technology brings new potentials for communication between people and computers in heterogeneous environments. Computing hardware becomes more powerful and ubiquitous thanks to the ever increasing availability of distributed and mobile digital devices.When we combine the strengths from both above areas, we come to an emerging interdisciplinary research field of distributed and mobile geometry processing. This thesis will address the fundamental data structure and geometry representation problems in this field. More specifically, I will present a wide range of high-quality algorithms to produce efficient geometric data structures finely adapted to distributed and mobile geometry processing. The resulting geometric structures and representations are with four important features (compactness, progressiveness, robustness, and security), and are prone to be of crucial usage in diverse 3D multimedia communication applications like distributed CAD, CSCW, movie/animation production, 3D mobile services, online internet games, 3D online documentation, and so on