Mass: Multiresolutional Adaptive Solid Subdivision

In this survey paper, we discuss subdivision geometry, subdivision schemes, its analysis and applications, especially from the view of solid modeling. Subdivision technique has been widely accepted in computer graphics and geometric design applications. However, it has been largely ignored in solid modeling. The first few sections are devoted to the history of subdivision modeling and the review of existing subdivision schemes in detail. We also briefly review other solid modeling techniques. Next, we discuss the current mathematical technique to analyze subdivision schemes on both regular and extraordinary topologies. We provide examples of analysis on the schemes in prior sections. We discuss problems involving solid scheme analysis and suggest possible solutions. In addition, we review prior work using subdivision technique in various applications. The latter part of the paper devote to our novel subdivision solid schemes, ongoing research topics, and new ideas. We demonstrate the potential of subdivision solids by a variety of examples. Attractive features of subdivision solids are compared and addressed. We conclude the paper with the summary and the expectation for future of subdivision technique in solid modeling.