Efficient, tight bounding volumes for subdivision surfaces.

摘要

Subdivision surfaces provide a simple and yet powerful tool for graphics applications and computer aided geometric design. They fill the gap between polyhedral and spline modeling and have matured to an important high-end modeling method. Being able to bound the subdivision surfaces is crucial for common tasks such as accurate rendering or intersecting surfaces.; This thesis gives a framework for constructing tight bounding volumes for subdivision surfaces, by decomposing the surface into patches, the patches into combinations of basis functions, and pre-computing and tabulating of the bounds for these basis functions. A subtle point here is to establish the basis property of the functions that define subdivision surface locally.; We verify the effectiveness of these bounding volumes with concrete algorithms for interference detection, adaptive tessellation and rendering. Prior to this thesis, no correct and efficient algorithm existed for these applications.