Hierarchical implicit surface refinement

Abstract

A novel method of hierarchical implicit modeling is presented in which an implicit object is modeled using a hierarchy of implicit surfaces. The hierarchy provides both layered local refinement and global deformation. Local refinement allows the introduction of higher-level detailed surfaces. Global deformation changes the overall shape of the surface while maintaining the integrity of surface details. The model is gradually refined by introducing appropriate new primitives in specified surface areas. Refinement constraints, such as a local area constraint and a level constraint, are designed to be applied to the implicit object so as to achieve finer control of the local surface. The method provides a dynamic representation of implicit surfaces and can be used in modeling complex implicit objects, animating the surfaces, and simulating the deformations of various objects.