Hierarchical D-NURBS surfaces and their physics-based sculpting

In this paper we present Hierarchical D-NURBS as a new shape modeling representation which generalizes powerful, physics-based D-NURBS for interactive geometric design. Our Hierarchical D-NURBS can be viewed as a collection of standard D-NURBS finite elements, organized hierarchically in a tree structure and subject to continuity constraints across the shared boundaries of adjacent D-NURBS elements at different levels. The layered and composite construction of hierarchical D-NURBS affords users the effective creation of local features and their flexible, global/local control at different level of details. Within the framework of Hierarchical D-NURBS, users can interactively sculpt NURBS geometry more intuitively and conveniently through both global and local toolkits. Based on the data structure of Hierarchical D-NURBS, we have developed a prototype software equipped with various physics-based toolkits in the form of geometric constraints and simulated forces. Our modeling system allows users to undertake the design tasks of point manipulation, normal editing, curvature control, curve fitting, and area sculpting in interactive graphics and CAD/CAM.