Generalized hierarchical NURBS for interactive shape modification

Abstract

In a three dimensional (3D) environment, having the capability of local shape refinement and modification is highly desired for interactive free-form shape design. The introduction of hierarchical B-spline has provided a nice mechanism to control the influence of refinement to the locality for tensor-product B-spline surfaces. This paper extends the idea of hierarchical B-splines to non-uniform rational B-spline (NURBS) surface and a generalized hierarchical NURBS (H-NURBS) is proposed. Based on the modification of control points or weights of the H-NURBS surface, we can paste a NURBS surface onto an existing H-NURBS surface. Two approaches with different mechanisms are proposed: the base plus detail mechanism and the replacement mechanism. Different kinds of interactive devices like mouse, stylus and glove can be used to manipulate the H-NURBS.