A unified architecture for the computation of B-spline curves and surfaces

Abstract

B-Splines, in general, and Non-Uniform Rational B-Splines (NURBS), in particular, have become indispensable modeling primitives in computer graphics and geometric modeling applications. In this paper, a novel high-performance architecture for the computation of uniform, nonuniform, rational, and nonrational B-Spline curves and surfaces is presented. This architecture has been derived through a sequence of steps. First, a systolic architecture for the computation of the basis function values, the basis function evaluation array (the BFEA), is developed. Using the BFEA as its core, an architecture for the computation of NURBS curves is constructed. This architecture is then extended to compute NURBS surfaces. Finally, this architecture is augmented to compute the surface normals, so that the output from this architecture can be directly used for rendering the NURBS surface.