Interpolation of NURBS Surfaces by Using the Extended Branch Structure of Basis Functions

This paper focuses on the design of the extended branch structure for rapidly and simultaneously interpolating non-uniform rational B-spline (NURBS) surfaces and their partial derivatives on CNC machines. NURBS surfaces are concerned in the applications of molding process. However, the copious and complicated operations usually limit the applications of NURBS surfaces in CNC machining systems. In this paper, by considering the derivatives of basis functions, an extended branch structure is derived such that the computation time can be significantly reduced in computing NURBS surfaces and their partial derivatives. According to the machining results on a 3-axis vertical machining center, the extended branch structure is feasible to implement on CNC machines and is more efficient than existing approaches in computation.