Explicit matrix representation for NURBS curves and surfaces Original Research Article

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally spaced knot and Bézier curves and surfaces can be obtained by these formulae. The coefficient formulae and the coefficient matrix formulae developed in this paper express non-uniform B-spline functions of arbitrary degree in explicit polynomial and matrix forms. They are useful for the evaluation and the conversion of NURBS curves and surfaces in CAD/CAM systems.