Coefficient formula and matrix of nonuniform B-spline functions

The paper derives a coefficient formula of nonuniform B-spline functions of arbitrary degree from the Coxde Boor recursive algorithm. An efficient numerical algorithm for the coefficient matrix of nonuniform B-spline functions is also presented that is based on this formula. The results in the paper are useful for the evaluation and conversion of NURBS curves and surfaces in CAD/CAM systems. They will promote the application of product data-exchange standards in industry.