The multivariate quartic NURBS surfaces

In this paper, we construct a kind of multivariate quartic nonuniform rational B-spline (NURBS) surfaces by using bivariate quartic B-spline bases in the multivariate spline space S-4(2)(Delta(mn)((2))), and discuss some properties of this kind of NURBS surfaces with multiple knots on the type-2 triangulation. Compared with the bicubic (rational) Bezier surfaces, the new multivariate NURBS surfaces on the knot vectors of the form U = {0, 0, 0, 0, 1, 1, 1, 1} and V = {0, 0, 0, 0, 1, 1, 1, 1} have similar properties at the four edges of the surfaces. Several examples show that our multivariate B-spline surfaces are better than the corresponding bicubic Bezier surfaces. (C) 2003 Elsevier B.V. All rights reserved.