Nonnegative surface fitting with Powell-Sabin splines

G. Chang and T.W. Sederberg, Nonnegative quadratic Bézier triangular patches, Comp. Aided Geom. Design 11 (1994) 113–116.

P. Dierckx,Curve and Surface Fitting with Splines, Monographs on Numerical Analysis (Clarendon Press, Oxford, 1993).

P. Dierckx, S. Van Leemput and T. Vermeire, Algorithms for surface fitting using Powell-Sabin splines, IMA J. Numer. Anal. 12 (1992) 271–299.

G. Farin, Triangular Bernstein-Bézier patches, Comp. Aided Geom. Design 3 (1986) 83–127.

R.H.J. Gmelig-Meyling and P.R. Pfluger, On the dimension of the spline spaceS 2 1 (Δ) in special cases, in:Multivariate Approximation Theory III, eds. W. Schempp and K. Zeller (Birkhäuser, Basel, 1985) pp. 180–190.

C.A. Micchelli and A. Pinkus, Some remarks on nonnegative polynomials on polyhedra, in:Probability, Statistics, and Mathematics, eds. T. Anderson, K. Alhreya and D. Iglehart (Academic Press, New York, 1989) pp. 163–185.

B. Mulansky and J.W. Schmidt, NonnegativeC 1 interpolation of scattered data using Powell-Sabin splines, Technical report, Technische Universität Dresden (March 1993).

E. Nadler, Nonnegativity of bivariate quadratic functions on a triangle, Comp. Aided Geom. Design 9 (1992) 195–205.

The NAG Fortran Library Manual-Mark 15 (The Numerical Algorithms group, Oxford, 1991).

C.C. Paige and M.A. Saunders, LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software 8 (1982) 43–71.

C.C. Paige and M.A. Saunders, Algorithm 583 LSQR: Sparse linear equations and least squares problems, ACM Trans. Math. Software 8 (1982) 195–209.

M.J.D. Powell and M.A. Sabin, Piecewise quadratic approximations on triangles, ACM Trans. Math. Software 3 (1977) 316–325.

J.W. Schmidt, Positive, monotone, and S-convexC 1-interpolation on rectangular grids, Computing 48 (1992) 363–371.

L.L. Schumaker, On the dimension of spaces of piecewise polynomials in two variables, in:Multivariate Approximation Theory, eds. W. Schempp and K. Zeller (Birkhäuser, Basel, 1979). pp. 396–412.

L.L. Schumaker, Bounds on the dimension of spaces of multivariate piecewise polynomials, Rocky Mt. J. Math. 14 (1984) 251–264.

L.L. Schumaker, Numerical aspects of spaces of piecewise polynomials on triangulations, in:Algorithms for Approximation, eds. J.C. Mason and M.G. Cox (Clarendon Press, Oxford, 1987) pp. 373–406.

K. Willemans and P. Dierckx, Surface fitting with boundary conditions by means of Powell-Sabin splines, Technical report, K.U. Leuven, Dept. Comp. Science, Report TW 199 (October 1993).

K. Willemans and P. Dierckx, Surface fitting using convex Powell-Sabin splines, J. Comp. Appl. Math. (1994).