The P-splines of Eilers andMarx (Stat Sci 11:89– 121, 1996) combine aB-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as reduced rank smoothers: (i) the basis and the penalty are sparse, enabling efficient computation, especially for Bayesian stochastic simulati...

Given A spline curves and A patch surfaces that are implicitly de ned on triangles and tetrahedra we determine their NURBS representations We provide a trimmed NURBS form for A spline curves and a parametric tensor product NURBS form for A patch surfaces We concentrate on cubic A patches providing a C continuous surface that interpolates a given triangulation together with surface normals at th...

Algorithms are presented for computing a quadratic spline interpolant with variable knots which preserves the monotonicity and convexity of the data. It is also shown that such a spline may not exist for fixed knots.

Given a convex function f without any smoothness requirements on its derivatives, we estimate its error of approximation by C 1 convex quadratic splines in terms of ! 3 (f; 1=n).

In this paper we present an approximation method of surfaces by a new type of splines, which we call fairness bicubic splines, from a given Lagrangian data set. An approximating problem of surface is obtained by minimizing a quadratic functional in a parametric space of bicubic splines. The existence and uniqueness of this problem are shown as long as a convergence result of the method is estab...

The aim of the present study was the estimation of (co) variance components and genetic parameters for body weight of Moghani sheep, using random regression models based on B-Splines functions. The data set included 9165 body weight records from 60 to 360 days of age from 2811 Moghani sheep, collected between 1994 to 2013 from Jafar-Abad Animal Research and Breeding Institute, Ardabil province,...

An algorithm for refining an essentially unrestricted mesh of points into a bivariate C 1 surface is given. The algorithm generalizes the construction of quadratic splines from a mesh of control points. It gives an explicit parametrization of the surface with quadratic and cubic pieces. When the mesh is regular then a quadratic spline surface is generated. Irregular input meshes with non quadri...