Splines are part of the standard toolbox for the approximation of functions and curves in Rd . Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a “spline” with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be ...

Powell-Sabin splines are C-continuous quadratic splines defined on an arbitrary triangulation. Their construction is based on a particular split of each triangle in the triangulation into six smaller triangles. In this article we give an overview of the properties of Powell-Sabin splines in the context of computer aided geometric design. These splines can be represented in a compact normalized ...

This paper presents the use of Powell-Sabin splines in the context of isogeometric analysis for the numerical solution of advectiondiffusion-reaction equations. Powell-Sabin splines are piecewise quadratic C functions defined on a given triangulation with a particular macro-structure. We discuss the Galerkin discretization based on a normalized Powell-Sabin B-spline basis. We focus on the accur...

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.