Given a triangulation 4 of a polygonal domain, we nd a reenement of 4 by choosing u t in a neighborhood of the center of the inscribed circle of each triangle t 2 4, connecting u t to the vertices of the triangle t, and connecting u t to u t 0 if t 0 2 4 shares an interior edge with t or to the midpoint v e of any boundary edge e of t. The resulting triangulation is a triangulation of Powell-Sa...

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k + kh + h) for the solution of quasi-linear parabolic equation   , , , , xx x t u f x t u u u  , 0< x <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline app...

Article history: Received 6 January 2013 Received in revised form 13 June 2013 Accepted 30 September 2013 Available online 17 October 2013

We study the reconstruction of cardinal splines f(t), from their average samples yn = f ∗h(n), n ∈ Z, when the average function h(t) has support in [−1/2, 1/2]. We investigate the existence and uniqueness of the solution of the following problem: for given dates yn, find a cardinal spline f(t), of a given degree, satisfying yn = f ∗ h(n), n ∈ Z. 1 Spline interpolation and average sampling First...

Article history: Received 29 July 2015 Received in revised form 4 May 2016 Accepted 19 May 2016 Available online 2 June 2016

This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces from quadmeshes that include T-junctions, where surface strips start or terminate. All mesh nodes can be interpreted as control points of geometrically-smooth, piecewise polynomials that we call GT-splines. GT-splines are B-spline-like and cover T-junctions by two or four patches of degree bi-4. They c...

T-meshes are formed by a set of horizontal line segments and a set of vertical line segments, where T-junctions are allowed. See Figure 1 for examples. Traditional tensor-product B-spline functions, which are a basic tool in the design of freeform surfaces, are defined over special T-meshes, where no T-junctions appear. B-spline surfaces have the drawback that arises from the mathematical prope...