in the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. nurbs and t-splines are two different computational geometry technologies which are studied in this work. among features of b-spline basis functions the possibility of enhancing a b-spline basis with discontinuities b...

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct ...

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the...

Abstract We prove quartic convergence of cubic spline interpolation for curves into Riemannian manifolds as the grid size tends to zero. In contrast in Euclidean space, where this result is classical, operator no longer linear. Still, concepts from linear setting may be generalized case, we try use intrinsic formulations and avoid charts much possible.

Most of the approaches of Content-Based Image Retrieval (CBIR) presume a linear relationship between different image features, and the efficiency of such systems was limited due to the difficulty in representing high-level concepts using low-level features. In this paper, a new architecture for a CBIR system is proposed; the Splines Neural Network-based Image Retrieval (SNNIR) system. SNNIR mak...

We characterize of the Bernstein-Bezier (BB) form of an implicitly deened bivariate polynomial over a triangle, such that the zero contour of the polynomial deenes a smooth and single sheeted real algebraic curve segment. We call a piecewise G k-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree n A-splines can...

In this paper we give a new definition of minimally and quasi-minimally supported C quartic bivariate B-splines associated with the four-directional mesh of the plane, introduced in [7,19], which is convenient to show that theses B-splines satisfy the refinement equation and we determine the associated matrix mask, we prove that the family of these B-splines is stable and the associated subdivi...