T-splines is a recently developed surface modelling technique which is a generalization of B-splines and allows true local refinement. Another well established method supporting local refinement is hierarchical B-splines. This paper presents algorithms for transformation between T-splines and hierarchical (rational) B-splines. With the transformation, a surface expressed in terms of T-splines c...

The present research investigates the implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics. NURBS and T-splines are two different computational geometry technologies which are studied in this work. Among the features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities ...

A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...

in this paper, we solve a linear system of second-order boundary value problems by using the quadratic b-spline nite el- ement method (fem). the performance of the method is tested on one model problem. comparisons are made with both the analyti- cal solution and some recent results.the obtained numerical results show that the method is ecient.

This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementation of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction. The approach was tested by implementing hierarchical B-splines, truncated hierarchical B-splines, decoupled hierarchical B-splin...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

We first review B-splines and splines constructed using B-splines as the basis functions.

For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...

A variety of techniques to facilitate fast graphical display of curves and surfaces for interactive CAGD purposes have been developed, in the past years. Many of these are commonly referred to as subdivision algorithms PI. In this paper we propose a method for subdividing simplex splines, i.e., splines that can be defined over non-regular grid partitions. There is a relatively exhaustive theory...

This paper presents a new kind of splines, called non-uniform algebraic-trigonometric B-splines (NUAT B-splines), generated over the space spanned by {1, t, . . . , tk−3, cos t, sin t} in which k is an arbitrary integer larger than or equal to 3. We show that the NUAT B-splines share most properties of the usual polynomial B-splines. The subdivision formulae of this new kind of curves are given...