In this work a family of tension trigonometric curves analogous to those of cubic Bézier curves is presented. Some properties of the proposed curves are discussed. We propose an efficient interpolating method based on the tension trigonometric splines with various properties, such as partition of unity, geometric invariance and convex hull property, etc. This new interpolating method is applied...

Abstract Using a set of modified cubic trigonometric B-splines as test functions, a new differential quadrature technique is proposed for the 1D and 2D transient advection-diffusion equations of order α ∈ (0, 1]. The weighted coefficients are determined via solving the system of algebraic equations with a strictly diagonally dominant tri-diagonal matrix. Then, the original equation is converted...

A method of generating cubic blending spline curves based on weighted trigonometric and hyperbolic polynomial is presented in this paper. The curves inherit nearly all properties of cubic B-splines and enjoy some other advantageous properties for modeling. They can represent some conics and some transcendental curves exactly. Here weight coefficients are also shape parameters, which are called ...

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...

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curve or surface). In this paper, we characterize a new family of compactly supported piecewise-exponential basis functions that are smooth and s...

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...