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...

Two main technologies are available to design and represent freeform surfaces: NonUniform Rational B-Splines (NURBS) and subdivision surfaces. Both representations are built on uniform B-splines, but they extend this foundation in incompatible ways, and different industries have therefore established a preference for one representation over the other. NURBS are the dominant standard for Compute...

<div class="section abstract"><div class="htmlview paragraph">In regions at war, the increasing use of improvised explosive devices (IEDs) is main threat against military vehicles. Large cabin”s penetrations and high gross accelerations are primary threats occupants” survivability. The survivability under an IED event largely depends on design vehicle armor. Under a blast load, armo...

In this paper, the performance of finite element method based on Lagrange basis functions and Non Uniform Rational B-Splines (NURBS) Iso-Geometric Analysis (IGA) are systematically studied for solving time-harmonic acoustic scattering problems. To assess their performance, numerical examples presented with truncated absorbing boundary conditions. first two , we eliminate domain truncation error...

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been pr...

In this paper, we present a boundary integral based approach to isogeometric analysis and shape optimization. For analysis, it uses the same basis, Non-Uniform Rational B-Spline (NURBS) basis, for both representing object boundary and for approximating physical fields in analysis via a Boundary-Integral-Equation Method (BIEM). We propose the use of boundary points corresponding to Greville absc...

We introduce the several possible ”NUERBS” forms of expo-rational B-splines, and discuss the hierarchy of these forms in the univariate case. We give some first instances of exploration of properties of the expo-rational NUERBS which depend not only on the NUERBS weights but also on the intrinsic parameters of the expo-rational Bsplines.