We propose an algorithm that integrates geometry parametrization and mesh movement using the control points of a B-spline mesh. An initial mesh is created using B-spline volumes in such a way that the control points mimic a coarse grid. The control points corresponding to the surface nodes are adopted as the design variables. Mesh movement is achieved by applying a standard movement algorithm t...

We give necessary and sufficient conditions for the total positivity of certain connection matrices arising in piecewise exponential spline spaces. These total positivity conditions are sufficient for existence of B-splines in such spaces, but they are far from being necessary. We give a necessary and sufficient condition for existence of B-splines in the case of piecewise exponential spline sp...

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines. Inner and outer polygonal approxim...

In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular perturbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spl...

B category, and a bubble attached to a node represents a set of archaeological records. The size of a bubble attached to a node reflects the number of records belonging to that category. The hyperbolic tree supports ‘‘focus + context’’ navigation; it also provides an overview of records organized in the archaeological digital library. It shows that the records are from seven archaeological site...

Evaluation routines are essential for any application that uses triangular B-spline surfaces. This paper describes an algorithm to efficiently evaluate triangular B-spline surfaces with arbitrary many variables. The novelty of the algorithm is its generality: there is no restriction on the degree of the B-spline surfaces or on the dimension of the domain. Constructing an evaluation graph allows...

Superconvergence of discontinuous Galerkin methods is an area of increasing interest due to the ease with which higher order information can be extracted from the approximation. Cockburn, Luskin, Shu, and Süli showed that by applying a B-spline filter to the approximation at the final time, the order of accuracy can be improved from O(hk+1) to O(h2k+1) in the L2-norm for linear hyperbolic equat...