In this paper we prove that there exists a unique positive symmetrical univariate B-spline with minimal support. It is obtained as linear combination of a minimal number of successive classical B-splines with multiple knots in the space, S d , of cardinal polynomial splines of class C and degree d. Next, we show that the approximation order in the space generated by the integer translates of th...

We present a new approach to the construction of piecewise polynomial or rational C k-spline surfaces of arbitrary topological structure. The basic idea is to use exclusively parametric smoothness conditions, and to solve the well known problems at extraordinary points by admitting singular parametrizations. The smoothness of the spline surfaces is guaranteed by specifying a regular smooth re-p...

C-B spline can not represent semi-circle and semi-elliptical arcs precisely. This paper will discuss the nature of C-B spline’s and C-Bézier curve’s endpoints. Then, on the basis of the analysis of their characteristics and by means of adding control points to make C-B spline dominate the first and last vertices of the polygon and get tangency with the first and end sides. Thus it has given out...

B-spline functions play important roles in both mathematics and engineering. To describe a numerical method for solving the boundary value problem of linear ODE with second-order by using B-spline. First, the cubic B-spline basis functions are introduced, then we use the linear combination of cubic B-spline basis to approximate the solution. Finally, we obtain the numerical solution by solving ...

This paper is devoted to the shape control of B-spline curves achieved by the modification of one of its knot values. At first those curves are described along which the points of a B-spline curve move under the modification of a knot value. Then we show that the one-parameter family of k order B-spline curves obtained by modifying a knot value has an envelope which is also a B-spline curve of ...

Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-s...

Sliding motion is a challenge for deformable image registration because it leads to discontinuities in the sought deformation. In this paper, we present a method to handle sliding motion using multiple B-spline transforms. The proposed method decomposes the sought deformation into sliding regions to allow discontinuities at their interfaces, but prevents unrealistic solutions by forcing those i...