Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

Abstract. We describe and demonstrate an arrow notation for deriving box-spline subdivision schemes. We compare it with the z-transform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We demonstrate the properties that can be derived easily using the arrow method: mask, stencils, con...

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational Bézier patch using quartic Bézier patch. We show that our approximation method yields G (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

Powell–Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and N...

We present a multigrid algorithm for the solution of the linear systems that arise from a finite element discretization of second order elliptic partial differential equations with Powell-Sabin splines. We show that the method yields a uniform convergence independent of the mesh size.

In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

one of the most important parts of range doppler algorithm is range cell migration correction. in this part, an interpolation approach is used to estimate data in their correct location. the interpolation method has a great influence on the quality of ultimate image. in this paper the interpolation method and different ways for increasing its accuracy was discussed. the performance of different...

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...

We propose a new method to approximate a given set of ordered data points by a spatial circular spline curve. At first an initial circular spline curve is generated by biarc interpolation. Then an evolution process based on a least-squares approximation is applied to the curve. During the evolution process, the circular spline curve converges dynamically to a stable shape. Our method does not n...

A numerical method based on B-spline is developed to solve the time-dependent Emden-Fowler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point at 0 x = . The error analysis of the method is described. Numerical results are given to illustrate the efficiency of the proposed method.