Hierarchical B-spline networks consist of multiple B-spline networks assembled in different level or cascade architecture. To identify the hierarchical B-spline networks and select important input features for each sub-B-spline network automatically, a predefined instruction/operator set was used. The structures of hierarchical B-spline networks were created and evolved by using Probabilistic I...

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...

Surface blending is a useful operation in geometric design for rounding sharp edges or corners. Meanwhile, NURBS has already become the de facto industrial standard in existing CAD/CAM systems. Therefore, it is required to study how to blend two B-spline surfaces. However, two arbitrary B-spline surfaces (called base surfaces) are hard to be blended with a B-spline surface (called blending surf...

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 ...