The construction of classical hierarchical B–splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only decreases the overlapping of supports ...

References: Prautzsch, H., 1984. Degree elevation of B-spline curves. CAGD 18 (12) Prautzsch, H., Piper, B., 1991. A fast algorithm to raise the degree of B-spline curves. CAGD 8 (4) Pigel, L., Tiller, W., 1994. Software-engineering approach to degree elevation of B-spline curves. CAD 26 (1) Liu, W., 1997. A simple, efficient degree raising algorithm for B-spline curves. CAGD 14 (7) Huang, Q.-X...

We construct a suitable normalized B-spline representation for C-continuous quintic Powell-Sabin splines. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction is based on the determination of a set of triangles that must contain a specific set of points. We are able to define control points and cubic control polynomials which are t...

We present the construction of a multivariate normalized B-spline basis for the quadratic C-continuous spline space defined over a triangulation in R (s ≥ 1) with a generalized Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction can be interpreted geometrically as the determination of a set of s-simplices ...

Object-based video coding requires the transmission of the object shape. This shape is sent as a binary α-plane. In lossy packetbased networks, such as the Internet, this information has a nonnegligible probability of not arriving at the receiver, and hence its loss needs to be concealed. In this paper we propose a shape concealment technique utilizing Hermite splines. The algorithm has the fol...

Stitching or merging B-spline curves is a frequently used technique in geometric modeling, and is usually implemented in CAD-systems. These algorithms are basically numerical interpolations using the least squares method. The problem, how to replace two or more curves which are generated separately and defined as B-spline curves, has well functioning numerical solutions, therefore, relatively f...

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...