A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

T-spline surfaces are a powerful tool in geometric modelling. A T-spline surface is an approximation of a T-grid data structure. T-grids support adaption operations like local refinement or merging of existing NURBS grids. Digital terrain models based on T-spline surfaces benefit from non-regular control grids. We show some exemplary application cases for T-spline based terrain modelling.

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...

This paper considers the problem of constructing a smooth surface to fit rows of data points. A special class of T-spline surfaces is examined, which is characterized to have a global knot vector in one parameter direction and individual knot vectors from row to row in the other parameter direction. These T-spline surfaces are suitable for lofted surface interpolation or approximation. A skinni...

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...

A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of ...

In this paper, a generalised spline filter, that has a unified description for both the linear spline filter and the nonlinear robust spline filter, is proposed. Based on the M-estimation theory, the general spline filter model can be solved by using an Iterated Reweighted Least Squared method which is also general for both the linear and nonlinear spline filter. The algorithm has been verified...

A rational cubic trigonometric spline with two shape parameters which play an important role in manipulating the shape of the curve is described in this paper. Its algebraic analogue with shape parameters has been discussed. Spline is presented both in interpolatory and rational B-spline form and the properties of resulting Bsplines are also studied. Keywords— Computer aided geometric design, r...

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...

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...