Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is crucial to obtain desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric inte...

Non-uniform B-spline dictionaries on a compact interval are discussed. For each given partition, dictionaries of B-spline functions for the corresponding spline space are constructed. It is asserted that, by dividing the given partition into subpartitions and joining together the bases for the concomitant subspaces, slightly redundant dictionaries of Bsplines functions are obtained. Such dictio...

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

Previous theoretical (McCartin 1989a) and computational (McCartin 1989b) results on exponential splines are herein applied to provide approximate solutions of high order accuracy to nonlinear hyperbolic conservation laws. The automatic selection of certain "tension" parameters associated with the exponential spline allows the sharp resolution of shocks and the suppression of any attendant oscil...

Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B...

2 Representing a Circle 3 2.1 Quarter of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Degree 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Degree 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Half a Circle . . . . . . . . . . . . . . . . ....

We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n-point schemes of smoothness C are presented for n = 2, 3, 4 and even higher order, as well as a variety of non-uniform 6-point schemes with C continuity.