In this paper we consider discrete splines S(j), j ∈ Z, with equidistant nodes which may grow as O(|j|s) as |j| → ∞. Such splines are relevant for the purposes of digital signal processing. We give the definition of discrete B-splines and describe their properties. Discrete splines are defined as linear combinations of shifts of the B-splines. We present a solution to the problem of discrete sp...

This paper presents a new kind of splines, called non-uniform algebraic-trigonometric B-splines (NUAT B-splines), generated over the space spanned by {1, t, . . . , tk−3, cos t, sin t} in which k is an arbitrary integer larger than or equal to 3. We show that the NUAT B-splines share most properties of the usual polynomial B-splines. The subdivision formulae of this new kind of curves are given...

This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementation of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction. The approach was tested by implementing hierarchical B-splines, truncated hierarchical B-splines, decoupled hierarchical B-splin...

We review the theory of homogeneous splines and their relationship to special rational splines considered by J. SS anchez{Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of rational curves with rational oosets. We investigate geometric properties of these dual focal splines, and discuss...

We review the theory of homogeneous splines and their relationship to special rational splines considered by J. SS anchez{Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of rational curves with rational oosets. We investigate geometric properties of these dual focal splines, and discuss...

Piecewise L-splines are generalizations of L-splines, in the sense that they satisfy different differential equations in different mesh intervals. Prenter attempted in [P.M. Prenter, Piecewise L-Splines, Numer. Math. 18 (2) (1971) 243–253] to obtain results on piecewise L-splines by generalizing the results of Schultz and Varga on L-splines in [M.H. Schultz, R.S. Varga, L-Splines, Numer. Math. ...

In this paper, we offer an overview of a number results on the static rigidity and infinitesimal discrete structures which are embedded in projective geometric reasoning, representations, transformations. Part I considers fundamental case bar–joint framework d-space places particular emphasis invariance rigidity, coning between dimensions, transfer to spherical metric, slide joints pure conditi...

We present an approach for modeling and filtering digitally scanned images. The digital contour of an image is segmented to identify the linear segments, the nonlinear segments and critical corners. The nonlinear segments are modeled by B-splines. To remove the contour noise, we propose a weighted least q m s model to account for both the fitness of the splines as well as their approximate cur...

We characterize the dimension of fixed degree functional and implicit algebraic splines in three dimensional (x,y,z) space. For a a given planar triangulation T both functional and implicit algebraic splines interpolate specified Zi values at the vertices Vi = (XitY;) of T. For a three dimensional triangulation 57 the implicit algebraic splines interpolate the boundary vertices Vj = (Xj, Yj I Z...