Using their unitary extension principle, Ron and Shen have constructed a normalized tight frame for L2(R) consisting of spline functions with uniform knots. This paper constructs a normalized tight frame for L2((0,∞)) comprising spline functions with knots on a hybrid of uniform and geometric mesh. The construction is motivated by applications in adaptive approximation using spline functions on...

In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes. Mathematical subject classification: 14L35, 94B60.

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regre...

Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of simple base distribution. However, there are often applications that require more than invertibility. For instance, the computation energies and forces in physics requires second derivatives to be well-defined continuous. Smooth normalizing employ infinitely differentiable tra...

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while second DQM. resulting system of ODEs solved by SSP RK43 method after aforementioned spatially discretized. To assess success chosen tactics, a comparison errors shown. graphs can...

We define a parameterization for an n-holed tori based on the hyperbolic polygon. We model the domain using a manifold with 2n+ 2 charts, and linear fractional transformations for transition functions. We embed the manifold using standard spline techniques to produce a surface. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling, Curve, Surface, Solid, and Objec...

The effect of knot modifications on the shape of B-spline and NURBS curves is discussed in this paper. Theoretical results include the description of the path of curve points, obtained by the modification of a knot value, and the examination of the one-parameter family of curves. It is shown that this family has an envelope which is a lower order B-spline or NURBS curve. Applying these results ...

Both the 4-point and the uniform cubic B-spline subdivisions double the number of vertices of a closed-loop polygon P and produce sequences of vertices fj and bj respectively. We study the J-spline subdivision scheme Js, introduced by Maillot and Stam, which blends these two methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a family of limit curves, the ...