This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinh t, cosh t, tk−3, tk−4, . . . , t,1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of cur...

Splines are important tools for the flexible modeling of curves and surfaces in regression analyses. Functions constructing spline basis functions available R through base package splines. When to be modeled have known characteristics monotonicity or curvature, more efficient statistical inferences possible with shape-restricted Such splines, however, not The splines2 provides easy-to-use funct...

Future Mars rovers, such as the planned 2009 MSL rover, require sufficient autonomy to robustly approach rock targets and place an instrument in contact with them. It took the 1997 Sojourner Mars rover between 3 and 5 communications cycles to accomplish this on rocks. This paper describes the NASA Ames approach to robustly accomplishing single cycle instrument deployment, using the K9 prototype...

The notion of complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines. To derive properties of complex B-splines in R, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional simplices △∞. Based on this generalization several identities of mu...

The main goal of this paper is to present some generalizations of polynomial B-splines, which include exponential B-splines and the larger family of exponential pseudo-splines. We especially focus on their connections to subdivision schemes. In addition, we generalize a well-known result on the approximation order of exponential pseudo-splines, providing conditions to establish the approximatio...

We study the convergence of discrete and penalized least squares spherical splines in spaces with stable local bases. We derive a bound for error in the approximation of a sufficiently smooth function by the discrete and penalized least squares splines. The error bound for the discrete least squares splines is explicitly dependent on the mesh size of the underlying triangulation. The error boun...

Bounds are provided on how well functions in Sobolev spaces on the sphere can be approximated by spherical splines, where a spherical spline of degree d is a C r function whose pieces are the restrictions of homogoneous polynomials of degree d to the sphere. The bounds are expressed in terms of appropriate seminorms deened with the help of radial projection, and are obtained using appropriate q...

Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation diminishing, but also constructive algorithms ba...

gravity acceleration data have grand pursuit for marine applications. due to environmental effects, marine gravity observations always hold a high noise level. in this paper, we propose an approach to produce marine gravity data using satellite altimetry, high-resolution geopotential models and harmonic splines. on the one hand, harmonic spline functions have great capability for local gravity ...