We present an efficient algorithm for subdividing non-uniform B-splines of arbitrary degree in a manner similar to the Lane-Riesenfeld subdivision algorithm for uniform Bsplines of arbitrary degree. Our algorithm consists of doubling the control points followed by d rounds of non-uniform averaging similar to the d rounds of uniform averaging in the Lane-Riesenfeld algorithm for uniform B-spline...

Recently, a novel laser data based SLAM algorithm using B-Spline as features has been developed in [Pedraza et al., 2007]. EKF is used in the proposed BS-SLAM algorithm and the state vector contains the current robot pose together with the control points of the splines. The obervation model used for the EKF update is the intersections of the laser beams with the splines contained in the map. In...

We develop a method of constructing trivariate optimal smoothing splines using normalized uniform B-spline as the basis functions. Such splines are useful particularly for modeling dynamic shape of 3-dimensional deformable object by using two variables for 3D shape and one for time evolution. The trivariate splines are constructed as a tensor product of three B-splines, and an optimal smoothing...

Pseudo-splines constitute a new class of refinable functions with B-splines, interpolatory refinable functions and refinable functions with orthonormal shifts as special examples. Pseudo-splines were first introduced by Daubechies, Han, Ron and Shen in [Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal. 14(1) (2003), 1–46] and Selenick in [Smooth wavelet tight fra...

We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in ratio between subdomains overlap sizes. Our validated through a set of numerical experiments illustrate good behavior proposed with respect to model param...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We develop a spectrum of physical A-spline curve models using various energy formulations based on the theory of elasticity. Our bending and stretching energy formulations yield interactive physically based modeling with A-splines while preserving the advantages of free-form modeling of complex shapes. ...

Recently, we have introduced spaces of splines deened on trian-gulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangulations. ...

In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local vari...

The construction of weighted extended B-splines (web-splines), as recently introduced by the authors and J. Wipper for uniform knot sequences, is generalized to the nonuniform case. We show that web-splines form a stable basis for splines on arbitrary domains in R which provides optimal approximation power. Moreover, homogeneous boundary conditions, as encountered frequently in finite element a...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...