In this paper, we propose and validate a computationally efficient non-iterative domain decomposition procedure for calculating bivariate cubic L1 smoothing splines. This domain decomposition procedure involves calculating local L1 smoothing splines individually on overlapping “extended subdomains” that cover the global domain and then creating the global L1 smoothing spline by patching togethe...

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...

This essay reviews those basic facts about (univariate) B-splines that are of interest in CAGD. The intent is to give a self-contained and complete development of the material in as simple and direct a way as possible. For this reason, the B-splines are defined via the recurrence relations, thus avoiding the discussion of divided differences which the traditional definition of a B-spline as a d...

The asymptotic behaviour of penalized spline estimators is studied in the univariate case. We use B -splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya-Watson kernel estimators with ‘equivalent’ kernels depending upon m. The ...

This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result,...

In this paper we introduce an improvement in the path planning algorithm for the humanoid soccer playing robot which uses Ferguson splines and PSO (Particle Swarm Optimization). The objective of the algorithm is to find a path through other playing robots to the ball, which should be as short as possible and also safe enough. Ferguson splines create preliminary paths using random generated para...

This paper describes the problem of shape preserving approximation for data with speci ed tolerances Using the tool of generalized B splines GB splines for short simple one and three point algorithms of shape preserving local approximation with automatic choice of the tension parameters are de veloped In the two dimensional case tensor products of one dimensional splines are employed The result...

Easy to construct and optimally convergent generalisations of B-splines unstructured meshes are essential for the application isogeometric analysis domains with non-trivial topologies. Nonetheless, especially hexahedral meshes, construction smooth basis functions is still an open question. We introduce a simple partition unity that yields blended B-splines, referred as SB-splines, on semi-struc...