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...

We investigate adaptive least squares approximation to scattered data given over the surface of the unit sphere in IR 3. Two basic algorithms (as well as some modiications) are described and evaluated: knot insertion and knot removal. x1. Introduction Since their introduction by R. L. Hardy in the 1970s, radial basis functions have become a standard tool in CAGD and approximation theory for the...

References: Prautzsch, H., 1984. Degree elevation of B-spline curves. CAGD 18 (12) Prautzsch, H., Piper, B., 1991. A fast algorithm to raise the degree of B-spline curves. CAGD 8 (4) Pigel, L., Tiller, W., 1994. Software-engineering approach to degree elevation of B-spline curves. CAD 26 (1) Liu, W., 1997. A simple, efficient degree raising algorithm for B-spline curves. CAGD 14 (7) Huang, Q.-X...

In this paper we continue our earlier research [4] aimed at developing efficient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms w...

We propose a flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces. The method allows to remove knots in arbitrary order minimizing the displacement of control points when a knot is re-inserted. Geometric detail subtracted from a shape by knot removal is represented by an associated wavelet coefficient replacing one of the control points at a coarser level of ...

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...

B-patches are the analogue to B-spline segments for triangular surfaces and are the main building block in the new multivariate B-spline surfaces recently developed in [8). This paper discusses algorithms for B-patches and presents algorithms for computing the polar form, for evaluation, for differentiation, for computing continuous joints, and for knot insertion .

We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-dimini...

OBJECTIVE To report one case of intrapyelic loop of a guide wire during double J catheter insertion. METHODS We report the case of a 24 year-old female, with the diagnosis obstructive uropathy secondary to pelvic tumor who required double J catheter insertion for urinary diversion. A loop of the guide wire was formed during the procedure which was finally solved without aggressive measures. ...