In this paper we provide the guidelines for the direct degree elevation of NURBS curves. Through the analysis of linear equation systems of quartic and lower degree splines we derive a direct relation between the knot vector of a spline and the degree elevation coefficients. We also present a direct degree elevation scheme and several algorithms based on the discovered relation. Experimental re...

O. Ismail, Senior Member, IEEE Abstract— This paper presents an efficient method for degree elevation of interval B-spline curves. The four fixed Kharitonov's polynomials (four fixed B-spline curves) associated with the original interval B-spline curve are obtained. The method is based on the matrix identity. The B-spline basis functions are represented as linear combinations of the B-splines o...

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 show the degree reduction of Bézier curves in a matrix representation. Most degree reduction algorithms have been described as a set of recursive equations which are based on the inverse problem of degree elevation. However, degree elevation can be easily expressed in terms of matrices. Motivated by this observation, we represent most well known degree reduction algorithms in ...

We give a new, simple algorithm for simultaneous degree elevation and knot insertion for B-spline curves. The method is based on the simple approach of computing derivatives using the control points, resampling the knot vector, and then computing the new control points from the derivatives. We compare our approach with previous algorithms and illustrate it with examples.  2004 Elsevier B.V. Al...

This paper presents a method to selectively elevate the degree of an S-Patch of arbitrary dimension. We consider not only S-Patches with 2D domains but 3D and higher-dimensional domains as well, of which volumetric cage deformations are a subset. We show how to selectively insert control points of a higher degree patch into a lower degree patch while maintaining the polynomial reproduction orde...

A new class of single-valued curves in polar coordinates obtained by a transformation of a subset of rational B ezier curves into Cartesian coordinates has recently been presented in (SS anchez-Reyes, 1990), and independently considered by P.de Casteljau, who called these curves focal B ezier. These curves are trigonometric polynomials that can be represented by a basis similar to the Bernstein...