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Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes .
The properties of Bézier curves and uniform B-splines were well known, but the staff had to gain an understanding of non-uniform B-splines and rational Bézier curves and try to integrate the two. It was necessary to convert circles and other conics to rational Bézier curves for the curve/curve intersection.
When the weight is equal to 1, a NURBS is simply a B-spline and as such NURBS generalizes both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points which makes NURBS curves "rational". By evaluating a NURBS at various values of the parameters, the curve can be traced through space; likewise ...
In computer graphics, non-uniform rational mesh smooth (NURMS) or subdivision surface technique is typically applied to a low-polygonal mesh to create a high-polygonal smoothed mesh. Usage [ edit ]
While developed for Inkscape it is a library that can be used from any application. It provides support for basic geometric algebra, paths, distortions, Boolean operations, plotting implicit functions, non-uniform rational B-spline (NURBS) and more. 2Geom is free software released under LGPL 2.1 or MPL 1.1. [22] [23]
Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. . Currently, it is necessary to convert data between CAD and FEA packages to analyse new designs during development, a difficult task since the two computational geometric approaches are diffe
NURBS are an extension of B-splines, so everything to do with the basis functions and the knots really belongs on B-spline (unless I'm mistaken and regular B-splines don't include non-uniform knots). My understanding is that non-uniform knot vectors are a part of B-splines and so the difference between B-splines and NURBS is that NURBS are ...
In the mathematical subfield of numerical analysis, de Boor's algorithm [1] is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves.