https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline

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.It is a type of curve modeling, as opposed to polygonal modeling or digital sculpting.

https://whatis.techtarget.com/definition/nonuniform-rational-B-spline-NURBS

nonuniform rational B-spline (NURBS): NURBS (nonuniform rational B-splines) are mathematical representations of 2- or 3-dimensional objects, which can be standard shapes (such as a cone) or free-form shapes (such as a car). NURBS are used in computer graphics and the CAD/CAM industry and have come to be regarded as a standard way to create and ...

https://wikimili.com/en/Non-uniform_rational_B-spline

Non-uniform rational B-spline Last updated December 28, 2019 A NURBS curve. See also this animated version.. Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. It offers great flexibility and precision for handling both analytic (surfaces defined by common mathematical formulae) and modeled ...

https://www.cl.cam.ac.uk/teaching/2000/AGraphHCI/SMEG/node5.html

Thus, non-uniform rational B-splines encompass almost every other possible 3D shape definition. Non-uniform rational B-spline is a bit of a mouthful and so it is generally abbreviated to NURBS. We have already learnt all about the the B-spline bit of NURBS and about the non-uniform bit. So now all we need to know is the meaning of the rational bit and we will fully(?) understand NURBS ...

https://wiki.mcneel.com/rhino/nurbs

The word NURBS is an acronym for non-uniform rational B-spline. Non uniform rational B-splines can represent 3D geometry. Why use NURBS to represent 3D geometry? NURBS geometry has five important qualities that make it an ideal choice for computer aided modeling. There are several industry standard ways to exchange NURBS geometry. This means that customers can and should expect to be able to ...

https://journals.sagepub.com/doi/full/10.1177/0954410011421704

With the improving capabilities of computational fluid dynamics (CFD) for the prediction of aerodynamic performance, CFD tools are now being increasingly used for aerodynamic design optimization in...

https://runten.tripod.com/NURBS

NURBS - Non Uniform Rational B-Splines This python module is a port of Mark Spink's SCILAB/MATLAB toolbox to python with help of NumPy. As a Naval Architect i often encounter NURBS in my work. Either through CAD or technical calculations. Wanting to learn more about NURBS I searched the web and found quite few codes available for free. Some vere written in C++, witch is not easy accessable for ...

www.cad.zju.edu.cn/home/zhx/GM/008/00-nurbs1.pdf

Bézier is a subset of nonrational B-splines Non-Uniform Rational B-Spline NURBS Nonrational B-spline Bézier. 12/18/2006 State Key Lab of CAD&CG 5 Rational B-spline curves – Overview • Rational B-splines provide a single precise mathematical form for: lines planes conic sections (circles, ellipses . . .) free form curves quadric surfaces sculptured surfaces. 12/18/2006 State Key Lab of ...

https://www.cs.drexel.edu/~david/Classes/CS430/Lectures/L-09_BSplines_NURBS.pdf

– Rational • x(t), y(t), z ... • Basic idea: four dimensional non-uniform B-splines, followed by normalization via homogeneous coordinates – If P i is [x, y, z, 1], results are invariant wrt perspective projection • Also, recall in Cox-deBoor, knot spacing is arbitrary – knots are close together, influence of some control points increases – Duplicate knots can cause points to ...

https://www.cl.cam.ac.uk/teaching/2000/AGraphHCI/SMEG/node4.html

B-splines. B-splines are a more general type of curve than Bezier curves. In a B-spline each control point is associated with a basis function . (87) There are n + 1 control points, . The Ni,k basis functions are of order k (degree k -1). k must be at least 2 (linear), and can be no more than n +1 (the number of control points).