Editing Non-uniform rational B-spline (section)

{{Short description|Method of representing curves and surfaces in computer graphics}}
[[File:NURBstatic.svg|thumb|250px|A NURBS curve. (See also: the [[:File:Spline01.gif|animated creation of a NURBS spline]].)]]
[[File:NURBS surface.png|alt=Green-shaded NURBS surface|thumb|250px|A NURBS surface]]
'''Non-uniform rational basis spline''' ('''NURBS''') is a mathematical model using [[B-spline|basis splines]] (B-splines) that is commonly used in [[computer graphics]] for representing curves and [[Surface (mathematics)|surfaces]]. It offers great flexibility and precision for handling both analytic (defined by common mathematical [[formula]]e) and [[3D modeling|modeled shapes]]. It is a type of [[3D modeling#Process|curve modeling]], as opposed to [[polygonal modeling]] or [[digital sculpting]]. NURBS curves are commonly used in [[computer-aided design]] (CAD), [[Computer-aided manufacturing|manufacturing]] (CAM), and [[Computer-aided engineering|engineering]] (CAE). They are part of numerous industry-wide standards, such as [[IGES]], [[ISO 10303|STEP]], [[ACIS]], and [[PHIGS]]. Tools for creating and editing NURBS surfaces are found in various [[3D computer graphics software|3D graphics]], [[Rendering (computer graphics)|rendering]],<ref>{{cite web | url=https://www.willgibbons.com/rendering-software/ | title=Why KeyShot became the most popular product rendering software | date=3 October 2022 }}</ref> and [[3D Animation|animation]] software packages.

They can be efficiently handled by computer programs yet allow for easy human interaction. NURBS surfaces are functions of two [[parameter]]s mapping to a surface in [[three-dimensional space]]. The shape of the surface is determined by [[Control point (mathematics)|control points]]. In a compact form, NURBS surfaces can represent simple [[Geometric shape|geometrical shapes]]. For complex organic shapes, [[T-Spline (mathematics)|T-splines]] and [[subdivision surfaces]] are more suitable because they halve the number of control points in comparison with the NURBS surfaces.

In general, editing NURBS curves and surfaces is intuitive and predictable.{{Citation needed|date=January 2021}} Control points are always either connected directly to the curve or surface, or else act as if they were connected by a rubber band. Depending on the type of user interface, the editing of NURBS curves and surfaces can be via their control points (similar to [[Bézier curve]]s) or via higher level tools such as ''spline modeling'' and ''hierarchical editing''.

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