Editing Non-uniform rational B-spline (section)

== History ==
[[File:Spline (PSF).png|thumb|A [[flat spline]], the physical namesake of the [[Spline (mathematics)|mathematical spline]]. Here the spline is held in place by pins rather than ducks.]]
Before computers, designs were drawn by hand on paper with various [[Technical drawing|drafting tools]]. [[Ruler]]s were used for straight lines, [[Compass (drafting)|compasses]] for circles, and [[protractor]]s for angles. But many shapes, such as the [[freeform curve]] of a ship's bow, could not be drawn with these tools. 

Although such curves could be drawn freehand at the drafting board, shipbuilders often needed a life-size version which could not be done by hand. Such large drawings were done with the help of flexible strips of wood, called splines. The splines were held in place at a number of predetermined points, by lead "ducks", named for the bill-shaped protrusion that the splines rested against. Between the ducks, the [[Elasticity (physics)|elasticity]] of the spline material caused the strip to take the shape that minimized the energy of bending, thus creating the smoothest possible shape that fit the constraints. The shape could be adjusted by moving the ducks.<ref name=mactech>{{cite web|last1=Schneider|first1=Philip|title=NURB Curves: A Guide for the Uninitiated|url=http://www.mactech.com/articles/develop/issue_25/schneider.html|website=MACTECH|access-date=26 September 2014}}</ref><ref>{{Cite journal |last=Schneider |first=Philip |title=NURB Curves: A Guide for the Uninitiated |url=https://vintageapple.org/develop/pdf/develop-25_9603_March_1996.pdf#page=50 |format=PDF |journal=[[Develop_(Apple_magazine)|develop]] |publication-date=March 1996 |issue=25 |pages=48–74}}</ref>

In 1946, mathematicians started studying the spline shape, and derived the piecewise [[polynomial]] formula known as the [[spline (mathematics)|spline curve]] or spline function. [[Isaac Jacob Schoenberg|I. J. Schoenberg]] gave the spline function its name after its resemblance to the mechanical spline used by draftsmen.<ref>{{cite journal
|first = I. J.
|last = Schoenberg
|title = Spline Functions and the Problem of Graduation
|journal = [[Proceedings of the National Academy of Sciences of the United States of America]]
|publisher = [[National Academy of Sciences]]
|date = August 19, 1964
|volume = 52
|issue = 4
|pages = 947–950
|doi=10.1073/pnas.52.4.947|pmc = 300377
|pmid=16591233
|bibcode = 1964PNAS...52..947S
|doi-access = free
}}</ref>

As computers were introduced into the design process, the physical properties of such splines were investigated so that they could be modelled with mathematical precision and reproduced where needed. Pioneering work was done in [[France]] by [[Renault]] engineer [[Pierre Bézier]], and [[Citroën]]'s physicist and mathematician [[Paul de Casteljau]]. They worked nearly parallel to each other, but because Bézier published the results of his work, Bézier curves were named after him, while de Casteljau's name is only associated with related algorithms.

NURBS were initially used only in the proprietary [[Computer aided design|CAD]] packages of car companies. Later they became part of standard computer graphics packages.

Real-time, interactive rendering of NURBS curves and surfaces was first made commercially available on [[Silicon Graphics]] workstations in 1989. In 1993, the first interactive NURBS modeller for PCs, called NöRBS, was developed by CAS Berlin, a small startup company cooperating with [[Technische Universität Berlin]].{{Cn|date=August 2023}}