Historical background Non-uniform rational B-spline

a spline

before computers, designs drawn hand on paper various drafting tools. rulers used straight lines, compasses circles, , protractors angles. many shapes, such freeform curve of ship s bow, not drawn these tools. although such curves drawn freehand @ drafting board, shipbuilders needed life-size version not done hand. such large drawings done of flexible strips of wood, called splines. splines held in place @ number of predetermined points, called ducks ; between ducks, elasticity of spline material caused strip take shape minimized energy of bending, creating smoothest possible shape fit constraints. shape tweaked moving ducks.

in 1946, mathematicians started studying spline shape, , derived piecewise polynomial formula known spline curve or spline function. i. j. schoenberg gave spline function name after resemblance mechanical spline used draftsmen.

as computers introduced design process, physical properties of such splines investigated modelled mathematical precision , reproduced needed. pioneering work done in france renault engineer pierre bézier, , citroën s physicist , mathematician paul de casteljau. worked parallel each other, because bézier published results of work, bézier curves named after him, while de casteljau’s name associated related algorithms.

at first nurbs used in proprietary cad packages of car companies. later became part of standard computer graphics packages.

real-time, interactive rendering of nurbs curves , surfaces first made commercially available on silicon graphics workstations in 1989. in 1993, first interactive nurbs modeller pcs, called nörbs, developed cas berlin, small startup company cooperating technical university of berlin. today professional computer graphics applications available desktop offer nurbs technology, realized integrating nurbs engine specialized company.