Editing Spline (mathematics) (section)

{{Short description|Mathematical function defined piecewise by polynomials}}
{{For|the drafting tool|Flat spline}}
[[Image:Parametic Cubic Spline.svg|thumb|Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with {{math|''C''<sup>2</sup>}} [[parametric continuity]]. Triple knots at both ends of the interval ensure that the curve interpolates the end points]]

In [[mathematics]], a '''spline''' is a [[Function (mathematics)|function]] defined [[piecewise]] by [[polynomial]]s.
In [[interpolation|interpolating]] problems, [[spline interpolation]] is often preferred to [[polynomial interpolation]] because it yields similar results, even when using low [[Degree of a polynomial|degree]] polynomials, while avoiding [[Runge's phenomenon]] for higher degrees. 

In the [[computer science]] subfields of [[computer-aided design]] and [[computer graphics]], the term ''spline'' more frequently refers to a piecewise polynomial ([[Parametric equation|parametric]]) [[curve]]. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through [[curve fitting]] and interactive curve design.

The term spline comes from the flexible [[Flat spline|spline]] devices used by shipbuilders and [[technical drawing|draftsmen]] to draw smooth shapes.