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- Spline_(mathematics) abstract "In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots).In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon. In computer graphics splines are popular curves 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 most commonly used splines are cubic spline, i.e., of order 3—in particular, cubic B-spline and cubic Bézier spline. They are common, in particular, in spline interpolation simulating the function of flat splines.The term spline is adopted from the name of a flexible strip of metal commonly used by draftsmen to assist in drawing curved lines.Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with function values and first n-1 derivatives that agree at the points where they join. The abscissa values of the join points are called knots. The term "spline" is also used for polynomials (splines with no knots) and piecewise polynomials with more than one discontinuous derivative. As such, splines with no knots are generally smoother than splines with knots, which are generally smoother than splines with multiple discontinuous derivatives. Splines with few knots are generally smoother than splines with many knots; however, increasing the number of knots usually increases the fit of the spline function to the data. Knots give the curve freedom to bend to more closely follow the data.".
- Spline_(mathematics) thumbnail Quadratic_spline_six_segments.svg?width=300.
- Spline_(mathematics) wikiPageExternalLink introduction-to-splines.
- Spline_(mathematics) wikiPageExternalLink SymmetricalSplineCurves.
- Spline_(mathematics) wikiPageExternalLink Intro.htm.
- Spline_(mathematics) wikiPageExternalLink CubicSplinesMod.html.
- Spline_(mathematics) wikiPageExternalLink cubic-splines.
- Spline_(mathematics) wikiPageExternalLink spline_method.html.
- Spline_(mathematics) wikiPageExternalLink PSPLINE.
- Spline_(mathematics) wikiPageExternalLink CubicSpline.html.
- Spline_(mathematics) wikiPageExternalLink BezierSpline.aspx.
- Spline_(mathematics) wikiPageExternalLink ClosedBezierSpline.aspx.
- Spline_(mathematics) wikiPageExternalLink splines.pdf.
- Spline_(mathematics) wikiPageExternalLink splineDucks.htm.
- Spline_(mathematics) wikiPageExternalLink sisl.
- Spline_(mathematics) wikiPageExternalLink spline.
- Spline_(mathematics) wikiPageExternalLink simusoft_spline.html.
- Spline_(mathematics) wikiPageID "457680".
- Spline_(mathematics) wikiPageRevisionID "601120329".
- Spline_(mathematics) hasPhotoCollection Spline_(mathematics).
- Spline_(mathematics) subject Category:Interpolation.
- Spline_(mathematics) subject Category:Splines.
- Spline_(mathematics) type Artifact100021939.
- Spline_(mathematics) type BuildingMaterial114786479.
- Spline_(mathematics) type Lumber114943580.
- Spline_(mathematics) type Object100002684.
- Spline_(mathematics) type PhysicalEntity100001930.
- Spline_(mathematics) type Spline104282379.
- Spline_(mathematics) type Splines.
- Spline_(mathematics) type Strip104339638.
- Spline_(mathematics) type Whole100003553.
- Spline_(mathematics) comment "In mathematics, a spline is a sufficiently smooth polynomial function that is piecewise-defined, and possesses a high degree of smoothness at the places where the polynomial pieces connect (which are known as knots).In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results to interpolating with higher degree polynomials while avoiding instability due to Runge's phenomenon.".
- Spline_(mathematics) label "Funkcja sklejana".
- Spline_(mathematics) label "Funzione spline".
- Spline_(mathematics) label "Spline (mathematics)".
- Spline_(mathematics) label "Spline".
- Spline_(mathematics) label "Spline".
- Spline_(mathematics) label "Spline".
- Spline_(mathematics) label "Spline".
- Spline_(mathematics) label "Spline".
- Spline_(mathematics) label "Сплайн".
- Spline_(mathematics) label "スプライン曲線".
- Spline_(mathematics) label "样条函数".
- Spline_(mathematics) sameAs Spline.
- Spline_(mathematics) sameAs Spline.
- Spline_(mathematics) sameAs Spline.
- Spline_(mathematics) sameAs Spline.
- Spline_(mathematics) sameAs Funzione_spline.
- Spline_(mathematics) sameAs スプライン曲線.
- Spline_(mathematics) sameAs 스플라인_곡선.
- Spline_(mathematics) sameAs Spline.
- Spline_(mathematics) sameAs Funkcja_sklejana.
- Spline_(mathematics) sameAs Spline.
- Spline_(mathematics) sameAs m.02bvsh.
- Spline_(mathematics) sameAs Q735256.
- Spline_(mathematics) sameAs Q735256.
- Spline_(mathematics) sameAs Spline_(mathematics).
- Spline_(mathematics) wasDerivedFrom Spline_(mathematics)?oldid=601120329.
- Spline_(mathematics) depiction Quadratic_spline_six_segments.svg.
- Spline_(mathematics) isPrimaryTopicOf Spline_(mathematics).