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In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
Quarterly of Applied Mathematics. 4 (2): 45– 99. doi: 10.1090/qam/15914. Schoenberg, Isaac J. (1946). "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions:Part B.—On the Problem of Osculatory Interpolation. A Second Class of Analytic Approximation Formulae". Quarterly of Applied Mathematics. 4 (2): 112 ...
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
J. Schoenberg gave the spline function its name after its resemblance to the mechanical spline used by draftsmen. [ 4 ] 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.
Spline interpolation — interpolation by piecewise polynomials Spline (mathematics) — the piecewise polynomials used as interpolants; Perfect spline — polynomial spline of degree m whose mth derivate is ±1; Cubic Hermite spline. Centripetal Catmull–Rom spline — special case of cubic Hermite splines without self-intersections or cusps
In the mathematical subfield of numerical analysis, de Boor's algorithm [1] is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves.
In mathematics, bicubic interpolation is an extension of cubic spline interpolation ... Colour indicates function value. The black dots are the locations of the ...
In the mathematical subfield of numerical analysis, an I-spline [1] [2] is a monotone spline function. An I-spline family of order three with four interior knots. Definition