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The simplest spline has degree 0. It is also called a step function. The next most simple spline has degree 1. It is also called a linear spline. A closed linear spline (i.e, the first knot and the last are the same) in the plane is just a polygon. A common spline is the natural cubic spline.
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...
Colour indicates function value. The black dots are the locations of the prescribed data being interpolated. Note how the color samples are not radially symmetric. Bilinear interpolation on the same dataset as above. Derivatives of the surface are not continuous over the square boundaries. Nearest-neighbor interpolation on the same dataset as ...
Regression splines. In this method, the data is fitted to a set of spline basis functions with a reduced set of knots, typically by least squares. No roughness penalty is used. (See also multivariate adaptive regression splines.) Penalized splines. This combines the reduced knots of regression splines, with the roughness penalty of smoothing ...
Thin plate spline; Polyharmonic spline (the thin-plate-spline is a special case of a polyharmonic spline) Radial basis function (Polyharmonic splines are a special case of radial basis functions with low degree polynomial terms) Least-squares spline; Natural neighbour interpolation
Radial basis function (RBF) — a function of the form ƒ(x) = φ(|x−x 0 |) Polyharmonic spline — a commonly used radial basis function; Thin plate spline — a specific polyharmonic spline: r 2 log r; Hierarchical RBF; Subdivision surface — constructed by recursively subdividing a piecewise linear interpolant Catmull–Clark subdivision ...
The following JavaScript implementation takes a data set and produces a monotone cubic spline interpolant function: /* * Monotone cubic spline interpolation * Usage example listed at bottom; this is a fully-functional package.
In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. [1] The Akima spline was published by Hiroshi Akima in 1970 from Akima's pursuit of a cubic spline curve that would appear more natural and smooth, akin to an intuitively hand-drawn curve.