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A common spline is the natural cubic spline. A cubic spline has degree 3 with continuity C 2, i.e. the values and first and second derivatives are continuous. Natural means that the second derivatives of the spline polynomials are zero at the endpoints of the interval of interpolation.
Dynamic cubic splines with JSXGraph; Lectures on the theory and practice of spline interpolation; Paper which explains step by step how cubic spline interpolation is done, but only for equidistant knots. Numerical Recipes in C, Go to Chapter 3 Section 3-3; A note on cubic splines; Information about spline interpolation (including code in ...
Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing, bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling, when speed is not an issue.
The most familiar example is the cubic smoothing spline, but there are many other possibilities, including for the case where is a vector quantity. Cubic spline definition [ edit ]
Any series of 4 distinct points can be converted to a cubic Bézier curve that goes through all 4 points in order. Given the starting and ending point of some cubic Bézier curve, and the points along the curve corresponding to t = 1/3 and t = 2/3, the control points for the original Bézier curve can be recovered. [9]
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.
Solving an interpolation problem leads to a problem in linear algebra amounting to inversion of a matrix. Using a standard monomial basis for our interpolation polynomial () = =, we must invert the Vandermonde matrix to solve () = for the coefficients of ().
These functions are shown in the plot at the right. For example, with a 9-point linear function (moving average) two thirds of the noise is removed and with a 9-point quadratic/cubic smoothing function only about half the noise is removed. Most of the noise remaining is low-frequency noise(see Frequency characteristics of convolution filters, below