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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 Fortran 77) TinySpline:Open source C-library for splines which implements cubic spline interpolation
The Hermite formula is applied to each interval (, +) separately. The resulting spline will be continuous and will have continuous first derivative. Cubic polynomial splines can be specified in other ways, the Bezier cubic being the most common. However, these two methods provide the same set of splines, and data can be easily converted between ...
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 ]
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.
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.
Example showing non-monotone cubic interpolation (in red) and monotone cubic interpolation (in blue) of a monotone data set. Monotone interpolation can be accomplished using cubic Hermite spline with the tangents m i {\displaystyle m_{i}} modified to ensure the monotonicity of the resulting Hermite spline.
Note that similar generalizations can be made for other types of spline interpolations, including Hermite splines. In regards to efficiency, the general formula can in fact be computed as a composition of successive C I N T {\displaystyle \mathrm {CINT} } -type operations for any type of tensor product splines, as explained in the tricubic ...
A Lozenge diagram is a diagram that is used to describe different interpolation formulas that can be constructed for a given data set. A line starting on the left edge and tracing across the diagram to the right can be used to represent an interpolation formula if the following rules are followed: [5]