Search results
Results From The WOW.Com Content Network
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 ...
Spline curve drawn as a weighted sum of B-splines with control points/control polygon, and marked component curves. In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.
Linear interpolation uses a linear function for each of intervals [x k,x k+1]. Spline interpolation uses low-degree polynomials in each of the intervals, and chooses the polynomial pieces such that they fit smoothly together. The resulting function is called a spline.
If a C 0 function is insufficient, for example if the process that has produced the data points is known to be smoother than C 0, it is common to replace linear interpolation with spline interpolation or, in some cases, polynomial interpolation.
Smoothing splines are function estimates, ^ () , obtained from a ... This interpolating spline is a linear operator, and can be written in the form ^ = ...
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
This guarantees that the graph of the function will be composed of polygonal or polytopal pieces. Splines generalize piecewise linear functions to higher-order polynomials, which are in turn contained in the category of piecewise-differentiable functions, PDIFF.