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Construction

Create splines including B-form, tensor-product, NURBs and other rational splines

Functions

bspline Plot B-spline and its polynomial pieces
csape Cubic spline interpolation with end conditions
csapi Cubic spline interpolation
csaps Cubic smoothing spline
cscvn "Natural" or periodic interpolating cubic spline curve
getcurve Interactive creation of cubic spline curve
ppmak Put together spline in ppform
rpmak Put together rational spline
rscvn Piecewise biarc Hermite interpolation
rsmak Put together rational spline for standard geometric shapes
spap2 Least-squares spline approximation
spapi Spline interpolation
spaps Smoothing spline
spcrv Spline curve by uniform subdivision
splinetool Experiment with some spline approximation methods
spmak Put together spline in B-form
stmak Put together function in stform
tpaps Thin-plate smoothing spline
spterms Explain spline terms
franke Franke's bivariate test function
titanium Titanium test data

Examples and How To

Cubic Spline Interpolation

Use cubic splines to interpolate smooth data, choosing knots and smoothness.

Vector-Valued Functions

Use vector-valued splines to plot curves through given points.

Fitting Values at N-D Grid with Tensor-Product Splines

Use vector-valued splines to approximate gridded data in any number of variables using tensor-product splines.

Fitting Values at Scattered 2-D Sites with Thin-Plate Smoothing Splines

Use the thin-plate smoothing spline for work with scattered bivariate data. Tensor-product splines are good for gridded (bivariate and even multivariate) data.

Constructing and Working with ppform Splines

Learn how to construct ppform splines.

Constructing and Working with B-form Splines

Learn how to construct B-form splines.

Multivariate Tensor Product Splines

Learn how to construct multivariate splines.

Constructing and Working with Rational Splines

Learn how to construct rational splines.

Constructing and Working with stform Splines

Learn how to construct stform splines.

Least-Squares Approximation by Natural Cubic Splines

The construction of a least-squares approximant usually requires that one have in hand a basis for the space from which the data are to be approximated.

Solving A Nonlinear ODE

This section discusses these aspects of a nonlinear ODE problem:

Construction of the Chebyshev Spline

This section discusses these aspects of the Chebyshev spline construction:

Approximation by Tensor Product Splines

Because the toolbox can handle splines with vector coefficients, it is easy to implement interpolation or approximation to gridded data by tensor product splines, as the following illustration is meant to show.

Concepts

Introducing Spline Fitting

Tools for interactive and programmatic spline fitting in Curve Fitting Toolbox™.

Curve Fitting Toolbox Splines and MATLAB Splines

How Curve Fitting Toolbox extends the splines (or piecewise-polynomial functions) of MATLAB®.

Types of Splines: ppform and B-form

Learn about the definitions of the ppform and B-form splines.

B-Splines and Smoothing Splines

Learn about the definitions of the B-form and smoothing splines.

Multivariate and Rational Splines

Learn how to construct multivariate and rational splines.

The ppform

Learn about the definition of the ppform spline.

The B-form

Learn about the definition of B-form splines.

List of Terms for Spline Fitting

Terms and definitions presented in order such that the explanation of each term only uses terms discussed earlier

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