Spline Construction

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

Using the Curve Fitter app or the fit function, you can fit cubic spline interpolants, smoothing splines, and thin-plate splines. Other Curve Fitting Toolbox™ functions allow more specialized control over spline construction. For example, you can use the function csapi for cubic spline interpolation. For more information, see How to Construct Splines.

Functions

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B-Spline Fitting

bspline Plot B-spline and its polynomial pieces

Spline Interpolation

`csape`	Cubic spline interpolation with end conditions
`csapi`	Cubic spline interpolation
`cscvn`	“Natural” or periodic interpolating cubic spline curve
`rscvn`	Piecewise biarc Hermite interpolation
`spapi`	Spline interpolation
`tpaps`	Thin-plate smoothing spline

Smoothing Spline Fitting

`csaps`	Cubic smoothing spline
`spaps`	Smoothing spline
`spcrv`	Spline curve by uniform subdivision
`tpaps`	Thin-plate smoothing spline

Least-Squares Fitting

spap2 Least-squares spline approximation

Spline Creation

`ppmak`	Put together spline in ppform
`rpmak`	Put together rational spline
`rsmak`	Put together rational spline for standard geometric shapes
`spmak`	Put together spline in B-form
`stmak`	Put together function in stform

Data Sets

titanium Titanium test data

Test Functions

franke Franke's bivariate test function

Interactive Tools

`bspligui`	Experiment with B-spline as function of its knots
`getcurve`	Interactive creation of cubic spline curve
`splinetool`	Experiment with some spline approximation methods
`spterms`	Explain spline terms

Topics

Introduction to Splines

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.
NURBS and Other Rational Splines
Learn about the definitions of rational splines.

Fundamental Spline Methods

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:
Chebyshev Spline Construction
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.
How to Construct Splines
This example shows how to construct splines in various ways using the spline functions in Curve Fitting Toolbox™.
Construct and Work with the B-form
This example shows how to construct and work with the B-form of a spline in Curve Fitting Toolbox™.
Construct and Work with the PPFORM
This example shows how to construct and work with the ppform of a spline in Curve Fitting Toolbox™.
How to Choose Knots
This example shows how to select and optimize knots using the optknt and newknt commands from Curve Fitting Toolbox™.

Fitting Splines to Data

Cubic Spline Interpolation
This example shows how to use the csapi and csape commands from Curve Fitting Toolbox™ to construct cubic spline interpolants.
Cubic Smoothing Splines
This example shows how to use the csaps and spaps commands from Curve Fitting Toolbox™ to construct cubic smoothing splines.
Fitting a Spline to Titanium Test Data
This example shows how to use commands from Curve Fitting Toolbox™ to fit a spline to titanium test data with manual and automatic selection of knots.

Spline Applications

Splines in the Plane
This example shows how to use the spmak, spcrv, cscvn and rscvn commands from Curve Fitting Toolbox™ to construct spline curves in the plane.
Constructing Spline Curves in 2D and 3D
This example shows how to use the cscvn command from Curve Fitting Toolbox™ to construct cubic spline curves in two and three dimensions.
Smoothing a Histogram
This example shows how to use spline commands from Curve Fitting Toolbox™ to smooth a histogram.
Bivariate Tensor Product Splines
This example shows how to use the spline commands in Curve Fitting Toolbox™ to fit tensor product splines to bivariate gridded data.
Solving a Nonlinear ODE with a Boundary Layer by Collocation
This example shows how to use spline commands from Curve Fitting Toolbox™ solve a nonlinear ordinary differential equation (ODE).
Construct Chebyshev Spline
This example shows how to use commands from Curve Fitting Toolbox™ to construct a Chebyshev spline.

Featured Examples

Construct and Work with the B-form

Construct and work with the B-form of a spline in Curve Fitting Toolbox™.

Open Live Script

Construct and Work with the PPFORM

Construct and work with the ppform of a spline in Curve Fitting Toolbox™.

Open Script

Constructing Spline Curves in 2D and 3D

Use the cscvn command from Curve Fitting Toolbox™ to construct cubic spline curves in two and three dimensions.

Open Live Script

Splines in the Plane

Use the spmak, spcrv, cscvn and rscvn commands from Curve Fitting Toolbox™ to construct spline curves in the plane. This includes plotting tangents and computing the area enclosed by a curve.

Open Script