bspline

Plot B-spline and its polynomial pieces

Syntax

bspline(t)

bspline(t,window)

pp = bspline(t)

Description

bspline(t) plots the B-spline with knot sequence t, as well as the polynomial pieces of which it is composed. For more information about spline fitting, see About Splines in Curve Fitting Toolbox.

bspline(t,window) plots the B-spline with knot sequence t, as well as the polynomial pieces of which it is composed, in the subplot window specified by window.

pp = bspline(t) plots nothing and returns the ppform of the B-spline.

Examples

Plot a B-spline of Order 4

This example shows how to create a B-spline of order 4 using the bspline function.

Create a Knot Sequence and Plot the B-spline

This figure shows a B-spline of order 4 and the four cubic polynomials that composes it.

To replicate this figure in MATLAB ®, first create a knot sequence. A knot sequence must be non-decreasing.

t = [0 1.5 2.3 4 5];

As you have defined five knots, the B-spline will be of order 4.

Then plot the B-spline with knot sequence t, as well as its polynomial pieces, by using the bspline function.

bspline(t)

This B-spline consists of 4 polynomial pieces: the red, green, purple, and black curves in the plot, each of degree 3.

The vertical lines mark the knots t that you have previously defined.

The B-spline with knots t(i)≤····≤ t(i+k) is positive on the interval (t(i)..t(i+k)) and is zero outside that interval. It is piecewise-polynomial of order k with breaks at the sites t(i),...,t(i+k). These knots may coincide, and the precise multiplicity governs the smoothness with which the two polynomial pieces join there.

Plot Another B-spline in a New Subplot

Create a second knot sequence.

t2=[2 3 4 5];

Plot the B-spline with knot sequence t2 in the same figure but in a different subplot.

bspline(t,1)
bspline(t2 ,2)

Copyright 2019 The MathWorks, Inc.

Input Arguments

t — Knot sequence of spline

vector (default)

Non-decreasing sequence of the knots of the B-spline, specified as a vector.

Data Types: single | double

window — Subplot window

scalar (default)

Index of the subplot of a 2x2 window, specified as a scalar. This value must be less than 5.

Data Types: single | double

Output Arguments

pp — Spline in ppform

spline structure

Spline in ppform, returned as a structure with these fields. For more information on ppform, see The ppform

Form — Form of spline

pp

Form of the spline, returned as pp. pp indicates that the spline is given in piecewise polynomial form.

Breaks — Knot locations of spline

vector | cell array

Knot positions of the spline, returned as a vector or as a cell array of vectors for multivariate data. Vectors contain strictly increasing elements that represent the start and end of each of the intervals over which the polynomial pieces are defined.

Coefs — Coefficients of polynomials

matrix | array

Coefficients of polynomials for each piece, returned as a matrix or as an array for multivariate data.

Pieces — Number of polynomial pieces

scalar | vector

Number of polynomial pieces describing the spline, returned as a scalar or as a vector of numbers of pieces in each variable for multivariate data.

Order — Order of polynomials

scalar | vector

Order of the polynomial function describing each polynomial piece of the spline, returned as a scalar or as a vector containing the order in each variable for multivariate data.

Dim — Dimensionality

scalar

Dimensionality of the target function, returned as a scalar.

Version History

Introduced in R2006b