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Draw, manipulate and reconstruct B-splines.



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The package comprises of a graphical utility to place uniform B-spline control points and see how the B-spline is redrawn as control points or control point weights are adjusted, and functions to estimate B-splines with known knot vector, given a set of noisy data points either with known or unknown associated parameter values.

As regards the interactive interface, the user is shown a figure window with axes in which to choose control points of a uniform B-spline. As points are placed in the axes, the B-spline of specified order is drawn progressively. The user may terminate adding control points by pressing ENTER or ESC, or may place the last control point with a right mouse button click.

Once done, control points may be adjusted with drag-and-drop. Hold down the left mouse button over any control point and drag it to another location. Control point adjustment works in 3D; use the rotation tool to set a different camera position. It is also possible to explicitly set the x, y and z coordinates as well as the weight of a control point: click on the point, enter new values and hit ENTER.

As regards the non-interactive interface, functions include calculating and drawing basis functions, computing points of a (weighted or unweighted) B-spline curve with de Boor's algorithm, and estimating B-spline control points given noisy data, either with or without parameter values associated with the observed data points.

From a programmers' perspective, this example illustrates how to use nested functions to extend variable scope, implement drag-and-drop operations, combine normalized and pixel units for control docking and register multiple callbacks for a single event in an interactive user interface.


The simplest way to get started is to run "bspline_gui", which activates the figure window to place B-spline control points interactively. Examples are bundled to illustrate various B-spline curve computation and approximation methods.

Comments and Ratings (17)


naria (view profile)

its really good and helping. can any one tell if this package could be used to find control points of a particular interval or segment by providing a curve x,y point.
what i mean is that if i generate a b-spline curve, now i randomly select any x,y pair on curve data values, and i want to know form which control point segment this data point belongs?


Wouter (view profile)

(Not Matlab 2016b compatible)

Error using gui_bind_event (line 17)
Expected input to be one of these types:


Instead its type was matlab.ui.Figure.

I'm receiving this error :(

Expected input to be one of these types:


Instead its type was matlab.ui.Figure.

Mac Bekcheva

Hi, thanks for the excellent code.

I have a question about the value where the B-spline is to be evalued. can i evalue the B-spline for x = 0:0.1:3; as in the exemple for the basis functions where x = 0:0.1:3;?

Ligong Han

Ligong Han (view profile)

helpful and interesting, thanks!


karlosgk (view profile)

Henry Le

Hi, thank you for this! I have a question. I'm quite new to bsplines and matlab and I was wondering if there's anything out there in the matlab world that lets me measure the length of a cubic bspline generated in matlab from say this bspline package?


Fer (view profile)


Jim (view profile)

Great work!
I found a bug in bspline_basis.m. The last line in
function y = bspline_basis_recurrence(j,n,t,x)
should be:

    y(:) = t(j+1) <= x & x < t(j+2);

There should not be an equal in the second term x<t(j+2). If you plot the basis function using knot vector [0 1 2 3 4 5 6] and order 3, you will see the error.

Tom Lintern

Great code. I am pretty new with working with B-splines and am wondering if there is a way you would reccomend (with your code) to find the derivative of a given spline with a given set of control points?

Ben Fishler

Scratch last comment, got the control points to work...

Ben Fishler

Excellent code! 5 stars...
Only thing I can't seem to get to work is altering the control point locations post-zooming or rotating of the plot (the control points seem to change to non-interactive graph points after using any tools on the figure or camera toolbars) -- any suggestions?


Henry (view profile)

Agree with Evgeny Pr with the problem. Otherwise it's good!

Evgeny Pr

Evgeny Pr (view profile)

Thank you for good job!

I found one error in the function "bspline_wdeboor". The problem in if statement (if nargin > 5).
Must be:
if (nargin < 5)
    [Y,u] = bspline_deboor(n,t,P);
    [Y,u] = bspline_deboor(n,t,P,u);

The same approximation is unstable. Strongly depends on the knots vector.

Evgeny Pr

Evgeny Pr (view profile)



Fixed an issue with the last element in the knot vector (reported by Jolyn Loo).


Added computing knot vector and control points associated with derivative of B-spline curve (contributed by Joe Hays).


Added estimation without known B-spline curve parameter values.


Added control point weights and control point approximation from data.

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MATLAB 7.6 (R2008a)

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