spline uses the functions ppval, mkpp, and unmkpp.
Note that this y contains two more values (i.e., two more columns) than does x, hence y(:,1) and y(:,end) are used as endslopes.Īlgorithm A tridiagonal linear system (with, possibly, several right sides) is being solved for the information needed to describe the coefficients of the various cubic polynomials which make up the interpolating spline. Generate the plot of a circle, with the five data points y(:,2).,y(:,6) marked with o's. Uses the cubic spline to extrapolate and predict the population in the year 2000. Represent the census years from 1900 to 1990 and the corresponding United States population in millions of people. However, if y contains exactly two more values than x has entries, then y(:,1) and y(:,end) are used as the endslopes for the cubic spline. Ordinarily, the `not-a-knot' end conditions are used. Returns the pp-form of the cubic spline interpolant, for later use with ppval (and with functions available in the Spline Toolbox). If xx is a refinement of the mesh x, then yy provides a corresponding refinement of y. Returns the value at xx of the interpolating cubic spline. In particular, the given values may be vectors, in which case the spline function describes a curve that passes through the point sequence y(:,1),y(:,2). Examples are bundled to illustrate various B-spline curve computation and approximation methods.Spline (MATLAB Function Reference) MATLAB Function Referenceĭescription The spline function constructs a spline function which takes the value y(:,j) at the point x(j), all j. The simplest way to get started is to run "bspline_gui", which activates the figure window to place B-spline control points interactively.
#Matlab b spline interpolation how to#
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.Īs 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.įrom 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. Control point adjustment works in 3D use the rotation tool to set a different camera position. Hold down the left mouse button over any control point and drag it to another location. Once done, control points may be adjusted with drag-and-drop. 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.
As points are placed in the axes, the B-spline of specified order is drawn progressively. 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.Īs regards the interactive interface, the user is shown a figure window with axes in which to choose control points of a uniform B-spline.
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