B-splines

Draw, manipulate and reconstruct B-splines.

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.

USAGE

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.