BetaSpliner is a tool that allows the user to interactively manipulate Beta-splines. Beta-splines form a class of approximating splines and are a generalization of the more common B-spline. Their derivation is overviewed in [Barsky and Beatty, "Local Control of Bias and Tension in Beta-splines", 1983 Siggraph Proceedings, pp. 193-218].

 First, some vocabulary. In keeping with the world according to Barsky, the control polygon is a set of connected control points. These control points determine the shape of the spline curve. Each spline curve is composed of a set of spline segments. Each spline segment is influenced by exactly four control points and two shape parameters, bias and tension. Every control point has associated with it its own values of bias and tension. If the values of the shape parameters happen to be the same at each control point, then the spline curve is said to be uniformily shaped and the shape parameters are global. If the values are different, then the spline is continuously shaped and the shape parameters are local. The spline segments are joined together at points on the spline curve called joints.

 BetaSpliner depends heavily on code written for the program PathTool by Darlene Plebon. Some of the BetaSpliner's idiosyncracies are due to this dependence. In PathTool, a trajectory is composed of a combination of straight line segments and Bezier curves. In BetaSpliner, both control polygons and spline curves are trajectories. The only difference between control polygons and spline curves is that the field which contains the pointer to a spline curve is always NIL for a spline curve. The same field for a control polygon may or may not be set to NIL, depending on the number of control points in the control polygon.

 Since control polygons and spline curves are logically equivalent in the program, in some ways you can get away with murder and in others, it's easy to commit suicide. The ways and means of doing committing these actions will be detailed below.

 1. Specify a new control polygon.
 2. Select an existing control polygon.
 3. Delete the selected control polygon and associated spline.
 4. Move individual control points of the selected control polygon.
 5. Delete individual control points of the selected control polygon.
 6. Make the selected control polygon closed or open.
 7. Erase the screen.
 8. Specify local or global bias and tension.
 9. Invoke the simplification algorithm.
 10. Specify the error metric used in the simplification algorithm.
 11. Turn off and on a grid constrainer to aid in specifying control polygons.
 12. Translate the image to the right and to the left.
 13. Scroll the image up and down.

 What we mean by unofficial is that the following functions can be performed as a consequence of the original PathTool code, but no attempt has been made to make these actions either user-friendly or user-safe.

 1. Insert control points into the middle of an existing control polygon.
 2. Make Bezier curves in the middle of your control polygons.
 3. Make Bezier curves in the middle of your Beta-spline.

 1. Delete the control polygon but not the spline curve. Then try to manipulate the spline curve.
 2. Delete the spline curve but not the control polygon. Then try to manipulate the control polygon.
 3. Ill-formed real numbers in the button viewers. The correct format is n.n, not n, or .n. A negative sign is optional, however.

 Most of the functions can be invoked by a combination of mouse buttons, SHIFT and CONTROL keys, or through the menu and viewer buttons. Below is a summary of the mouse manipulations:

   Left      Middle   Right

no key Move control point       Select a control polygon or a spline

Shift  Add control point

Control Delete control point       Delete control polygon or a spline

 The following is a summary of the menu and viewer items: