Bezier curves without corners

This applet shows cubic Bezier curves defined by a sequence of control points. The control points are modified as necessary to make the curves join without corners.

You can move a control point by dragging it with the mouse, add a new one by clicking the mouse, and delete one by holding down the Shift key while clicking on it.

The tangent at control point 3 to the curve defined by controls 0123 is the line 23. The tangent at control point 3 to the curve defined by controls 3456 is the line 34. If controls 2, 3 and 4 are collinear (lie on the same line), then there will be no corner at 3. This applet makes sure that 2, 3 and 4 are collinear by adjusting 4 if you move 2, and so on.

However, the second derivative of the curve changes abruptly at 3, so the curve is not as smooth as a natural cubic spline or a B spline.


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lambert@cse.unsw.edu.au
Last modified: Thu Oct 31 02:27:42 MET