How could this be done?

Question

Given the following path: alt text http://img198.imageshack.us/img198/3692/curve.png

How could these smooth curves be generated given that the user provides the points and that cubic bezier is used? How would the control points or bezier handles be solved for, or how could I compute these points using cubic bezier given the user points above (the red squares) ? Basically I have an algorithm to solve for a cubic bezier curve given 4 points but the user only provides the points below so there are no control points, how do I obtain these?

Thanks

Answer 1

See http://en.wikipedia.org/wiki/Spline_interpolation#Cubic_spline_interpolation

Answer 2

Look up Catmull-Rom splines. Here's an introduction.

Further reading:

• Catmull-Rom splines - how do they work?
• http://actionsnippet.com/?p=1031
• http://www.cse.unsw.edu.au/~lambert/splines/CatmullRom.html (source)