A Kochanek Bartels spline is a lovely, flexible means for casting a curve through multiple points, and providing artistically useful control over the character of the curve. It is also known as a TCB spline, because the controls are Tension, Continuity, and Bias. It was originally developed for providing smooth keyframed animation control curves, but it is also useful for general graphics purposes. For one of my Apple Motion FxPlug projects, I developed a Objective C class to render a Kochanek Bartels spline in OpenGL. It includes an additional feature of interpolating colors between the target points.
I have placed the code on GitHub. Corrections/improvements welcomed.
And here's a taste of what happens if one sets the parameters outside of the standard -1 to 1 range. Here T = -4.38, C = -1.31, and B = 0.37: