Kochanek and Bartels Splines

This method of interpolation was developed in 1984 by Doris Kochanek and Richard Bartels. It uses cubic interpolating splines in key frame animation. The animator has the ability to change the tension, continuity and bias of these splines. Below we examine each parameter in isolation.

With the below example, each V shape represent 3 key frames, while the green line represents the F-Curve between them.

Tension Parameter

This controls how sharply the curve bends at a point. By increasing its value you can tighten the curve e.g. Tension = 1 By decreasing its value you can loosed or slacken the curve e.g tension = -1

Continuity Parameter

Controls the smoothness of transition between 2 consecutive curve segments at a point. By increasing this value the curve becomes more and more discontinuous. Increasing it above 1 exaggerates the sharpness of the curve. By decreasing the value e.g. -1 a sharp curve is introduced.

Bias Parameter

The bias parameter applies different weights to the points. As its value increases, the source chord becomes increasingly dominant. At the value b=1, the curve overshoots the control point (follow through in animation). When the value is -1 the path undershoots, allowing exaggeration/anticipation to be applied to an action.

From the above curve examples you can see they tie into several principles of animation.

Experimental Results

When Kochanek and Bartels splines were applied to keyframe animation, in order to enable animators to manipulate the splines, they found that mainly the tension parameter was reduced to -0.1 to -0.4. The bias and continuity values were left at their default.

Also they found that although there were differences between animator, individual animators consistently chose the same value for the 3 parameters.

Origins Marey Muybridge Fleischer Rob Bredow Q & A Debate Siggraph Panel CG Animation Pipeline Future Squash and Stretch Splines Experiment Summary Further Reading

(c) Shane Aherne 2005

Contact:  shane@shaneaherne.com