Equation 9 should read: p = sin(p theta_span) / sin(theta_span)
This page accompanies the paper "Modeling Tension and Relaxation for Computer Animation" by Michael Neff and Eugene Fiume presented at the Symposium for Computer Animation, San Antonio, Texas 2002. Here you can find a copy of the paper, as well as all the animations discussed in the paper. These pages are designed to accompany the paper, so they will be most useful after having read the paper.
Here we compare a wave done through actuated PD control, where the set point is switched to the end point of each pose, a kinematic wave and a wave created in our system that uses the same transition functions as the kinematic wave, but adds in relaxation effects. Notice the characteristic shaping of actuated motion that starts quickly and ends slowly. The kinematic wave is better, but more stiff than is natural. The addition of relaxation gives the wave a more relaxed, natural look. Please note that only two joints are being controlled in these animations, the elbow and the shoulder.
External Forces Acting on the Body and the Importance of Anticipation
How a character reacts to an external force depends on the amount of tension in his or her body. A character will change their tension based on whether or not they anticipate a blow.
Full Body Animations
Just for Fun
A number of figures have been put online that explain more about antagonistic control and the shaping behaviour of tension changes. Due to the large number of images, the figures have been included in a separate page. Click here.