arcs

The visual path of action from one extreme to another is always described by an arc. Arcs in nature are the most economical routes by which a form can move from one position to another. In animation, such arcs are used extensively, for they make animation much smoother and less stiff than a straight line for the path of action. In certain cases, an arc may resolve itself into a straight path, as for a falling object, but usually, even in straight line action, the object rotates.

In most 3D keyframe computer animation systems, the path of action from one extreme to another is controlled by the same spline that controls the timing (slow in and out) of the inbetween values. This may simplify computing the inbetweens but it has unfortunate effects. When a motion is slow, with many inbetweens, the arc of the path of action is curved, as desired. But when the action is fast, the arc flattens out the faster the action, the flatter the arc. Sometimes this is desirable. but more often, the path of even a fast motion should be curved or arced. Straight inbetweens can completely kill the essence of an action.

The spline that defines the path of action should be separate from the spline that defines the Liming or spacing of the inbetweens for several reasons: so that the arc of a fast action doesn't flatten out; so that you can adjust the timing of the inbetweens without effecting the path of action; so that you can use different splines to define the path of action (where a B-spline is appropriate for its smoothness) and the timing (a Catmull - Rom spline so you can adjust it's tension and direction controls to get slow in and out). This technique is not common, but research is being done in this area.