Interpolation-Based Animation - Computer Animation: Algorithms and Techniques - page 111

CHAPTER

4

Interpolation-Based Animation

This chapter presents methods for precisely specifying the motion of objects. While the previous chap-
ter presented basics of interpolating values, this chapter addresses how to use those basics to facilitate
the production of computer animation. With these techniques, there is little uncertainty about the posi-
tions, orientations, and shapes to be produced. The computer is used only to calculate the actual values.
Procedures and algorithms are used, to be sure, but in a very direct manner in which the animator has
very specific expectations about the motion that will be produced on a frame-by-frame basis. These
techniques are typified by the user setting precise conditions, such as beginning and ending values
for position and orientation, and having the intermediate values filled in by some interpolative proce-
dure. Later chapters cover “higher-level” algorithms in which the animator gives up some precision to
produce motion with certain desired qualities. The techniques of this chapter deal with low-level, more
precise, control of motion that is highly constrained by the animator.
This chapter starts off with a discussion of key-frame animation systems. These are the three-
dimensional computer animation version of the main hand-drawn animation technique. The next
section discusses animation languages. While animation languages can be used to control high-level
algorithms, they are historically associated with their use in specifying the interpolation of values.
Indeed, many of the language constructs particular to the animation domain deal with setting transfor-
mations at key frames and interpolating between them. The final sections cover techniques to deform
an object, interpolating between three-dimensional object shapes, and two-dimensional morphing.

4.1 Key-frame systems
Many of the early computer animation systems were key-frame systems (e.g., [ 3 ] [ 4 ][ 5 ][ 20 ] ). Most of
these were two-dimensional systems based on the standard procedure used for hand-drawn animation,
in which master animators define and draw the key frames of the sequence to be animated. In hand-
drawn animation, assistant animators have the task of drawing the intermediate frames by mentally
inferring the action between the keys. The key frames occur often enough in the sequence so that
the intermediate action is reasonably well defined, or the keys are accompanied by additional infor-
mation to indicate placement of the intermediate frames. In computer animation, the term key frame
has been generalized to apply to any variable whose value is set at specific key frames and from which
values for the intermediate frames are interpolated according to some prescribed procedure. These vari-
ables have been referred to in the literature as articulation variables ( avars )[ 24 ] , and the systems are
sometimes referred to as track based . It is common for such systems to provide an interactive interface