Digital Animation

To create the illusion of movement, an image is displayed on the computer screen then quickly
replaced by a new image that is similar to the previous image, but shifted
slightly. This technique is identical to how the illusion of movement is
achieved with television and motion pictures.

Tweening, short for in-betweening, is the process of generating
intermediate frames between two images to give the appearance that the first
image evolves smoothly into the second image. Inbetweens are the drawings
between the keyframes which help to
create the illusion of motion. Tweening is a key process in all types of animation, including computer
animation. Sophisticated animation software enables one to identify specific objects in
an image and define how they should move and change during the tweening process.
Software may be used to manually render or adjust transitional
frames by hand or use to automatically render transitional frames using interpolation of graphic
parameters.

In engineering and science one often has a number of data
points, as obtained by sampling or experiment, and tries to construct a function which
closely fits those data points. This is called curve fitting or regression analysis. Interpolation is a
specific case of curve fitting, in which the function must go exactly through
the data points.

A different problem which is closely related to interpolation is the
approximation of a complicated function by a simple function. Suppose we know
the function but it is too complex to evaluate efficiently. Then we could pick a
few known data points from the complicated function, creating a lookup table, and try to
interpolate those data points to construct a simpler function. Of course, when
using the simple function to calculate new data points we usually do not receive
the same result as when using the original function, but depending on the
problem domain and the interpolation method used the gain in simplicity might
offset the error.