ABSTRACT
A rotation applied to an object changes its orientation. This chapter shows that a combination of such rotations gives an object an arbitrary orientation. It presents how to rotate an object about an arbitrary axis, which is not necessarily a principal axis. The Euler transform is defined as a succession of rotations about three principal axes. The rotation axes can be taken from the fixed coordinate system, such as the world space, or from the object space that rotates together with the object. The Euler transform was presented with the world space, but it can be defined with respect to the object space. In real-time computer animation, the sequence of motions created by an artist is pyed back at run time. However, the artist does not define the motions of all frames. For a 60-fps animation, for example, much fewer than 60 frames are defined per second by the artist.
