On Transformations For Animation

This paper focuses on the transformation steps involved in implementing an arbitrary generic twodimensional animation. For instance, we are interested in depicting the motion of the earth rotating, and revolving around the sun, which could itself be translating. Unlike key-frame animation, the transformations discussed in this work are described algorithmically using certain primitives provided by an animation algebra. Such a process is most useful in building authoring systems and in virtual reality applications where the programmer is `unaware' of the nal use of his work. The usual method in producing an animation sequence is to divide the e ect into parts and render every part quickly, taking care to erase previous parts. In key-frame animation, a trial and error procedure is often adopted to generate intermediate positions when a linearity assumption cannot be made. An alternate method to generate a part is the use of a forward matrix transformation of the initial model, where the programmer needs to be aware of the parameters for producing each part. In this paper, we provide two methods to implement the algebra where the process of obtaining intermediate positions is automated, and analyse the complexity.