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This paper presents an incremental approach to the automated generation of 3D animation clips for the explanation of technical devices. It describes the system CATHI, which is part of the intelligent multimedia presentation system PPP. CATHI generates animation clips in the context of a coordinated multimedia document. The system is able to generate animation scripts and to present the corresponding animations with a minimal delay, i.e. within a few seconds. This allows it to be used for on-line and on-demand generation of presentations. The structure of the generated animation depends not only on the given communicative content. It is also influenced by a number of generation parameters. Furthermore, the design of the final animation depends on resource limitations, such as the available computing capacity and the graphical capacity of the output medium. The more powerful the machine is, the more complex the animation scripts generated by CATHI tend to be, but a fluent output within a given amount of time is achieved on (nearly) any machine - hence the name 'anymation'.