Animation of three-dimensional characters is still a mostly manual process. Applications such as computer games and motion capture for special effects in movies require continuous intervention from the artist, who needs to guide the movement almost step by step. In such examples the available tools provide controls mainly over local details, either in space or in time. This thesis uses two analytical frameworks to deal with the process of animation: harmonic and modal analyses, allowing the description of movements with a reduced set of controls. A GPU implementation of the resulting animations allows for real-time rendering of those. In particular, it allows applications such as interactive control tuning through design galleries animated in real-time or three-dimensional music visualization. Particularly, it allows the choice of control parameters through the use of animated galleries in realtime and the use of music frequencies to guide the animation.