A data reduction and representation method reduces the number of graphic articulation parameters (GAPs) that must be stored or transmitted to animate an object. A number of GAPs are identified that can be interpolated from other GAPs. A directed graph is created which depicts the identities of the “derived” GAPs, the “defining” GAPs from which derived GAPs can be interpolated, and the relationship between them. The GAPs reside at nodes on the graph which are interconnected with directed links that indicate the “parent” to “child” relationships, with each link representing an interpolation function which defines how the derived GAPs are interpolated from the defining GAPs. The graph and interpolation functions are conveyed to a decoder. Frames containing defining GAPs are then sent to the decoder, which performs the interpolations as directed by the graph and using the interpolation functions to reconstruct the derived GAPs.