The articulatory-acoustic relationship is many-to-one and non linear and this is a great limitation for studying speech production. A simplification is proposed to set a bijection between the vowel space (f1, f2) and the parametric space of different vocal tract models. The generic area function model is based on mixtures of cosines allowing the generation of main vowels with two formulas. Then the mixture function is transformed into a coordination function able to deal with articulatory parameters. This is shown that the coordination function acts similarly with the Fant's model and with the 4-Tube DRM derived from the generic model.