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The generation of area functions from measurements of the sagittal section is an important step in the study of the relation between vocal tract geometry and speech acoustics. We present a new model to perform this transformation, inspired by the [alpha beta] model of Heinz & Stevens (1965). Our model is based on analysis of a vocal tract cast for large sagittal dimensions and for small sagittal dimensions on CT scans of the vocal tract constriction zones for the three cardinal vowels [i, a, u] of French. We extracted two sets of coefficients, appropriate for large and small sagittal dimensions respectively. We then compared the predictions of the model with those of other models from the literature. Finally, the usefulness of this dual coefficient procedure for the acoustic simulation of vowels was tested using sagittal sections generated by an acoustic model of the vocal tract.