Description of dental arch form using the Fourier series

The aim of this study was to describe the form of the human superior dental arch using Fourier transformations. Forty models made in dental stone from impressions of the maxillary dental arch were used to obtain the reference data, which were expressed in Cartesian coordinates, from the mesovestibular cuspid vertices of molar teeth, vestibular cuspid of premolars, and incisal edge. Fourth-grade equations and Fourier series were calculated from these data. The results indicate that Fourier series more precisely express the form and size of different dental arches, with mixed or permanent dentition, than fourth-grade equations. Details of the mathematical procedure and the precision obtained were provided.