This paper investigates the use of the sinusoidal transform to represent co
nvex regions of the plane. Formulae are derived for the determination of va
rious geometrical features and relations in terms of sinusoidal transforms
and their Fourier descriptors. Necessary and sufficient conditions for a pe
riodic function to be the sinusoidal transform of a convex region are deriv
ed. Sinusoidal Fourier descriptors are shown to compare favourably with oth
er shape-representation schemes based on Fourier descriptors.