We model the supply and demand curves of electricity day-ahead auctions in a parsimonious way by building an appropriate algorithm to present the information about electricity prices and demand with far fewer parameters than the existing algorithm. We represent each curve using mesh-free interpolation techniques based on radial basis function approximation. We describe the results of this method for the day-ahead IPEX spot price of Italy and then use these representations to forecast supply and demand and find the intersection of the predicted supply and demand curves in order to obtain the market clearing price.