This paper deals with the scroll compressor, which is a machine used for compressing air or refrigerant. By using a novel reference frame, it proposes an original way of describing the geometry of the scroll wraps (represented as circle involutes) in which the symmetries are exploited in order to establish a thermodynamic model of the scroll compressor. This approach allows the chamber volumes to be analytically described without any special assumption and takes into account the discharge as a non-symmetrical process. The proposed geometric model is aimed to be coupled with the thermodynamic model by using the standardized VHDL-AMS language and should be then considered as preliminary to the scroll overall simulation and design of a functional virtual prototype. Simulations and experiments have shown good agreement.