The aim of this work is to introduce new ways to model the I-V characteristic of a PV cell or PV module using straight lines and Bézier curves. This is a complete novel approach, Bézier curves being previously used mainly for computer graphics. The I-V characteristic is divided in three sections, modeled with lines and a quadratic Bézier curve in the first case and with three cubic Bézier curves in the second case. The result proves to be accurate and relies on the fundamental points usually present in the PV cell datasheets: V_oc (the open circuit voltage), I_sc (the short circuit current), V_mp (the maximum power corresponding voltage) and I_mp (the maximum power corresponding current) and the parasitic resistances R_sh0 (shunt resistance at I_sc) and R_s0 (series resistance at V_oc). The proposed algorithm completely defines all the implied control points and the error is analyzed. The proposed method is validated for different temperatures and irradiances. The model is finally compared and validated using the least squares fitting method.