Tooth gear geometry is elementary for further analysis of load-carrying capacity, efficiency and noise excitation and thus offers a high potential for optimization. In this context a uniform mathematical framework for calculating tooth geometry of arbitrary gear types is reasonable. Based on the basic law of gear kinematics, the geometry of any type of gearing can be computed fast and analytical. Thereby the manufacturability of novel optimized tooth profiles, depending on their context of application can be developed. In particular, potential of non-standard gearings that are difficult to calculate so far can become accessible.