Delineating an ovoidal egg shape by length and breadth: A novel two-parametric mathematical model

Mathematical characterisation of an egg shape implies, among other things, the possibility of its description with simple and accurate formulae. Of mathematical models delineating ovoidal egg shape, Hügelschäffer's model is deemed standard and theoretically established. However, for its application and in addition to measuring the egg length (L) and its maximum breadth (B), one more parameter (w) is needed, which is the shift of the B-axis from the middle point of egg length. Measurement of w is quite laborious and does not always meet the required accuracy criteria. Previously, we introduced Narushin's model, which uses only two parameters, L and B, but it does not exactly outline the egg profile. To grapple with this problem, here we have developed a combination of the two models. The new two-parametric model is based on Hügelschäffer's model, while the parameter w has a sliding character, changing its value at the egg's sharp end as calculated following Narushin's model, to zero at the blunt end. The new model was tested for accurate reproducing the egg profile with an average error of 4.17% when the value of the parameter w changes according to linear dependence. This error was lower than when using three parameters in Hügelschäffer's model. Thus, we propose a new egg shape model, which we named a modified Hügelschäffer's model with two parameters. With its use, new formulae were derived for calculating the egg volume and surface area, the empirical validation of which showed an average error of 1.72% and 0.83%, respectively.