How oviform is the chicken egg? New mathematical insight into the old oomorphological problem

The chicken egg, a major food product, has been, as a model oviform object, the focus of advanced description in mathematical terms, and such a description has practical applications in engineering, industrial and biological disciplines. A precise mathematical description circumscribing major oomorphological characteristics, coupled with their non-destructive measurement, remains, to a certain extent, problematic and has not yet been achieved, hampering their effective control and use. A contour of any chicken egg can be accurately defined with Hügelschäffer's model by means of three main measures: length, L, maximum breadth, B, and a parameter w that corresponds to a distance of shifting the ellipse center to form an egg ovoid. The goal of the study was a comprehensive theoretical evaluation and development of basic geometrical formulae to define egg external traits by using Hügelschäffer's model and employing simulation modelling, digital imaging and image processing. As a result, we deduced novel geometrical formulae for the egg long circumference, C, volume, V, area of a plane curve obtained by the normal/orthogonal projection, A, surface area, S, distance parameter, w, and radius of curvature, R, at any point on the x-axis. For practical use in the poultry industry and food engineering, the proposed formulae can be instrumental in the non-destructive and accurate definition of the external parameters of any chicken egg.