A universal geometric model of egg shape with sine-based deformation

The study introduces a compact, universal mathematical model that accurately describes the contours of diverse avian eggs. A sine-based deformation term allows the model to capture nonlinear and periodic variations in egg geometry. As a result, it accurately represents a broad range of egg shapes, particularly pyriform forms. To validate the model, 60 chicken and 60 duck eggs were analysed by comparing theoretical volumes derived from the formula with measured volumes. The results showed that the root mean squared percentage error (RMSPE) in volume estimation was below 1%. Furthermore, the model was applied to contour analyses of egg images from eight bird species and to shape and volume verification for five Asian species. It also yielded compact, physically interpretable descriptors of egg geometry, including key geometric parameters. Overall, the proposed model demonstrated high adaptability and precision in fitting diverse egg shapes and holds strong potential for interdisciplinary applications in agriculture, engineering design, and product development. • Accurately models diverse avian egg shapes across species. • Captures nonlinear and pyriform geometric variations. • Provided concise and interpretable descriptors with low prediction error.