Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Biosystems Engineering

DOI: 10.1016/j.biosystemseng.2026.104482

Authors: Ching-Wei Cheng, Chia-Chun Lai, Ping-Kun Tsai, Ko-Jung Huang, Cheng-Han Li

Institutions: National Taichung University of Science and Technology, National Chung Hsing University

Language: English

Topic: Morphological variations and asymmetry

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

SDG: Zero hunger

Open Access status: hybrid

Estimated APC paid: $3,350