I guess the maths only related to the shape of the surface of the egg. How to parameterize them in 3D space. I didn't go through the article and I hope this makes sense, but from your text, this is what it seems.
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Hi. The authors discussed about material coordinates using mathematical equation which I didn't understand. I guess it was about when and how egg ellipticity changes.
Images I have given the link. May be it wasn't properly placed. Will take care next time. Thank you for suggestions.
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This is exactly what I meant: the maths behind the shape :)