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This question already has an answer here:

I think this is possible but I don't even know how to go about it.I know everything about ellipse but how can I adjust the shape of an ellipse to the shape of a normal egg

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marked as duplicate by Matthew Towers, Start wearing purple, Ayman Hourieh, MathOverview, Lord_Farin Jul 8 '13 at 12:01

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  • $\begingroup$ What do you mean by "egg"? An ellipsoid? A Cartesian oval? $\endgroup$ – Ron Gordon Jul 8 '13 at 11:07
  • $\begingroup$ A cartesian oval $\endgroup$ – DOCTOR NGILAZI BANDA JOSHUA Jul 8 '13 at 11:11
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The way that this is often achieved is by multiplying the usual equation of an ellipse with a shape function $g(x)$ that creates asymmetry with respect to reflection in the $y$-axis, combined with a graduation parameter $t$ $(0\leq t \leq 1)$ so that you get

$$\phi(x) = \sqrt{1 - (x/a)^2} + t~g(x)~(x^2-a^2)$$

with typically $b=1$, $a=1.3$. I have used $g(x) = x^3$ $(x\leq0)$, $g(x) = x^2$ $(x\geq0)$ with $t=0.1$, but the choice is quite broad, as long as it is asymmetric w.r.t. $x$.

I think there are different types of eggs and egg shapes, so there is probably no single $g(x)$ and $t$ that fits all eggs.

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