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I'd basically like to have 3D version of this article section or this section. So for my case, there are two angles for latitude and longitude to construct 3D egg. Any hint to extend the formula to 3D would be appreciated.

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"Fig. 2a Comparison between the egg shaped curve of $b=0.7a$ and the shape of an actual egg." Awesome. – Rahul Dec 29 '12 at 14:58
up vote 3 down vote accepted

So, you want the parametric form of the surface of revolution of a chosen curve.

If your curve given by some functions $x = f(\theta)$ and $y = g(\theta)$, the surface of revolution about the $x$-axis is parametrized by $$\begin{align} x &= f(\theta), \\ y &= g(\theta)\cos(\phi), \\ z &= g(\theta)\sin(\phi), \end{align}$$ where $\theta$ has the same range in as your input curve and $\phi$ goes from $0$ to $360$ degrees.

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That is embarrassingly simple. Thanks a lot. – Tae-Sung Shin Dec 29 '12 at 15:22

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