TITLE: easter problem - egg shapes
QUESTION [5 upvotes]: Inspired by an exceptionally silly article in today's newspaper I pose the following "egg parametrization problem".

Give an explicit function $ f(x,y,t) : \mathbb{R}^2\times I \to \mathbb{R}$ such that for each $t$ from interval $I$ the solution set of equation $f(x,y,t) = 0$ looks like an egg. 

I'm looking for function that provides most of the various egg shapes found in nature.

REPLY [10 votes]: Here is a nice Mathematica Demonstration (incidentally colored according to the Riemann zeta function), with the shape based on the mathematics of egg shapes described at an egg curves website www.mathematische-basteleien.de:
           
One of the neat constructions explained there is the Gardener's Egg: