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I have a superellipse which I will rotate it and then translate it. My question is that how to determine the origin will still be inside the superellipse after all the action?


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You can just transform the usual Cartesian equation for the superellipse to an inequality... – J. M. Oct 20 '11 at 23:28
After translation and rotation, how I can separate the cases? When should I use larger than a constant and when I should use less than a constant? – zmarcoz Oct 20 '11 at 23:56
up vote 1 down vote accepted

Take the equation of the Lamé curve to be


Taking your specified order of operations, the result after rotating by an anticlockwise angle $\varphi$ and translating the center of the superellipse to $(h,k)$ is


To test if some point $(x,y)$ you have is within that superellipse, all you need to do is to change the "$=$" to a "$\lt$"...

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OOOOOOOOOOOOO.........You are super good in MATH........... – zmarcoz Oct 21 '11 at 0:12

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