Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

Thanks

share|improve this question
    
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
add comment

1 Answer

up vote 1 down vote accepted

Take the equation of the Lamé curve to be

$$\left|\frac{x}{a}\right|^p+\left|\frac{y}{b}\right|^p=1$$

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

$$\left|\frac{(x-h)\cos\,\varphi-(y-k)\sin\,\varphi}{a}\right|^p+\left|\frac{(x-h)\sin\,\varphi+(y-k)\cos\,\varphi}{b}\right|^p=1$$

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

share|improve this answer
    
OOOOOOOOOOOOO.........You are super good in MATH........... –  zmarcoz Oct 21 '11 at 0:12
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.