hi,I need a conformal mapping that changes the superellipse to an

arsalan1

hi,
I need a conformal mapping that changes the superellipse to an easier shape.
if anyone send me any helpful thing (relative article, idea) I will be so pleased.

w4k4b4lool4

What is this superellipse, and what have you tried already?
Wakabaloola

arsalan1

(x/a)^2k+(y/b)^2k=1
its a super ellipse equation
its like rectangular with rounded corner.
ive tried some classic mapping like log ,sin, 1/z,...

chiro

Hey arsalan1 and welcome to the forums.

The equation you have given is a very simple equation in terms of describing the complex object you have given.

The other objects you have mentioned like log and sin are far more complex than the equation you have given.

Is there any specific reason or application you have in mind for requiring any transformation?

JJacquelin

Hi !

to plot the curve, use the function y(x) in attachment

Attached Thumbnails

 

arsalan1

@chiro
hi thanks for your attention
im looking for a mpping changes the super ellipse shape its not simple.
for example for ellipse conformal mapping uses compelet jacobi integral of first kind.

arsalan1

@jjacquelin
hi thanks for your attention
i have plot it its not my problem i wana map it to an other shape.like circle or ellipse.