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Re: Plotting a super ellipse

• To: mathgroup at smc.vnet.net
• Subject: [mg55159] Re: Plotting a super ellipse
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Tue, 15 Mar 2005 00:21:41 -0500 (EST)
• Organization: University of Washington
• References: <d1148h$dqj$1@smc.vnet.net> <d13jam$qlp$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"JC" <Eat at joes.com> wrote in message news:d13jam$qlp$1 at smc.vnet.net...
> On Sun, 13 Mar 2005 10:22:09 +0000 (UTC), Bob Hanlon <hanlonr at cox.net>
> wrote:
>
>>Clear[x,y];
>>
>>eqn=(x^(5/2)/1)+(y^(5/2)/(5/4)^(5/2))==20;
>>

<snip>

>>Needs["Graphics`"];
>>
>>ImplicitPlot[eqn,{x,0,xmax},
>>    ImageSize->230];
>>
>>
>>Bob Hanlon
>>
>
> Bob,
>
> Thank you very much for your response. It worked.  Now I will just
> need to decipher it so I can change the  variables to adjust the
> curve, but that is not a big problem.
>
> One question.  The plot produced only was for one quarter of the super
> ellipse. Is there a way to get the entire ellipse to plot?
>

JC,

As written, your equation only has real solutions in the first quadrant. If 
you raise a negative number to the power 5/2 or 2.5, you surely cannot 
expect a real number. Perhaps your equation was supposed to include absolute 
values? Such as

aeqn = Abs[x]^2.5 + Abs[y]^2.5/1.25^2.5 == 20;

The above equation has roots in all 4 quadrants, and ought to be able to be 
plotted. Unfortunately, using ImplicitPlot with the above equation has 
problems, because ImplicitPlot calls Solve, and Solve converts Abs[x] into x 
|| -x and then gives up. A workaround is to use Sqrt[x^2] instead of Abs[x]. 
So, let

aeqn = Sqrt[x^2]^2.5 + Sqrt[y^2]^2.5/1.25^2.5 == 20;

Now, if you use ImplicitPlot you will get a plot on all 4 quadrants.

ImplicitPlot[aeqn,{x, -20^.4, 20^.4}]

Carl Woll