Talk:Superellipse

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[edit] "Characteristics"

I propose a new section called "Characteristics" or perhaps "Uses" that would mention some of the interesting and useful attributes of superellipses, and why they were used where they were. Comments? karlchwe

[edit] "Generalization" stub

I'm by no means a mathematics expert, but it looks like the article could be cleaned up a little, and the "Generalization" stub eliminated, if it were just incorporated into a ntoher section of the article. It doesn't look to me like there's much else to be said about the generalization. Zhankfor



Axell, here are the requested graphs for n=2 (it is really a circle as it is said in the article):

Image:Supell n 2.jpg

n=3/2:

image:supell_n32.jpg

and n=1/2 (really looks like an astroid):

image:supell_n12.jpg

Best regards. --XJamRastafire 16:59 Dec 19, 2002 (UTC)

In the n = 1/2 case, each of the four parts is really part of a parabola. Derivation:
\begin{align} \sqrt{\frac{x}{a}} + \sqrt{\frac{y}{b}} &= 1 \\ \sqrt{\frac{y}{b}} &= 1 - \sqrt{\frac{x}{a}} \\ \frac{y}{b} &= \left(1 - \sqrt{\frac{x}{a}}\right)^2 \\ \frac{y}{b} &= 1 - 2\sqrt{\frac{x}{a}} + \frac{x}{a} \\ 2\sqrt{\frac{x}{a}} &= 1 + \frac{x}{a} - \frac{y}{b} \\ 4\frac{x}{a} &= \left(1 + \frac{x}{a} - \frac{y}{b}\right)^2 \\ 4\frac{x}{a} &= 1 + 2\frac{x}{a} - 2\frac{y}{b} + \frac{x^2}{a^2} - 2\frac{xy}{ab} + \frac{y^2}{b^2} \\ 0 &= 1 - 2\frac{x}{a} - 2\frac{y}{b} + \frac{x^2}{a^2} - 2\frac{xy}{ab} + \frac{y^2}{b^2} \\ \end{align}
is a conic section with discriminant B^2 - 4AC = \left(\frac{2}{ab}\right)^2 - 4\frac{1}{a^2}\frac{1}{b^2} = 0, which means that it is a parabola. --Spoon! (talk) 23:21, 25 May 2008 (UTC)
- and in the case a = b = 1, they have axes x=\pm y and vertices (x,y)=(\pm\frac14,\pm\frac14). I didn't know! Please find a nice way to include it in the article. If (part of) the derivation is included, there should be a link to something about conics and their discriminants.--Noe (talk) 12:37, 26 May 2008 (UTC)

[edit] Why is the ellipsis, a punctuation mark, listed in the "see also" section of this page?

Could this be moved to the more grammatically correct "superellipse"? It's not about an ellipse that is especially amazing, it's about a curve that goes beyond an ellipse. 84.70.169.233 10:57, 18 April 2006 (UTC)

[edit] Knuth's Metafont

Like Bezier curves, superellipses are easier to implement with integer arithmetic than are circular arcs, so Knuth used superellipses instead of circular arcs in his Metafont type-design software.

Say what?? The arithmetic of superellipses is if anything more difficult than that of ordinary ellipses. Knuth's definition of the Computer Modern type family contains a variable squarerootoftwo which may be set to 1.414 for classical ellipses, or to lower values for more square superellipses; but whatever the setting, Metafont approximates the curve with cubic splines. Can anyone cite something to contradict my understanding? —Tamfang 03:45, 3 August 2006 (UTC)

[edit] See also: Astroid

I removed the following two entries from the "See also" list:

  • Astroid, a specific superellipse
  • Astroid, a particular ellipsoid (n = 2⁄3, a = b = 1)

and replaced them by one:

  • Astroid, the superellipse with n = 2⁄3 and a = b = 1

[edit] Intro image

is it a squircle? —The preceding unsigned comment was added by Circeus (talk • contribs) 18:46, 7 January 2007 (UTC).