Talk:Superquadrics

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Range of parameters

The interval of parametric-variable u is shown as -pi/2<=u<=pi/2. This interval refers to the superellipsoid and not the general superquadric.

For the case of the supertoroid then the u interval extends to -pi<=u<=pi. For clarification refer to p147 of:

AH Barr "Rigid Physically Based Superquadrics", Graphic Gems III, Academic Press, 1992.

I suggest that either the parametric intervals are removed or the above clarification made. —Preceding unsigned comment added by Hedgehog0 (talk • contribs) 11:36, 29 March 2009 (UTC)[reply]

Supertoroids are treated in a separate article. Note that the implicit equation given in this article does not include them. --Jorge Stolfi (talk) 20:57, 31 March 2009 (UTC)[reply]

Meaning of "superquadric"

Superquadrics cover both ellipsoids and toroids and hence the parametric range applies to both.
If the "superquadrics" article is in fact a "superellipsoids" article then this should be made more clear.
I was coding up both superquadric ellipsoids and toroids and naturally assumed that this article applied to both, which it does not.
There's superquadrics, superellipsoids and supertoroids. I still don't think this article clearly separates the 3. (Unsigned coment by User:Hedgehog0)

Well, we clearly have a nomenclature problem here.
If we take away the "super" for the moment, then the nomenclature is well established: ellipsoids are special cases of quadrics (= surfaces defined by 2nd degree equations), while the torus is not a quadric (it requires a 4th degree equation at least). The classification of algebraic surfaces by degrees is an old and rich area of mathematics, so we cannot argue with that.
Now, all the "super" things (superellipses, superellipsoids, superquadrics, and supertoroids) are ugly, mathematically speaking. They are not even algebraic surfaces, except when the exponents are integers (or certain rationals, perhaps). They are not preserved by affine or projective maps. So, not only the names, but the very objects have practically no history in mathematics. They seem to be rather ad-hoc inventions, mostly by computer graphics people. It is not surprising that the nomenclature is rather inconsistent.
The name "superellipse" was apparently coined in the 1960's (perhaps by Piet Hein, in connection with the Sergels Tor design) for the Lamé curves whose implicit equation (apart from scaling) is X^r + Y^r = 1 for arbitrary r. That name has apparently stuck. By that single example, "super" could be taken to mean "replace the exponent 2 in the implicit equation by a generic exponent r". Extending that logic to 3D, one would expect that a "superellipsoid" would be defined by X^r + Y^r + Z^r = 1. However, not long after, Hein came up with the "superegg" which is obtained by rotating a superellipse along one of its axes. The implicit equation of that is (X^2 + Y^2)^(r/2) + Z^r = 1 for some r. I don't know the history after that, but apparently two generalizations became popular in computer graphics. Definition (1) is a surface where each parallel is a Lamé curve of expoent r, and each meridian is a Lamé curve of some other exponent t. The equation for that is (X^r + Y^r)^(t/r) + Z^t = 1, and therefore it includes Hein's superegg. POV-ray's "superellipsoid" primitive uses this equation. Definition (2) replaces the three 2's in the equation of the ellipsoid X^2 + Y^2 + Z^2 by three arbitrary exponents, X^r + Y^s + Z^t = 1. Here is a reference. These surfaces are a bit more elegant, mathematically speaking, and have a larger variety of shapes; but they do not include Hein's superegg.
In the late 80's or early 90's, Barr used "superellipsoid" in the sense (1). He then added an extra "offset" parameter to the *parametric* equation of the superellipsoid to creae a "supertoroid", and called the whole family "superquadrics". Now, a sphere is a quadric, and one can obtain a torus by adding an offset to the parametric equation of a sphere; but that does not make the torus a quadric...
So, which nomenclature do we follow? I propose that we look for more references to "superquadrics". If Barr is the only one, or the most popular one, well, we will have to revise the articles. Sigh. --Jorge Stolfi (talk) 15:54, 11 April 2009 (UTC)[reply]

From looking at a few papers on the net, it seems that Barr's definition of "superquadric" is indeed the most popular one, and that this article should be renamed "Lamé surface"^[1] I will do so if no one objects. Al the best, --Jorge Stolfi (talk) 16:35, 11 April 2009 (UTC)[reply]

^ Z. Nadenik (2005), "Lame surfaces as a generalisation of the triaxial ellipsoid", Studia Geophysica et Geodaetica, 49 (3), Springer: 277–288, doi:10.1007/s11200-005-0010-8, ISSN (Print) 1573-1626 (Online) 0039-3169 (Print) 1573-1626 (Online) {{citation}}: Check |issn= value (help); Unknown parameter |month= ignored (help)

Purpose of code block

Of what practical use is the code block? I think that most programmers that understand superquadrics don't require this code block. —Preceding unsigned comment added by Hedgehog0 (talk • contribs) 11:40, 29 March 2009 (UTC)[reply]

I agree. --Jorge Stolfi (talk) 20:57, 31 March 2009 (UTC)[reply]

Sorry, but I'm a programmer and just came across the term "superquadrics" for the first time. Wanted to know what it is and looked it up in the Wikipedia. For me the source is helpfull as I can understand it and even use it for some quick tests. If it wouldn't have been here I would probably have searched for it right away. Some people actually think in source, sorry ;-). JB --92.195.43.155 (talk) 22:18, 4 July 2013 (UTC)[reply]

[1] Z. Nadenik (2005), "Lame surfaces as a generalisation of the triaxial ellipsoid", Studia Geophysica et Geodaetica, 49 (3), Springer: 277–288, doi:10.1007/s11200-005-0010-8, ISSN (Print) 1573-1626 (Online) 0039-3169 (Print) 1573-1626 (Online) {{citation}}: Check |issn= value (help); Unknown parameter |month= ignored (help)

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