Jholsenback: moved Reference:Superellipsoid to Reference:Superquadric Ellipsoid: a wiki-docgen change

2012-07-23T19:22:12Z

moved Reference:Superellipsoid to Reference:Superquadric Ellipsoid: a wiki-docgen change

Jholsenback: 1 revision: Reference Migration Initial Load

2012-03-15T19:08:58Z

1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)

2012-03-11T22:27:02Z

1 revision: Initial Load (TF)

New page

[[Category:Objects]]
[[Category:Finite Solid Primitives]]
{{#indexentry:superquadric}}
{{#indexentry:superellipsoid, keyword}}
{{#indexentry:keyword, superellipsoid}}
The <code>superellipsoid</code> object creates a shape known as a 
superquadric ellipsoid object. It is an extension of the quadric
ellipsoid. It can be used to create boxes and cylinders with round edges and
other interesting shapes. Mathematically it is given by the equation:

<table class="centered" width="465x" cellpadding="0" cellspacing="10">
<tr>
<td>
[[Image:RefImgSqemath.png|center|445px]]
</td>
</tr>
<tr>
<td>
Superquadric Ellipsoid Formula
</td>
</tr>
</table>

The values of <code>e</code> and <code>n</code>, called
the east-west and north-south exponent, determine the shape
of the superquadric ellipsoid. Both have to be greater than zero. The sphere
is given by e = 1 and n = 1.

The syntax of the superquadric ellipsoid is:
<pre>
SUPERELLIPSOID:
superellipsoid {
<Value_E, Value_N>
[OBJECT_MODIFIERS...]
}
</pre>

The 2-D vector specifies the <code>e</code> and <code>
n</code> values in the equation above. The object sits at the origin and
occupies a space about the size of a <code>
box{<-1,-1,-1>,<1,1,1>}</code>.

Two useful objects are the rounded box and the rounded cylinder. These are
declared in the following way.
<pre>
#declare Rounded_Box = superellipsoid { <Round, Round> }
#declare Rounded_Cylinder = superellipsoid { <1, Round> }
</pre>

The roundedness value <code>Round</code> determines the roundedness of the
edges and has to be greater than zero and smaller than one. The smaller you
choose the values, the smaller and sharper the edges will get.

Very small values of <code>e</code> and <code>n</code>
might cause problems with the root solver (the Sturmian root solver cannot be
used).

← Older revision	Revision as of 19:22, 23 July 2012
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← Older revision	Revision as of 19:08, 15 March 2012
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Reference:Superquadric Ellipsoid - Revision history

Jholsenback: moved Reference:Superellipsoid to Reference:Superquadric Ellipsoid: a wiki-docgen change

Jholsenback: 1 revision: Reference Migration Initial Load

Jholsenback: 1 revision: Initial Load (TF)