[Plugin] Superellipsoid 1.0

[Plugin] Superellipsoid 1.0

Postby Regular Polygon » Fri Jul 09, 2010 8:25 pm

OK, enough about the superellipse. This plugin draws its 3D cousin, the Superellipsoid. The superellipsoid varies between a round shape (an ellipsoid), and a square shape (the rectangular bounding box). If all three axes are equal, it varies between a sphere and a cube. Here is an example of a superellipsoid that is halfway between a sphere and a cube, (i.e. 50% square).

sup1.png


The degree of squareness can vary in two directions: horizontal and vertical. The horizontal cross section is a superellipse with one degree of squareness. And the vertical cross section is also a superellipse with an independent degree of squareness.

sup2.png


In the picture above, the superellipsoids get more square horizontally as you move along the red axis, and more square vertically as you move along the green axis. The squareness values vary from 0% at the origin (the sphere) to 90% in each direction.

You can also consider negative squareness values. The more negative the value, the more the surface contracts in towards the center.

sup3.png


In this picture, the horizontal squareness varies along the red axis from –90 to +90, and the vertical squareness varies along the green axis from –90 to +90.

The Superellipsoid plugin is at: regularpolygon.org/plugins/superellipsoid.php.

Thanks.
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Last edited by Regular Polygon on Thu Dec 08, 2011 7:30 am, edited 3 times in total.

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Re: [Plugin] Superellipsoid 1.0

Postby massimo » Sat Jul 10, 2010 7:33 am

Thank you, it works like a charm. :thumb:
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Re: [Plugin] Superellipsoid 1.0

Postby Regular Polygon » Sat Jul 10, 2010 8:21 am

massimo wrote:Thank you, it works like a charm. :thumb:


Thank you massimo. After no replies since I posted it 11 hours ago, I was afraid this topic was going to sink into oblivion on page 2. :roll:
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Re: [Plugin] Superellipsoid 1.0

Postby notareal » Sat Jul 10, 2010 8:32 am

:thumb: Nice addition!
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Re: [Plugin] Superellipsoid 1.0

Postby TIG » Sat Jul 10, 2010 9:37 am

Thanks for another interesting tool in your toolset... :D
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Re: [Plugin] Superellipsoid 1.0

Postby Regular Polygon » Sat Jul 10, 2010 9:55 am

TIG wrote:Thanks for another interesting tool in your toolset... :D


Thanks TIG, and everyone else. I don't deny that my interests are probably offbeat, if not peculiar.
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Re: [Plugin] Superellipsoid 1.0

Postby thomthom » Sat Jul 10, 2010 10:27 am

Good stuff!
Looking forward to the 4D version! :D
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Re: [Plugin] Superellipsoid 1.0

Postby TIG » Sat Jul 10, 2010 10:29 am

Sometimes out of weird ideas comes unexpectedly good results... :ugeek:
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Re: [Plugin] Superellipsoid 1.0

Postby Regular Polygon » Sat Jul 10, 2010 10:43 am

thomthom wrote:Good stuff!
Looking forward to the 4D version! :D


Glad you like it. Actually, I am running out of ideas for geometry. I'll probably move on to tools or something else.
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Re: [Plugin] Superellipsoid 1.0

Postby massimo » Sat Jul 10, 2010 10:47 am

my interests are probably offbeat, if not peculiar

Really? What about some wooden pillars in the Herzog & De Meuron style? Just one click :)
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Re: [Plugin] Superellipsoid 1.0

Postby Regular Polygon » Sat Jul 10, 2010 11:06 am

massimo wrote:Really? What about some wooden pillars in the Herzog & De Meuron style? Just one click :)


That's interesting. They sure look like superellipsoids -- or maybe just ordinary ellipsoids.
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Re: [Plugin] Superellipsoid 1.0

Postby Jim » Sat Jul 10, 2010 6:17 pm

If you scale a superellipsoid, does it remain one? For example a 2d sin wave can be scaled along both its axes and still remains a sin wave. Does this hold true for these 3d shapes?

Obviously, it is not true for cubes or spheres and other basic definitions.
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Re: [Plugin] Superellipsoid 1.0

Postby Regular Polygon » Sat Jul 10, 2010 8:55 pm

Yeah, it is true for superellipsoids, and ordinary ellipsoids. The length, width, and height are basically just scale factors of a unit superellipsoid. :geek:
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Re: [Plugin] Superellipsoid 1.0

Postby shura » Sat Jul 10, 2010 10:05 pm

Great! This is very useful and fun too. :thumb: Thanks a lot!
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Re: [Plugin] Superellipsoid 1.0

Postby putnik » Thu Jul 15, 2010 5:30 am

Thank you! flatland it ain't
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