[Plugin] Superellipsoid 1.0

Regular Polygon

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).

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.

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.

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.

massimo

Thank you, it works like a charm.

Regular Polygon

@massimo said:

Thank you, it works like a charm.

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.

notareal

Nice addition!

TIG

Thanks for another interesting tool in your toolset...

Regular Polygon

@tig said:

Thanks for another interesting tool in your toolset...

Thanks TIG, and everyone else. I don't deny that my interests are probably offbeat, if not peculiar.

thomthom

Good stuff!
Looking forward to the 4D version!

TIG

Sometimes out of weird ideas comes unexpectedly good results...

Regular Polygon

@thomthom said:

Good stuff!
Looking forward to the 4D version!

Glad you like it. Actually, I am running out of ideas for geometry. I'll probably move on to tools or something else.

massimo

@unknownuser said:

my interests are probably offbeat, if not peculiar

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

Regular Polygon

@massimo said:

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.

Jim

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.

Regular Polygon

Yeah, it is true for superellipsoids, and ordinary ellipsoids. The length, width, and height are basically just scale factors of a unit superellipsoid.

shura

Great! This is very useful and fun too. Thanks a lot!

putnik

Thank you! flatland it ain't