WorldEdit Sphere Generation Equation

FAWE can now handle larger edits without crashing the server, so I'm making this information available.
Note: Try out Selection Commands (//sel) First

Spoiler: Try out Selection Commands

It's probably simpler to use the //sel commands to create rounded shapes.
Generation is an alternate option available if needed.

//sel sphere
Left click to select center, right click to extend.

//sel ellipsoid
Left-click to choose center, right-click to extend.
You can either right-click horizontally to select a horizontal ellipse, or right-click vertically to select a vertical ellipse. But if you want to select a ellipsoid area you need to right-click at least twice.

WorldEdit Generation Command: //g
Arbitrary shapes can be created on Build by selecting an area and using a math equation.
More information on the //g command and generation can be found here on the WorldEdit Wiki.

A great tool you can use for getting equations: K3DSurf : 3D Surface Generator

I used this and tweaked the formulas just a bit to make them work. I'm personally not great at math, so I'm sure someone better at math could make some cool things.



Getting Started

• Use //pos1 and //pos2 to select an area.
  
• Use the format: //g blockid equation

Generation side notes:

• -h makes the shape hollow, removing -h makes it solid.
• Inverting the function (multiply by negative 1) will usually swap the air and stone filled areas.

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Solid Sphere / Spheroid / Ellipsoid of Any Size

Spoiler

//g stone -x*x -y*y -z*z +1



If you select uneven corners:


If you make it only one block tall, you can generate a 1-block high cylinder.

Hollow Sphere / Spheroid / Ellipsoid of Any Size

Spoiler

//g -h stone -x*x -y*y -z*z +1

Produces same spheroid shapes as above with a hollow center.

Hollow Eight-Sided Diamond

Spoiler

//g -h stone abs(x)+abs(y)+abs(z) - 1

Tunneling Hyperboloid

Spoiler

//g -h stone -x^2 - y^2 + z^2 +0.3

"Pringle" Shape

Spoiler

//g -h stone -x*x - y + z*z

"Circle Around Cube" Shape

Spoiler

//g -h stone ((x^2 + y^2 - 1)^2 + z^2)* ((y^2 + z^2 - 1)^2 + x^2)* ((z^2 + x^2 - 1)^2 + y^2) - 0.075

"Box with Holes" Shape

Spoiler

//g -h stone (x^4) - y^4 -z^4 - (-x^2 - y^2 -z^2)

Enjoy!

 

I was kind of devastated at not having access to my own post in the Builder section when I needed the equations later. I wasn't about to go make them again... because maths.

lol.

At least these are copypaste now.