This question started as a minecraft question, but at the heart of it, it's my lack of mathematical understanding that's hindering me.
I'm trying to understand how one mathematical formula changes format from a "y=" format to another. I'm only dealing with 3D shapes, like spheres or cylinders... or a torus.
I understand that a volume of a Torus is
But when written in a command parser a Torus of major radius 0.75 and minor radius 0.25 is written as
(0.75-sqrt(x^2+y^2))^2+z^2 < 0.25^2
with inputs as x,y,z.
From what I can understand, the command parser will place points or blocks on any value that is greater then what is after the < symbol, in this case its 0.25^2
The proper command parser's syntax can be found here http://wiki.sk89q.com/wiki/WorldEdit/Expression_syntax but from what I gather, the syntax is extremely common.
I've tried to understand what exactly is occurring in the transformation from one formula format to another, but I don't understand torus formula really either. Can someone show me an example of a simpler 3d shape, like a cone or a cube?
For reference, check the bottom of this page this page under Arbitrary shapes .