# Plotting 3D Regions

How can I plot a simple 3D region such as

$$x^2+y^2+z^2<16$$

in Blender?

If I can't do that directly, how can I turn it into

$$x=\dots$$ $$y=\dots$$ $$z=\dots$$

So I can use Mesh --> Math Function --> XYZ Surface?

Or is there a script that can plot

$$x^2+y^2+z^2<16$$

by brute-forcing for each $x$, $y$, and $z$ values of step size $d$ then plotting that?

This method is using the Math Function Mesh that you mentioned in the question. Maybe someone else will come along with a script. For obvious reasons, you can't use X, Y, or Z values in the equations since that would setup circular dependencies. You must use U and V:

X equation: 4 * cos(u) * sin(v)

Y equation: 4 * sin(u) * sin(v)

Z equation: 4 * cos(v)

Where: 0 < u < 3.14159

and: -3.14159 < v < 3.14159

Note that you will need to remove doubles and flip the normals (Ctrl + N) after creation. Also note that you can enter precise values for U and V and they will be applied but they will only be displayed in the text box with two decimal points. Make sure that U wrap is disabled or else you will get overlapping faces. This is after removing doubles and fixing normals: