Generating a Sphere with Voxel

Question

I have been playing around with voxeljs, I'm new to 3D programming, and it says in the doc that this code generates the "sphere world":

generate: function(x,y,z) {
   return x*x+y*y+z*z <= 20*20 ? 1 : 0 // sphere world
},

How is this actually generating a sphere? From my simple understanding, I think that it's basically "looping" through each "chunk" in the 3D world? Any further explanation or a point to a good tutorial on this would be a huge help!

Answer 1

This is based on the distance formula in three-dimensional space, since you can define a sphere as every point within a certain distance of the center point.

The distance between any two objects is equal to the square root of (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2.

The above function is flagging each voxel if they are within 20 units of the origin. Since the origin is (0, 0, 0), the distance function simplifies down to square root of x1^2 + y1^2 + z1^2. This also throws in another optimization by getting rid of the square root, and comparing the result to 20^2.

Answer 2

Your function says:

If the voxel at (x, y, z) is part of the sphere, return 1, else 0.

The author applies the sphere equation. Your sphere is formed by the following set of voxels:

That basically means a voxel is part of the sphere, if the distance to the center (0, 0, 0) is less than the radius. The distance is calculated using the Pythagorean Theorem. By squaring the radius (in your case 20) you can compare it to the squared distance without calculating a square root.