Question

I’m trying to determine if two cubes overlap. I’ve read up on overlapping rectangles, but I’m not sure how to translate it into the third dimension.

My goal is to generate a number of randomly positioned and sized non-overlapping cubes.

These cubes are represented on a x,y,z Cartesian plane.

Answer 1

You should be able to modify Determine if two rectangles overlap each other? to your purpose fairly easily.

Suppose that you have CubeA and CubeB. Any one of 6 conditions guarantees that no overlap can exist:

Cond1.  If A's left face is to the right of the B's right face,
           -  then A is Totally to right Of B
              CubeA.X2 < CubeB.X1
Cond2.  If A's right face is to the left of the B's left face,
           -  then A is Totally to left Of B
              CubeB.X2 < CubeA.X1
Cond3.  If A's top face is below B's bottom face,
           -  then A is Totally below B
              CubeA.Z2 < CubeB.Z1
Cond4.  If A's bottom face is above B's top face,
           -  then A is Totally above B
              CubeB.Z2 < CubeA.Z1
Cond5.  If A's front face is behind B's back face,
           -  then A is Totally behind B
              CubeA.Y2 < CubeB.Y1
Cond6.  If A's left face is to the left of B's right face,
           -  then A is Totally to the right of B
              CubeB.Y2 < CubeA.Y1

So the condition for no overlap is:

Cond1 or Cond2 or Cond3 or Cond4 or Cond5 or Cond6

Therefore, a sufficient condition for Overlap is the opposite (De Morgan)

Not Cond1 AND Not Cond2 And Not Cond3 And Not Cond4 And Not Cond5 And Not Cond6