Is there a way to build an object through intersection?

Question

I am really stumped by this logo I am trying to animate, and I am not sure what to search for or how to phrase a search query. I have been trying to use the Boolean Modifier with this approach, but the problem is that the object I am trying to animate is gone after the mesh I am intersecting the object with moves away from the object.

The setup that I have got so far:

1. Start with a torus, and then add a sphere that is slightly big as the thickness of the torus.
2. Create a circular path such that the path roughly goes through the center of a circle made from a cross-section of the torus. (Basically, the path is inside and centered around the torus).
3. Constrain the sphere to follow the circular path. Now I have a sphere that goes around a torus.

Now I want to do this:

• As the circular sphere goes around the torus, the intersection of the sphere and the torus is revealed.

• As the sphere moves away from the newly revealed part, it stays there and does not disappear.

  A nice bonus is if there is a way to add a glow to the object only when it is inside the sphere.

Answer 1

A way to do it would be to array the boolean sphere with a rotating empty (or along a curve if your final shape is something else than a torus):

Create your torus, in Object mode create a sphere at the torus center, switch to Edit mode, move the sphere so that it contains a torus segment, the sphere origin must stay at the center of the torus:

Back to Object mode, create an empty at the same location:

Give your sphere an Array modifier, disable Constant Offset, enable Object Offset and choose the empty as Object, choose a Count around 20, but the amount will actually depend on the sphere size compared to the torus size:

At frame 0 of your Timeline keyframe the empty, at frame X rotate it as much as necessary on the Z axis so that all the sphere iterations cover the whole torus, keyframe again when you're good:

Give your torus a Boolean modifier with the sphere as Object. For the torus Boolean, choose Exact instead of Fast, and enable the Self option to make it work properly. It works fine in 2.9, you won't have the same options in the previous versions so I'm not sure this method will work properly. If your boolean is buggy, try another method like the sphere arrayed along a curve instead of a boolean:

Answer 2

You almost have it. In your last photo if you select the sphere and press Ctrl + A and apply its position, it'll move the object origin back to the center.

Then you can just rotate it around the Z axis.

Whatever material properties you set for the torus will only be shown for the visible portion, including volumes.