Does my model need to be a continuous mesh for 3D printing?

Pretty much as the title. For example I’m modeling a robot. It’s easier to model it part by part. But if I want to 3D print it, do I need to merge parts into one and retopo it?

I googled it and found this:

But I don’t get it. What’s the difference between “overlapping” and “intersecting”…?

Thia is a bad example because there should be an invisible made pquad in the the first one too:

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The diagram you posted is a bit confusing.

I don’t think there’s a difference here between Intersecting and Overlapping.
The problem in the second picture is the “non-manifold” part.

Cura handles overlapping/intersecting very well. I usually don’t bother with Boolean modifiers, because Cura handles it so well.

It is important to make sure each of your solid pieces is manifold though. The “3D-Print toolbox” can help you find problems in your mesh.

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Thank you for your reply! I’ll definitely check 3D-Print Toolbox.