I scatter a few hundred points on the surface of a concave low-poly air-tight mesh and fracture that with vornoi fracture for the purpose of getting interesting patterns on the surface of the mesh. (I do not generate the inside mesh). To further process the result I want to turn all pieces into one air-tight mesh again.
The issue that I face is that there are huge gaps between the pieces. The fuse node always messes things up even more. It fuses points on the same pieces instead of fusing points with the neighbouring pieces, because the gaps are larger than the distances between points on individual pieces. I even tried raying the fractured object onto the original and had roughly the same result. Playing with the cut-offset made matters only worse.

1. Is there a better way to cut a vornoi pattern into a (3D) mesh? A method where nothing gets separated in the first place?

2. How do you avoid creating such gaps in the first place? I would imagine this causes huge issues when the intention is to prefracture an object and you realize that the object looks broken before the pieces separate.

3. The issue does not occur so much on 2D geometry. I considered turning the UVs into a mesh, fracturing that and turning the result back into a 3D mesh, but how would I match the pieces along the UV seams?

You want to fracture the object and then turn it back to one object Yes?
You can use switch node and connect either fracture object and main object to it.
With simple expression You can change between these objects in any time as you wish.

Thank you NimaNolan, but that is not the problem. I just want the pattern that the vornoi pieces make as cuts on my geometry.

do you have a non-zero value in the Cut Plane Offset parameter?
You shouldn't get gaps unless you create them with this parameter.

@johm
I get relatively large, irregular gaps without using the offset. Strange, right? I suspect it is because of the geometry that I “fracture”.
However, I am reasonably sure this counts as a bug in the vornoi fracture method.

Currently I deal with the issue by raying the pieces onto the original geo (at minimal distance), then fusing them, then selecting border-edges and fusing those at larger distance.