Questions about vertex dilation algorithm

[ZorAttC]

In the vertex dilation algorithm, each vertex searches for other vertices within a radius of approximately one quarter of a voxel.
However, the three-dimensional reconstructed triangles are not connected. They overlap in visualization, but are not connected in topological structure.I dont see this part in the paper. How you guys deal with it?

[ziv-lin]

Two neighborhood triangles are connected if they share the same point or the same edge.

Regarding the topological structure you mentioned, can you explain further what this is and how it is used? In CG communities, topological structures might have different definitions in various applications.

[ZorAttC]

I suppose there is a triangle in each voxel. After vertex dilation,there will be more triangles to fill the gap but the new triangles will overlap as I think in the figure.This will make the triangles look like they are not coming from the same surface, but have some glitches.