Hi Pierro - offset does a join step to glue segments together, but curve joining in Moi is meant to form a single directional path, not one that has internal branches in it. So joining in MoI is meant to join curve arrangements where there are only 2 segments that come out from any single point. Your structure has many junctures where there are numerous lines radiating out from a shared endpoint. When the joiner processes that big bunch of branching connections, it's going to end up with a fairly random join that makes an open curve that wanders all over the place.

If you select just the boundary of one cell at a time and then do offset you should then get better behavior, that will join into a proper closed curve which will then offset for you better.

Start by selecting the boundaries of one single cell, then run Offset, set the distance based mode, put in your distance and then click in the center of the cell to complete the offset towards the inside, and then click once in empty space to clear the selection, then click on the boundaries for another cell, right-click to repeat the offset command, click inside the cell to complete the offset, and then repeat until you have finished all cells.

The other way that this could work as a single batch operation would be if all the cells were prepared as closed curves that overlapped sides with one another rather than single lines forming a branching structure.

Then once you have the cells offset, like Stefan writes above to form the curved interior cells run Draw curve > Freeform > Control points and snap one control point onto the corner point of each offset shrunken cell.

- Michael