I think it got really complicated when the initial shape was not convex. If its convex initially,then at best you can split all the groups in two, and in most of the puzzles you had to split all the groups in half (possibly not evenly if the group is odd) because you the number of lines you were allowed to make was roughly ceil(log_2) the number of dots.

But when its not convex you can potentially do better than just splitting all groups in half, and i found those the most challenging levels (i think it was either 20 or 21 that was like that)