Complexity of union (computational geometry) I'm courrently rading "Computational Geometry" from Mark de Berg, Otfried Cheong,
Marc van Kreveld, Mark Overmars and found the following theorem 13.9.


  Let $S$ be a collection of convex polygonal pseudodiscs with n
  edges in total. Then the complexity of their union is at most $2n$.


I'm not really sure what this should mean (this might be a a language barrier). First I thought that this would be the time complexity, but I'm now pretty much unsure about this.
The complexity of a union of objects is the number of pieces in the boundary of the union. In the plane "complexity of boundary" is equivalent (upto a constant factor) to "number of vertices". But in general the boundary complexity is the sum of complexities of all objects needed to describe the boundary (vertices, edges, faces, and so on). It's just that in the plane the number of vertices in the boundary is the same as the number of edges (because the boundary is a set of cycles in this case)