State of the union (of geometric objects)
Pankaj K. Agarwal, János Pach, Micha Sharir · Contemporary mathematics - American Mathematical Society · 2008
Let C be a set of geometric objects in R d .The combinatorial complexity of the union of C is the total number of faces of all dimensions on its boundary.We survey the known upper bounds on the complexity of the union of n geometric objects satisfying various natural conditions.These bounds play a central role in the analysis of many geometric algorithms, and the techniques used to attain these bounds are interesting in their own right.