Improved Bounds for the Union of Locally Fat Objects in the Plane.

We show that, for any gamma > 0, the combinatorial complexity of the union of n locally gamma-fat objects of constant complexity in the plane is n/gamma(4)2(O(log* n)). For the special case of gamma-fat triangles, the bound improves to O(n log* n + n/gamma log(2) 1/gamma).