Improved bound for the union of fat triangles
Esther E. Ezra, Boris S. Aronov, Micha Sharir · 2010
We show that, for any fixed δ > 0, the combinatorial complexity of the union of n triangles in the plane, each of whose angles is at least δ, is O(n2 α(n) log ∗ n), with constant of proportionality depending on δ. This considerably improves the twenty-year-old bound O(n log log n), due to Matousek et al. [29,30].