We present a new method to implement in constant amortized time the
ip operation of the so-called Greedy Flip Algorithm, an optimal algorithm to compute the visibility graph or the visibility complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses simple data structures and only the left-turn or counterclockwise predicate; it relies, among other things, on a sum of squares like theorem for visibility complexes stated and proved in this paper. (The sum of squares theorem for a simple arrangement of lines states that the average value of the square of the number of vertices of a face of the arrangement is a O(1).) 1
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