A 'sum of Squares' Theorem for Visibility Complexes a 'sum of Squares' Theorem for Visibility Complexes

We present a new and simpler 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/complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses only the incidence structure of the visibility complex and only the primitive predicate which states that the angle of a rst bitangent is less than the angle of a second bitangent, both bitangents being tangent to the same convex. The method relies on a 'sum of squares' like theorem for visibility complexes stated and proved in this paper. (The \sum of squares" theorem for an 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).)