A region of a polygon in which the visible vertices are a fixed set of vertices is called a Sichtregion (viewing region) in the textbook of Rolf Klein, Algorithmische Geometrie (1996), Section 4.3.2. A polygon is partitioned into at most O(n3) viewing regions, according to Theorem 4.19 of the book. This is an improvement over the trivial bound O(n4) in my paper, and it holds also for the complexity of the partition Z, of which the viewing regions are a refinement: nZ=O(n3). This improves the overall bound of the paper from O(n9) to O(n7) closed-form expressions.
Moral: It can be worth while to read textbooks.