Considering Adjacent Sets for Computing the Visibility Region

This paper explores the problem of the paving of the union of adjacent contractors. The focus is first put on the analysis of the topology of a set operator, which can be stable or not stable. Then, depending on the stability of the union operator, solutions are proposed to avoid fake boundaries in stable and non-stable union of sets. For stable unions of sets, a boundary preserving form will be developed to add a set overlapping the fake boundary in the expression of the union, whereas for non-stable union of sets, a boundary approach will be developed to avoid fake boundaries. Some problem-specific solutions are also developed to avoid fake boundaries. As an example, an enhancement of the separator on the visibility constraint is proposed. This avoids fake boundaries while characterizing the set of non-visible points from an observation point relative to a polygon.