Point Visibility
Subir Ghosh · Cambridge University Press eBooks · 2007
Problems and Results Determining the visible region of a geometric object from a given source under various constraints is a well-studied problem in computational geometry [30]. The visibility polygon V(q) of a point q in a simple polygon P is the set of all points of P that are visible from q . In other words, V ( q ) = { p ∈ P | q sees p }. A similar definition holds in a polygon with holes or an arrangement of segments. The problem of computing the visibility polygon V(q) of a point q is related to hidden line elimination problem and it is a part of the rendering process in computer graphics [115]. Figure 2.1 shows V ( q ) in a simple polygon, a polygon with holes, and a line segment arrangement. By definition, any V(q) is a star-shaped polygon and q belongs to the kernel of P . The visibility polygon of a point in a line segment arrangement may not be always bounded. Let ab be an edge on the boundary of V(q) such that (i) no point of ab , except the points a and b , belong to the boundary of P , (ii) three points q, a and b are collinear, and (iii) a or b is a vertex of P . Such an edge ab is called a constructed edge of V ( q ).