Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 2001.Thesis (Master's) -- Bilkent University, 2001.Includes bibliographical references leaves 92-96The Art Gallery Problem is the problem of determining the number of observers
necessary to cover an art gallery such that every point is seen by at least one
observer. This problem is well known and has a linear time solution for the 2
dimensional case, but little is known about 3-D case. In this thesis, the dominance
relationship between vertex guards and point guards is searched and found that a
convex polyhedron can be constructed such that it can be covered by some number
of point guards which is one third of the number of the vertex guards needed. A new
algorithm which tests the visibility of two vertices is constructed for the discrete
case. How to compute the visible region of a vertex is shown for the continuous case.
Finally, several potential applications of geometric terrain visibility in geographic
information systems and coverage problems related with visibility are presented.Düger, İbrahimM.S
