Handouts: none
2/4/09: Guarding Polygons, Triangulation

Review of basics about g(P), w(P), g_V(P), w_V(P).

Extensions to the basic model:
(1) allow holes in the polygon P;
(2) consider 3D and terrains;
(3) restrict range of visibility of a camera and the angle of viewing (less than 360 degrees);
(4) allow mobile guards (as in the "watchman route problem") or cameras that can be controlled and moved; I discuss some about the watchman route problem and sketch why it is "NP-hard" for polygons with holes (reduction from planar TSP);
(5) doing the best we can with a GIVEN number of guards (i.e., to maximize area of coverage, etc);
(6) multiple coverage of points (e.g., we may want to have each point of the polygon seen by 2 or more guards, possibly with the views coming from substantially different directions)
(7) angle of incidence constraint: for good quality viewing of a wall, we want to see it approximately "head on" (nearly orthogonally).


Introduction to triangulations:
Properties of Triangulations of Simple polygons

I covered in detail: Lem 1.2.1, 1.2.2, Thm 1.2.3