CSC 274b-aa
Spring 2000
Courtney Christman
Sophomore, Class of 2002
CSC 274: Computational Geometry
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Problem Set 1
Tuesday, February 8, 2000

Textbook, page 9, ch. 1.1.4 (Exercises)

Ex. 1, Guarding the walls
Construct a polygon P and a placement of guards such that the guards see every point of @ P, but there is at least one point interior to P not seen by any guard.

Ex. 2, Clear visiblity, point guards

What is the answer to Klee's question for clear visiblity (Section 1.1.2)? More specifically, let G '(n) be the smallest number of point guards that suffice to clearly see every point inany plygon of n verticies. Point guards are guards who may stand at any pint of P; these are distinguished from vertex guards who may stand at any point of P; these are distinguised from vertex guards who may be stationed only at vertices. Are clearly seeing guards stronger or weaker thatn the usual guards? What relationship between G'(n) and G(n) follows from their relative strength? (G(n) is defined in Section 1.1.2) Does Fisk's proof establish [n/3] sufficiency for clear visibility? Try to determine

Ex. 3, Clear visiblity, vertex guards

Textbook, page 15, ch. 1.2.5 (Exercises)

Ex. 1, Sum of exterior angles

Ex. 2, Realization of triangulations

Ex. 3, Extreme triangulations

Ex. 6, Mouths of non-convex polygons