#### 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