Spring 2000

Ileana Streinu

- Discussion of solutions to Problem set 1. For the extra credit problems, see bottom of the page.
- How to create an HTML applet with Cinderella.
- Create the drawing, save it in some file
**cindy1.cdy**. - From the File menu, choose Export as HTML. This creates the
HTML page, say
**page.html**which will invoke the cindy1.cdy file. - Put these two files (cindy1.cdy and page.html) in the public.html directory of your class account.
- Copy the
**cindyrun.jar**file from the 274b/handout directory into your public_html directory:

`cp ~274b/handout/cindyrun.jar .`

- That's it: try it now. Here's an example.

- Create the drawing, save it in some file

- Regarding the
solution for the first problem in the problem set (Construct a
polygon P and a placement of guards such that the guards see every point
of the boundary of P, but there is at least one point interior to P not
seen by any guard). In class, I showed the
triangle with a 'spike' at each vertex (and three guards)
resulting in a polygon with 6 vertices.

Can you get a solution with fewer (5 or 4) vertices? - Use Cinderella to work on the exercise for Extra Credit problem 1. Create 4-gons and 5-gons, and for each of them, try all the possible placements of few (1,2,3) vertex guards. For each vertex guard, draw (in Cinderella) the visible region (as a polygon, highlighted in Cinderella). Save the examples as Cinderella applets, and link them from your class web page, together with a conclusion to the question (whether it is or it is not possible to have an example with fewer than 6 vertices).
- Make an argument on how to move the vertex guards in Fisk's proof to be interior and cover everything (assuming clear visiblity). Be as precise as you can about where in the interior of the polygon you will move a vertex guard given by Fisk's proof.
- For problem 3 in section 1.1.4, prove or disprove that
**G'(n)= n**("Elif's conjecture"). - Extra Extra Credit Problem: Get information from Ileana on how to solve problem 4 in section 1.2.5 (How many distinct triangulations are there of a convex polygon of n vertices?) This involves remembering something you did in Discrete (Catalan numbers), and a bit of independent reading.

Last modified February 15, 2000.