Thursday, March 23, 2000
Model: Tuesday, March 28, 2000.
Duality and mini-presentation: Tuesday, April 4, 2000, in class
Model of a convex polytope
Construct a 3d model of a convex polyhedron (your choice, but
please do not all do the cube or tetrahedron!).
Dual of Convex Hull Algorithms
This assignment is a bit special: it is not just about
solving a problem or two, but also about presenting your
solution. It is meant to give you some practice, useful for the final
presentation of your project at the end of the semester.
In class, I explained the point/line duality and we've seen that
questions about configurations of points dualize to questions
about line arrangements. The purpose of this homework assignment
is to have each of you "implement" these ideas by dualizing one
of the 2d convex hulls algorithms we did in class, to an
algorithm computing the upper envelope of a set of lines.
Translate the corresponding algorithm into an algorithm for
computing the upper envelope of a set of lines. Present the
algorithm, in the dual setting, in a short 10 minute presentation
on Tuesday, April 4. The presentation should include a very short description
of the problem, a dictionaru of dual concept used for dualizing
the algorithm, and a presentation of the algorithm in parallel
with the original primal one.
Since this is practice for the final presentation, you can use
whatever form of presentation you feel more comfortable with. It
can be done using just plain blackboard and chalk, or using an
overhead projector (just let me know ahead of time so that I
bring one to class), or from computer slides (e.g., html files,
Powerpoint - whatever). You can include an applet, if you find
one on the web illustrating your algorithm.
I also ask you to write the main ideas in the form of an HTML
file, and draw the pictures in Cinderella. Link it from your web
page. If two students are assigned the same algorithm, they both
should do it, separately: this is meant as individual work.
Last modified March 21, 2000.