Favorite computational geometry videos:

Mesh Collapse Compression

Algorithm compresses a polyhedron into a vertex and string of integers that represents the polyhedron.
This representation, if truly as simple as the video suggested, is well suited for manipulation via genetic algorithms.  This gives me an idea for a game/a-life that I'm working on.

Metamorphosis of the Cube

This one was beautiful in its elegant simplicity.  It lacked the annoying and incomprehensible narration present in many of the others; it was able to convey the problem/solution visually.  Unfolding the cube
to a polygon, arbitrarily? partitioning the polygon then folding it up along the edges of the partition into a polyhedron.
Geodesics and Waves

Not quite sure what their point was, but very pretty.


Shortest Paths and Visibility Graphs

This chapter(15) explains the use of visibilty graphs to find a shortest route from P to Q, where P and Q lie in the plane.  In order that the problem is not trivial, also lying in this plane is S, the disjoint set of simple polygons that lie cluttered about between P and Q.  I think disjoint means that none of the polygons share vertices, but I'm not sure.  The motivation for solving this problem, as presented in the chapter, is to get a robot from its current position to some goal as quickly as possible.

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