Re: Voronoi applet?

Paul Burchard (burchard@CS.Princeton.EDU)
Mon, 23 Dec 1996 02:26:18 -0500

Chuck Biehl wrote:
> Actually, I had in mind that there would be straight Voronoi edges
> which would be tangent to the point of contact of the two expanding
> circles. This actually makes more sense in terms of the meaning of the
> VD, I think.

This is great -- questioning the very definitions and axioms on which
the theory is built! How about getting students involved in the debate?
They might come up with a lot of creative situations where something
vaguely like VD is useful, but where standard VD won't apply.

I don't want to taint the discussion too much...but before shutting up I
will offer one "thought experiment" relating to your concept of steadily
expanding spheres/circles of influence. Consider 2 points, and make
point A's circle of influence expand ever-so-slowly while point B's
blasts out like an explosion. By the time point A's circle is barely
visible, point B's circle will have already blasted past A and be about
to hit the moon.

As you can see, the region that point A has any chance of influencing
can be no more than some tiny blob around A. The exact shape of this
blob may not be obvious, but what is clear from this experiment is that
the boundary of the region cannot be a straight line! (If you don't
like the results of this experiment, how should its implicit assumptions
about the meaning of "expanding spheres of influence" be changed?)