On Thu, 10 Feb 2000 15:47:25 -0600, David Fontaine wrote:
>"SamuelT." wrote:
>
>>     It was made with MegaPov (Superpatch works too).
>
>Oh! See, I was looking fot this "metric" thing and could not find it. What
>does it do?

It changes the distance metric used to determine which centroid is
closest.  metric 2 is the default, which corresponds to what's known
as the 2-norm, |V|_2=sqrt(V.x^2+V.y^2+V.z^2).  This is also usually
called the Pythagorean Theorem.  metric 1 is commonly called the 
"taxicab distance" as it's the distance a taxicab would drive if it 
had to follow city streets in a standard block pattern.
It's |V|_1=V.x+V.y+V.z.  In general, POV raises each component of
the vector to the specified power, then adds them together, then 
raises them to the reciprocal power (i.e. 1/2 if the metric was 2.)

In the limit as the metric approaches infinity, the norm is equal to
whichever of V.x, V.y, or V.z is largest.  In the space between 2 and
infinity, neat things can happen.

Now ask me about form. :)

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