On 11 Feb 2000 08:54:52 +0100, Thomas Willhalm wrote:
>ron### [at] povrayorg (Ron Parker) writes:
>
>> On Thu, 10 Feb 2000 15:47:25 -0600, David Fontaine wrote:
>> >"SamuelT." wrote:
>> >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.  
>
>You probably meant |V|_1 = |V.x| + |V.y| + |V.z|. In Germany they call this
>the Manhattan metric, because standard block pattern aren't standard
>here.

Whoops, you're right.  Thanks for the correction.

>Perhaps we should start to distinguish between "metric" and "norm".
>"metric" denotes something that can be interpreted as a distance
>between to points. "norm" denotes something that can be interpreted
>as the distance of a point to the origin in a vector space.

Yes, my description was a little sloppy there.  I was thinking of the
closest centroid as the origin in each case, but of course it isn't.

-- 
These are my opinions.  I do NOT speak for the POV-Team.
The superpatch: http://www2.fwi.com/~parkerr/superpatch/
My other stuff: http://www2.fwi.com/~parkerr/traces.html

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