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July 10th, 2010, 04:05 AM   #1
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Configuration centered at the origin

I have two configurations (set of points, each with its x and y coordinate) that should be compared.
In order to do this, I should perform the operation so that both configurations are centered at the origin.
I understand that the operations are to be performed on x and y axis, but I'm not sure how to do this.
Any suggestions are welcome.
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July 10th, 2010, 04:28 AM   #2
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Re: Configuration centered at the origin

How are they to be centred? Probably you want the centroid, but it depends what the points represent.
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July 10th, 2010, 06:43 AM   #3
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Re: Configuration centered at the origin

The configurations should have centroids at the origin. I've found this, but I'm not sure what it means:
"Subtract the mean vectors for the configurations from each
of the respective points in order to have the centroids at the
origin"
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July 10th, 2010, 07:13 AM   #4
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Re: Configuration centered at the origin

Suppose that one configuration of points is

Then the centroid will be at

So to place the centroid at the origin, subtract that centroid's coordinates from each point's coordinates:


For example take the triangle with vertices {(2,3), (5,-1), (3,). The centroid is at ((2+5+3)/3, (3+(-1)+/3) = (10/3, 10/3), so subtract 10/3 from every coordinate to centre the triangle at the origin.
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