# [GRASS-user] calculating centre of mass?

Vishal Mehta vishalm1975 at gmail.com
Tue Feb 28 12:22:09 EST 2012

```hi all,

i'm interested in estimating the centre of population of a city and how it
might have changed in 10 years. i have a vector polygon layer for each
year, which is the ward population. each layer has 198 polygons(wards) with
population attributes for each polygon(ward). The distribution of
population within a ward is not known, hence assumed uniform for now.

is there a module in GRASS for calculating this. i know we can calculate
geographic centroids, but was'nt sure if there was one for this kind of
thing.

Otherwise i could do it manually by extracting the geographic centroid of
each polygon, then the coordinates of the population centre would be:

xhat = sum(Pi Xi) /(sum(Pi)
yhat = sum(Pi Yi) / sum(Pi)

where Xi, Yi are each polygon i's geographic centroids; and Pi are each
polygon's population
coordinates are in UTM.

what do you think?

Thanks,
Vishal
--
Vishal K. Mehta, PhD
Scientist
Stockholm Environment Institute - US
133 D St Suite F
Davis CA 95616
www.sei-us.org
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