[R-sig-Geo] Dividing a polygon into several smaller polygons of different sizes

Guillermo Podesta gpodesta at rsmas.miami.edu
Thu Mar 12 15:58:22 CET 2009

```Dear list,

We are working on an agent-based simulation of agricultural production
in the Pampas of Argentina. Very briefly, we want to ask the list for
tips about how to divide a polygon (e.g., a county, or administrative
division) into several smaller polygons of different sizes. Each of
the smaller polygons would represent the geographic boundaries of one
simulated farm (or “pseudo-farm”).

A more detailed explanation of the problem

We are modifying the space (or environment) of our agent-based model
from a regular grid to a GIS space. In the current regular grid, each
point in the grid represents a simulated farm. In the GIS space, a
farm will be represented by a polygon describing its geographic
boundaries.

We have a shape file describing the contour of a county (or
administrative division); this county is the area to model. However,
we do NOT have actual cadastre information with the boundaries of all
farms inside the county. What we do have is information from the
Argentine Agricultural Census containing: (a) the number of farms (N)
inside the county (this is the _approximate_ number of farms we want
to simulate) and (b) a frequency distribution of farm sizes in the
county (e.g., 45 farms with areas from 50 to 99 hectares, 30 farms
between 100 and 150 hectares, and so on
).

Also, we can create a vector of N simulated sizes by using the size
frequency information in the Census and sampling inside each size
interval (e.g., if the Census says there are 3 farms between 500 and
1000 hectares, we can simulate their sizes as 536, 777 and 900
hectares).

Using the information above, we would like to create approx. N
simulated farms (or “pseudo-farms”) inside the county of interest,
including their boundaries. I guess another way of framing the
question is to say we want to “fit” N polygons of different sizes
inside a larger polygon (that represents the county where farms are
located). A couple of details that may help: (a) N does not have to be
exactly the number in the census (i.e., plus or minus 2-3% does not
matter), (b) we do not have to fill the entire county with farms
(empty areas can represent cities, forests, etc), although the
"non-farm" area cannot be huge.

Is there any way of doing this using the R spatial libraries?
Suggestions or pointers are most welcome and we thank in advance all

Regards!

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Guillermo P. Podestá
University of Miami Rosenstiel School of Marine & Atmospheric Science
4600 Rickenbacker Causeway Miami FL 33149-1098, USA
E-mail: gpodesta at rsmas.miami.edu
Voice:  +1.305.421.4142   Fax: +1.305.421.4622
http://www.rsmas.miami.edu/divs/mpo/people/Faculty/Podesta/index.htm

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