# Divide skewed, irregular polygons into equal area sub-polygons

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### #1 Carri Marschner Posted 08 September 2010 - 04:14 PM

Carri Marschner

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I have six polygons of highly irregular shape (bits sticking off, scalloped edges, rotated so none of them are N/S aligned), and I need to subdivide them into different scales of sub-polygons of equalish area. I've been attempting to do this by putting a grid of points across them and building Theissen polygons around them, which would be ideal because it would match methodology used at other scales in this experiment.

I've tried both fishnet and Hawth's tools, and they both create a grid of points that's lined up N/S - not points that line up with the geometry of the existing polygons. If I built Theissen polygons around them, they would be of decidedly unequal area. Do you have suggestions on how to add a grid of points that will fit to the polygon to be filled, or another way to subdivide polygons into equal area?

Thank you for any of your thoughts on the subject.

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Carri Marschner
Cary Institute for Ecosystem Studies
Millbrook, NY
www.caryinstitute.org

### #2 Craig Jr Posted 10 September 2010 - 10:39 AM

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I have six polygons of highly irregular shape (bits sticking off, scalloped edges, rotated so none of them are N/S aligned), and I need to subdivide them into different scales of sub-polygons of equalish area. I've been attempting to do this by putting a grid of points across them and building Theissen polygons around them, which would be ideal because it would match methodology used at other scales in this experiment.

I've tried both fishnet and Hawth's tools, and they both create a grid of points that's lined up N/S - not points that line up with the geometry of the existing polygons. If I built Theissen polygons around them, they would be of decidedly unequal area. Do you have suggestions on how to add a grid of points that will fit to the polygon to be filled, or another way to subdivide polygons into equal area?

Thank you for any of your thoughts on the subject.

Hi Carri,
Have you checked out Jennes Enterprises? There are some free tools to create different shape grids: http://www.jennessen...peat_shapes.htm you can possibly create grids then split the polygons on your map.

Craig

### #3 Gretchen Peterson Posted 10 September 2010 - 12:06 PM

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One solution would be to convert your polygons to raster cells at a sufficient resolution to capture their original outlines well. Then get the centroid of every cell. The centroids could then be used as your grid of points.

Off the top of my head I can't remember if Arc has a specific function for returning centroids of cells, but I know that it definitely has one for returning centroid of polygons. Therefore, if you can't find the function for centroid of cell, you could always convert those cells back to polygons and get the centers of those. This is a rather complicated procedure but if you only have to do it once on a few polygons it might be the best.

### #4 Carri Marschner Posted 13 September 2010 - 08:27 AM

Carri Marschner

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Craig: the Jennes tools look very useful, and thank you for sending them on. I'm not sure how I'd get them to fill the polygons evenly without a lot of trial and error, but it's a possibility.

Gretchen, thank you for the workaround. This would probably work the best, but it still leaves me using human judgement to pick the best centroid for polygons of a given number/size per area. Since there doesn't seem to be a straightforward way to automate selection of areas to equalize the size of sub-polygons, we are going back to merging individual Thiessen polygons associated with the finer scale data collection by hand, weighting decisions for equalish area and similar numbers of sample points per subsection. It's not the best solution, but it'll do.

Carri
Carri Marschner
Cary Institute for Ecosystem Studies
Millbrook, NY
www.caryinstitute.org

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