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Divide irregular polygon into equal areas by angle

Question asked by knkeeley on Jan 15, 2018
Latest reply on Jan 17, 2020 by stolstov-esristaff

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I have an irregular polygon feature that I need to split into x number of equal area features. I need to be able to have the divisions be something other than north/south or east/west.

Example:

The black polygon in this case needs to be divided into 3 equal area polygons. I manually split these, but I need it to be more precise and the splits need to be aligned in parallel to each other. They need to be able to be calculated with an angle/rotation specification, and not just north/south or east/west.

What I have tried:

This excellent code is the closest I have gotten to splitting an irregular polygon up into equal areas. Unfortunately, it only runs for north/south or east/west lines. I can't figure out how to rotate it and I don't have enough coding experience/time to efficiently edit it for my needs.
Fishnet Tool (as suggested by this, this, this, and this) and this has an angle of rotation. However, this creates a grid, but not equal areas. Also, it is for the feature extent not shape.
I cannot use the Parcel Fabrics tool (as suggested by this, this, this, and this) as I don't have the necessary licensing for it.

It really blows my mind that this isn't a tool that exists/is readily available.

Any advice/suggestions is welcomed. Or, if you really want to be a super hero, edit the code so I can specify an angle for rotation. Thank you very much!

Dan_Patterson

Jan 15, 2018 1:54 PM

Correct Answer

for the hero that wants to take it on, it is far easier to rotate polygon by the desired rotation angle, proceed with Alex's implementation, then rotate result back.

This will work with projected coordinates. Take the polygon, subtract the centroid value from the polygon points (ie a translation to the origin). Rotate by your desired angle (rotation). Do the work (rotate the reverse) and translate back to the original location.

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Dan_Patterson

Jan 15, 2018 1:54 PM

for the hero that wants to take it on, it is far easier to rotate polygon by the desired rotation angle, proceed with Alex's implementation, then rotate result back.

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knkeeley @ Dan_Patterson on Jan 16, 2018 6:30 AM

Thank you so much, Dan!

I don't know why it didn't occur to me to manually rotate it, run the tool, and then rotate it back. That works perfectly. You're the hero I needed but not the one I deserved.

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dkwiens

Jan 15, 2018 2:12 PM

I'd stick to editing Alex Tereshenko's code.

The main thing to edit is the template line coordinates used for cutting the polygons:

pnt_arr.add(arcpy.Point(x_min, y_max)) # top left
pnt_arr.add(arcpy.Point(x_min, y_min)) # bottom left

Suppose you want a cut line 45 degrees from NW to SE. You'd change the coordinates to:

x_diff = math.tan(math.radians(45)) * (y_max - y_min)
pnt_arr.add(arcpy.Point(x_min - x_diff, y_max))
pnt_arr.add(arcpy.Point(x_min, y_min))

... then keep trying cutting as you go right. Like picture below (maybe makes it more confusing...).

Unfortunately, I don't believe there's any way to avoid coding on this one. You'd also have to do some extra coding to accommodate all possible line angles.

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knkeeley @ dkwiens on Jan 16, 2018 6:31 AM

The picture does indeed make it better! Thanks for your thinking on this. I'll play around editing the code with this soon!

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KKramer-esristaff

Jan 16, 2018 1:21 PM

For anybody who runs across this thread and is looking for this functionality, please see Split irregular polygons into equal parts, add your vote and any specific user requirements in the comments.

This idea is Under Consideration for inclusion as a geoprocessing tool in ArcGIS Pro.

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knkeeley @ KKramer-esristaff on Jan 16, 2018 1:26 PM

This is great to know! Thanks, Kory. Definitely looking forward to having this integrated.

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stolstov-esristaff

Jan 17, 2020 7:27 PM

ArcGIS Pro now has this tool to divide polygons into equal areas:

Subdivide Polygon—Data Management toolbox | ArcGIS Desktop

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7 Replies

Dan_Patterson Jan 15, 2018 1:54 PM
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Correct Answer
for the hero that wants to take it on, it is far easier to rotate polygon by the desired rotation angle, proceed with Alex's implementation, then rotate result back.
This will work with projected coordinates. Take the polygon, subtract the centroid value from the polygon points (ie a translation to the origin). Rotate by your desired angle (rotation). Do the work (rotate the reverse) and translate back to the original location.
1 person found this helpful
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- knkeeley @ Dan_Patterson on Jan 16, 2018 6:30 AM
  Mark Correct
  Correct Answer
  Thank you so much, Dan!
  
  I don't know why it didn't occur to me to manually rotate it, run the tool, and then rotate it back. That works perfectly. You're the hero I needed but not the one I deserved.
  Like • Show 1 Like1
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dkwiens Jan 15, 2018 2:12 PM
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Correct Answer
I'd stick to editing Alex Tereshenko's code.

The main thing to edit is the template line coordinates used for cutting the polygons:
```
pnt_arr.add(arcpy.Point(x_min, y_max)) # top left
pnt_arr.add(arcpy.Point(x_min, y_min)) # bottom left
```
Suppose you want a cut line 45 degrees from NW to SE. You'd change the coordinates to:
```
x_diff = math.tan(math.radians(45)) * (y_max - y_min)
pnt_arr.add(arcpy.Point(x_min - x_diff, y_max))
pnt_arr.add(arcpy.Point(x_min, y_min))
```
... then keep trying cutting as you go right. Like picture below (maybe makes it more confusing...).

Unfortunately, I don't believe there's any way to avoid coding on this one. You'd also have to do some extra coding to accommodate all possible line angles.
1 person found this helpful
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- knkeeley @ dkwiens on Jan 16, 2018 6:31 AM
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  The picture does indeed make it better! Thanks for your thinking on this. I'll play around editing the code with this soon!
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KKramer-esristaff Jan 16, 2018 1:21 PM
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For anybody who runs across this thread and is looking for this functionality, please see Split irregular polygons into equal parts, add your vote and any specific user requirements in the comments.
This idea is Under Consideration for inclusion as a geoprocessing tool in ArcGIS Pro.
1 person found this helpful
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- knkeeley @ KKramer-esristaff on Jan 16, 2018 1:26 PM
  Mark Correct
  Correct Answer
  This is great to know! Thanks, Kory. Definitely looking forward to having this integrated.
  Like • Show 1 Like1
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stolstov-esristaff Jan 17, 2020 7:27 PM
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ArcGIS Pro now has this tool to divide polygons into equal areas:
Subdivide Polygon—Data Management toolbox | ArcGIS Desktop
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