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Finding the furthest point location from the edge inside a polygon.

The_Claw

Is there a way to find a point or points (such as rectangle) inside a polygon that is the furthest from the edge of the polygon? Centroid and centroid inside don’t work.

An example of what I’m wanting to do is: I own a parcel of land and want to build a house as far from the property lines as possible, how can I find this point?

I'm using ArcGIS Desktop 10.6 advanced with access to the extra extensions.

I would think this would have multiple uses but haven't been able to search and find any info on a way to do this.

This is my first post, hopefully it is in the right place. Thanks

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DanPatterson

Centroid is the center of mass and should meet your condition if you have convex polygons, including a rectangle.

What example did you find that this was not the case?

Addendum

For concave polygons, the "thickness" may approximate what you are looking for, but it has a limited scope in complex concave polygons

How Zonal Geometry works—ArcGIS Pro | Documentation

The_Claw

Thanks for responding in the snapshot below you can see where centroid places the points. I tried a few different ways at creating centroids. In a circle or a rectangle it gives a point that is equidistant from the sides but in all other complex polygons it does not give a point that is furthest from an edge. An inverted buffer is about the closest I could get to what I was searching for but is not the actual solution I'm looking for. Thanks again.

DanPatterson

circle and rectangle are correct

the one in the middle is probably as close as you are going to get... it looks like an inscribed circle would yield centroids similar to the two points in the middle.

The two on the right are what my addendum was referring to... zonal geometry with the "thickness" option.

You would have to use a really small cell size. It will effectively find an inscribed circle and find the centroid. It represents the farthest distance. Fot the tow right one, that would be on the upper portion. For the bottom, flipped C, it would be on the bump-up on the lower branch... since it appears that the inscribed circle would be greater than in the other corners.

If this are parcels of land you are considering buying, I would skip the two on the right. As for the circle, fencing would be a real pain. The rectangle is popular and the one in the middle.... well, it is just interesting 🤔

The_Claw

I'm looking into the zonal thickness as it seems to give an accurate internal buffer distance of the greatest possibly value from the perimeter. Maybe with a few more steps I can get closer to what I'm looking for.

I'm surprised there isn't an easy answer. It seems like this query would have lots of real world applications that others would want to use. Especially military. I have a range and want to test munitions as far as possible from any other encroachments...etc....

Thanks again for your help.

DanPatterson

The only other options which yield similar results are to derive the medial axis of the polygon (vector processing) and roll a circle along it, stopping at the thickest point. The raster approximate equivalent ..."thickness" approximates this

DanLee

The following workflow can get you close:

Run Multiple Ring Buffer tool with a list of negative distances on your input parcels. The values in the list could be -1, -3, -5, -7, -10, - 20, -40, -60, -80, - 100, -120, -140, etc. The idea is to “shrink” each parcel polygon to a “central” area. The smaller the distance intervals are, the better accuracy will be achieved. Let’s call the output parcel_mBuffers.
Run Summary Statistics tool on parcel_mBuffers with ORIG_FID as the Case Field and specify “distance” field as the Statistics Field and “MIN” as Statistic Type. Name the output parcel_mBuffers_statsDIST.
Run Join Field tool to transfer MIN_distance from parcel_mBuffers_statsDIST to parcel_mBuffers through the common ORIG_FID fields.
Use Select Layer By Attributes to select the most inner buffers from parcel_mBuffers by the expression “distance = MIN_distance”. Now, any location inside a selected feature is farther away from the boundary of its containing parcel than anywhere outside the selected feature.

If you want one location for each parcel, run Feature To Point tool on the selected features with the Inside option. The result should be very close to what you need.

The_Claw

I'll give this a shot. I actually have over 300 polygons I'm attempting to find these interior points on and they range in size from 1,000 acres to over 500,000 acres. I'll see if there is anyway to batch these or come up with a system using the zonal thickness to narrow down the buffering. Looks like it will be some work.

Thanks

ThomasHoman

Good Morning,

Any thoughts on doing a buffer on the parcel with a negative value. Many locations might have a 20 ft setback or similar so entering -20 ft would give you the smaller useable footprint. Trying to get to single point would only be relevant for a very small structure like a birdhouse 😉

Just a thought.

Tom Homan

Gila County GIS

DanLee

I wondered about the size range of your parcels. You can narrow down the buffering by:

a. Starting with relatively "large" negative distances, say -1000, - 2000, -3000, etc. to run Multiple Ring Buffer on all parcels. Large and wide parcels will get the buffers while other parcels will be skipped.

b. Use the steps I described above to identify the most inner/central polygons (or points) for these parcels.

c. Use Select Layer By Location to select original parcels that contain the identified central polygons (or points) and invert the selection. Now you have the smaller parcels to process.

d. Repeat the above with relatively "smaller" negative distances, e.g. -100, -200, -300, etc. on the selected parcels. If Multiple Ring Buffer still skips features (see processing messages), finish the steps for identifying the inner polygons/points for this round and repeat the process with reduced distances, -5, -10, - 20, etc. for the remaining parcels.

Note: after the second round, if there are still remaining parcels to process, you would need to Append the identified inner (central) polygons to those identified previously. Then select parcels that contain them and switch selection to get the remaining parcels for processing.

With 3 iterations, you can cut down the total buffering time a lot already. You can put the steps in a model or script. Run it with a different list of buffer distances each round. Hope that's worth the trouble. 🙂

DanPatterson

If your polygons are that big, Zonal thickness will be the quickest and you certainly don't need to nail down the offset distances to sub-meter precision

Anonymous User

Hi:

The problem with zonal geometry is that it doesn't report the locations of those maximum values.

I recommend using Euclidean Distance, followed by Zonal statistics, followed by Con, to compute and extract those locations. The input to euclidean distance will be the negation of your polygons (i.e. all cells not in the polygons). Let me know if that makes sense or if I need to elaborate further.

-jt

GaryBarden

Not to get completely off track but this is the closest thread I could find to what I'm trying to figure out. I want to figure out the opposite of this. I have a point within a polygon and I want to find the distance to the furthest point on the edge of the polygon. I know I could use the measure tool and try to figure it out manually, but my polygon has a very irregular edge, and I need to run this against multiple polygons, so I figured I could merge the polygons and run it against the single point.

Anonymous User

HI Gary

Do you need to measure distance 'as the crow flies' (the distance from P to 'a' in the figure below) or staying inside the polygon (the distance from P to 'b')?

In the former case, you can use a da cursor and the python geometry apis to find the farthest distance from your query point. In the second case you can use the Spatial Analyst DistanceAccumulation and Con tools.

Here are a few more details.

In the first case, you could get a quick approximate solution by densifying the input polygon boundary and then looping over all vertices in the polygon to find the farthest vertex from the query point.

In the second case you need to create a raster that represents the background portion of the polygon. For example, for the "C" shaped polygon above, the background raster would be these gray cells. After rasterizing the polygon, the IsNull and CON tools can be used together to create it.

You can then specify the gray raster as the 'barrier' parameter to DistanceAccumulation and the point P as the source parameter. Your output 'accumulation' raster will be the distance from each interior cell to P (travelling on the shortest path to P inside the polygon). You can then find the location(s) that have that maximum distance by using the CON tool, along with the 'max' value from the output accumulation raster's statistics.

At Pro 2.9, the second case will be a bit easier: you'll be able to simply specify the polygon as the 'mask' environment for the DistanceAccumulation tool. You won't have to first create the complement as the barrier.

Let me know if this helps.

-Jim TenBrink

spatial analyst team

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