Average width of an irregular shaped buffer

[DanCrawford]

Hello!

I've been asked to calculate the average width of a set of irregular donut shaped buffers.  Is anyone aware of a tool that can accomplish this?  So far I've had to add to perpendicular lines from the inner boundary to the outer boundary at a given spacing then average their lengths.  This is obviously too time consuming though.

Another thing I tried was to take concentric circles and measure the distance from the outer circle to the inner circle.  I then take that length and make a ratio with the difference of the two circle diameters.  Now I convert my irregular buffer into polylines and use the line lengths to come up with the base for my ratio calculation (the larger perimeter less the smaller perimeter).  It seems to work but I'm really not a math whiz.

Any suggestions would be appreciated.
Thanks.

[DavidPike]

I would consider something along the lines of creating a point at the centroid of the donuts then creating a line due north with length of the maximum buffer distance, or using the donuts geometry to decide. Create points at intersections of that line and the donut's edges then create a line between those points and grab the line length.

Actually even better would be to clip that line to the buffer then take the shape length.

[DanPatterson_Retired]

A picture would help, but since you say you have an internal polyline, then I might suggest that you create the perpendicular transect lines along it at a dense spacing.  Intersecting the transect lines with the irregular shaped buffer with lines as the output will give you the data that you are looking for and you can carry on with your summary.

Rather than doing it manually,

Generate Transects Along Lines—Data Management toolbox | Documentation 

is the tool that would remove the manual creation of the perpendiculars.

An added advantage of using the transect lines, is that you can use them to slice the polygon buffers and garner information on sequential area and side lengths .

[DanCrawford]

My irregular buffers are the two polygons in the middle.
Inner perimeter = 5754 m

Outer perimeter = 7466 m

Area = 1,056,515 square meters

On the lower polygon, I've added perpendicular lines and taken the average (approx 200m).

The two concentric circles are my attempt at translating the perimeters into concentric circles to see if there is a relationship between the area and and radii.

Using an annulas calculator and the dimensions from the buffer, I get 160 m.

[DanPatterson_Retired]

bottom middle, the long line should be removed even though it is a perpendicular.

What you really need is a medial axis (aka, skeleton of your shape in question.  You use that polyline which would be between the other two lines, to shoot your perpendiculars from, one set towards the outer line and one set towards the inner. 

In the first instance, you could approximate this from doing a Delaunay triangulation of the shape and connect the barycenters of the triangles to form the skeleton.  Of course, the triangulation within the hole needs to be removes as do any triangles on the outer shell that have no left neighbors (those are part of the convex hull and can be removed.