topic Are Multiple Ring Buffer Boundaries Inclusive or Exclusive? in Geoprocessing Questions

Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DonaldLund — Wed, 23 Mar 2016 18:10:57 GMT

So if you have Multiple Ring Buffer boundaries defined at say 20, 50, and 100 miles, which 'Ring' does a point at exactly 50 miles fall in? Are the boundaries inclusive or exclusive limits? I have scoured the internet for an answer and cannot find a single post that addresses this.

Thanks in advance for your comments.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 18:24:43 GMT

most classifications schemes in mathematics (ie random number generation, statistics and in programming languages are.. up to, but not inclusive. I would suggest you check it, but that depends upon how the geometry is represented. A buffer of 1 meter around a point is represented by a n-gon (360 sides generally) so inclusion can fail even if an entity is within the bounds.

If this is a mission critical test, you would be advised to select within some tolerance, then fine-tune your selection with actual euclidean comparisons. (ie 1 +/- 0.001 m, then do the actual math.)

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DarrenWiens2 — Wed, 23 Mar 2016 18:35:15 GMT

The boundaries are shared, it's not one or the other. A point on the boundary intersects both buffer geometries.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 18:43:41 GMT

The warning being to dissolve the buffers should be given so that the rings are indeed isolated. I would still check using point distance or simple calculation to confirm. In theory there will be duplicate rings then

Multiple Ring Buffer—Help | ArcGIS for Desktop

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

RuthBowers — Wed, 23 Mar 2016 18:48:26 GMT

This is a simple matter of selecting one of the rings in your output feature class and looking to see if the boundaries are inclusive or exclusive. It actually depends on how you set your parameters. That is--click on the Select Features tool, then click on one of the rings. You will see it highlight so you can see the area it covers.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 18:56:45 GMT

Is one wants a mutually exlusive buffer ring (ergo, a classification scheme), you need to do the dissolve the rings since selecting the inner ring will select both rings ie one extending from the center to 100 m and from the center to 200 m. If a true classification scheme for a multi-layers set of rings were implemented the boundary should not be shared otherwise you wouldn't have a a true mutually exclusive classification scheme. selecting the boundary between 0-100 and 100-200 should select one or the other, not both. Otherwise you have a 0-100 and and 0-200 classification scheme, which is valid, but not exclusive

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

RuthBowers — Wed, 23 Mar 2016 18:59:33 GMT

I think I misunderstood your question though. I believe if you did something like a spatial join, your point at 50 miles would create two spatial join records, one for each buffer polygon. That would leave it up to you to filter out your results. The thing that bothers me about this idea is that I have done such a thing many times, and I don't remember any issue with counts not adding up on the borders of buffers. If you have such data handy, it would be a simple thing to test.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DarrenWiens2 — Wed, 23 Mar 2016 19:08:18 GMT

Yes, the point on the boundary creates two spatial join records.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

RuthBowers — Wed, 23 Mar 2016 19:12:49 GMT

The more I think about this and remember... Yes, if you do a spatial join with a point on the border of two multi-ring buffers, your results will have records for "hits" with both buffers if you choose the parameter JOIN_ONE_TO_MANY. If you choose the parameter JOIN_ONE_TO_ONE, ArcGIS will rather arbitrarily choose one or the other, and you will only have one record. Is that the sort of thing you are wondering about?

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DarrenWiens2 — Wed, 23 Mar 2016 19:20:41 GMT

I'm guessing you want to make your legend something like the following, as you would do with most numerical classifications:

0 <= x < 20

20 <= x < 50

50 <= x < 100

but as (I think) we've shown, the "truth" with multiple ring buffers would be:

0 <= x <= 20

20 <= x <= 50

50 <= x <= 100

</beating a dead horse>

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 19:26:40 GMT

Darren, if you are using a select by location on those rings (assuming they are non-overlapping here) have you tried other rotation angles (fractional works best) to see if the ring is using some hidden 'tolerance' in its selection. Also, a calculation of the area of the ring inside a gdb and outside (shapefile) would give some clue as to the true geometry of the 'circle' n-gons will yield area less than expected based on the number of sides used to represent the circle.

if your suspicion of the 2nd classification scheme being the case, this should be noted in the help topic. I will flag it for clarification

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

ChrisDonohue__GISP — Wed, 23 Mar 2016 20:02:07 GMT

Also, won't a shapefile potentially provide a different result than a geodatbase, as the rings are not parametric curves in a shapefile (instead they are composed of many tiny straight line segments)?

(I'm not sure on this)

Chris Donohue, GISP

</Add Muddy Water>

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DarrenWiens2 — Sun, 12 Dec 2021 04:51:02 GMT

Here's another way that indicates that the boundaries are identical:

>>> point = 'mypoints' # a point
... pt_geom = [i for i in arcpy.da.SearchCursor(point,'SHAPE@')][0][0] # get geometry
... buff = pt_geom.buffer(20) # buffer point by 20m
... buff_line = buff.boundary() # convert to line
... ring_buffs_fc = 'buffs' # premade multiple ring buffers (10-20m, and 20-30m)
... ring_buffs = [i for i in arcpy.da.SearchCursor(ring_buffs_fc,['SHAPE@','distance'])] # get geometries
... mypoints = [] # points container, otional
... counts = [] # counts list
... reps = 100000 # how many times to test
... for i in range(reps): # start looping
...    new_point = buff_line.positionAlongLine(float(i)/reps,True) # create point at percentage along buffer line
...    count = 0 # reset counter
...    mypoints.append(new_point) # add point, optional
...    for ring_buff in ring_buffs: # test against ring buffers
...        if not ring_buff[0].disjoint(new_point): # see if disjoint
...            count += 1 # add to count
...    counts.append(count) # add count to list
... print (min(counts),max(counts)) # print min/max
... arcpy.CopyFeatures_management(mypoints,r'in_memory\points') # write points, optional
...
(2, 2) # each and every record intersects 2 ring buffers

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DonaldLund — Wed, 23 Mar 2016 21:09:44 GMT

This is EXACTLY what I'm talking about, wondering about, trying to do. I will do some analysis with my data set tomorrow to try to validate, although I suspect the likelihood of a floating point distance landing exactly at 50 miles, for example, is astronomical. One might have to test with a bogus data set to get conclusive results.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 21:19:21 GMT

are they true parametric rings or just calculated on an add need basis. I haven't seen the output of the geometry exported to some 'useable' format... at least with shapefiles, the n-gon representation was there and could be played with as could that for the ellipse. I test using euclidean calculations in situations of simple geometry constructs rather than using selectbylocation tools/code/methods or equivalent. This works easily for regular geometry, from triangles,rectangles, pent*, hex* n-gon circle and ellipse etc.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 21:34:21 GMT

Darren, I presume a spatial reference was defined for the layer since geometry errors have been noted when one isn't set (written on many times). I know what you are doing, but I will try yours against, exporting the buffer (aka.... circle) geometry and do a center to point on circle geometry. If this is done on a shapefile, then you get 'hit' points where the buffer is exact, but the interpoint shape is determined by a straight line, hence an n-gon. So if you do a 'within' or 'on' distance calculation it will fall short unless the distance is calculated to a 'hit' point. I haven't experimented yet with gdb featureclasses, so I am worried about positionAlongLine and how it operates. Does it generate the location from the equation of a circle? or are points pre-generated to define the shape..therein lies my question. Something else to add to the list. In any event, if the point does lie on the boundary of two shapes, that should be reported differently than 'within' or 'on', ... perhaps 'shared' would be better in keeping with classification principles, since the rings should represent locations on a continuum. thanks

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DarrenWiens2 — Wed, 23 Mar 2016 22:17:49 GMT

In my example above, if I calculate the distance between the points generated along the buffer line (20 m) to the original center point, they range from 19.999999999553737 to 20.000000000465356. However, they still "intersect" both geometries according to the software. I see what you're saying about n-gons, but if the software doesn't recognize it and the precision of the data almost certainly doesn't support it, then splitting hairs exactly with math doesn't do much good. Whether or not the buffers are true circles or n-gons, points falling on the boundary belong to both.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DanPatterson_Retired — Wed, 23 Mar 2016 22:34:43 GMT

Thanks Darren for the additional information.

Most aren't interested in the geometry and its implications... therein lies my interests.

Fuzzy boundaries would be a nice addition to vector world as they have added, to some degree, in raster world An overview of fuzzy classes—Spatial Analyst module | ArcGIS for Desktop

It opens up a whole new realm of questions that can be addressed in vector world that are now addressed solely in raster world.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

JoshuaBixby — Wed, 23 Mar 2016 22:54:56 GMT

Looking over the original question, I have some questions on terminology.

"Ring Buffer boundaries"
- By "ring", I assume you mean LinearRing. Then you mention "buffer", which gets us into Polygon realm. Then you mention "boundaries," which gets us back to a LinearRing. So what exactly are you asking about, a Polygon or a LinearRing?
"which 'Ring' does a point at exactly 50 miles fall in?"
- Fall in? That isn't really a standard term. Do you mean intersect, within? There are quite a few standard spatial predicates, "fall in" isn't one of them.
"Are the boundaries inclusive or exclusive limits?"
- Is this focused on the boundaries of a Polygon or LinearRing, both have boundaries.
- For geometry models that support OGC simple feature standards, the DE-9IM topological model describes the type of nuanced situation you are putting forward. That said, Esri's spatial predicates don't line up exactly with the DE-9IM in all cases.

I don't mean to get hung up on semantics, or sound pedantic, but being precise matters when talking about specificities like this question. Additionally, there isn't one universally correct answer. Different geometry models or geometry implementations can treat edge cases differently, so it is important to frame the question in the context of the geometry model you are interested in. Since you are posting on GeoNet, it is likely Esri's ArcGIS Desktop geometry model, but even that is complicated by Esri supporting OGC simple features.

Re: Are Multiple Ring Buffer Boundaries Inclusive or Exclusive?

DonaldLund — Thu, 24 Mar 2016 13:40:38 GMT

Polygons
Yes, intersect with
Yes, I am using ArcGIS Desktop

Basically, what I'm trying to ascertain is this: does a point at exactly 50 miles get assigned to and counted as a member of the 20 to 50 mile buffer, the 50 to 100 mile buffer, or both, when you spatially join a layer of xy data with a layer of multiple ring buffers.

Thanks