Centerline Between Polygons

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05-14-2013 06:21 AM
MatthewHinton1
New Contributor II
I am working to find planning jurisdictions for my county.  Each city within the county has a 5 mile planning radius, except one which has a 3 mile radius.  I have applied the appropriate buffers around each municipality, but I'm hoping to find a centerline between each municipality in areas where their planning jurisdictions overlap. This seems like it would be simple, but it's got me stumped at the moment.
18 Replies
DuncanHornby
MVP Frequent Contributor
What do you mean by centreline? What if you have multiple overlapping polygons, what do you envisage in that scenario? May be you should upload a sketch of what you are after?
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MatthewHinton1
New Contributor II
I'm not authorized to upload my work, but I have four polygons, one for each city in my county; none of the polygons overlap.  I need to develop a line to divide planning jurisdiction equally between each city where jurisdicitons overlap (polygon).
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RichardFairhurst
MVP Honored Contributor
Well I can say for sure your thought that this is simple is incorrect.  It is a complex optimization problem with multiple solutions, which rarely has a clear path, since it depends a lot on the restrictions you want to apply to the solution possibilities.  Such problems are much less likely to have a tool that will accomplish the result in one step and you typically have to design a custom solution from combining multiple tools that meet your solution criteria.

For example, is achieving an equal distribution of area more important or an equal distance of separation between boundaries more important.  That one choice will have a profound affect on the possible solutions.  Equal area is much harder to achieve, because it requires comparisons among several separate output features all of which are unknown at the start, while equal distance from boundaries is much simpler, since it only requires comparisons between input boundariess which are known at the start.
MatthewHinton1
New Contributor II
So hypothetically, if I had two polygons that are 10x10 miles, five miles apart on the same line of latitude, there is no tool that would draw a line exactly between the two polygons at the 2.5 mile "centerline"?
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RichardFairhurst
MVP Honored Contributor
So hypothetically, if I had two polygons that are 10x10 miles, five miles apart on the same line of latitude, there is no tool that would draw a line exactly between the two polygons at the 2.5 mile "centerline"?


I have yet to see a square city, let alone a side by side pair of square cities.  If it were that simple I could do it with standard editing tools.  Besides boundaries of city spheres of influence are never determined by strict geometric means, they are always determined politically by a body like a Local Agency Formation Commission.  A straight line that puts a freeway completely in one jurisdiction's boundary when another city has a legitimate competing interest in that freeway will never be determined to be the legitimate boundary between them simply by considering the degree the line conforms to a geometric calculation.
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MatthewHinton1
New Contributor II
I'm working for a city government, so I understand all that. Our governments have agreed to divide jurisdiction by the midway line between cities.  That's obviously difficult to get by eyeballing.  I have estimated a center line between my city and surrounding cities, but I would rather have something more scientific and exact.
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RichardFairhurst
MVP Honored Contributor
I'm working for a city government, so I understand all that. Our governments have agreed to divide jurisdiction by the midway line between cities.  That's obviously difficult to get by eyeballing.  I have estimated a center line between my city and surrounding cities, but I would rather have something more scientific and exact.


Agreements like that only last while the line has not been drawn.  As soon as it is drawn and the political calculations begin, it will shift.  So I would not spend excessive time worrying about survey precision of your line.  I guarantee that once politicians actually see the line they will only look at where it falls relative to prime real estate like freeways and business districts and developable areas or expensive barriers like mountain ranges and rivers, etc. to decide how much they will honor that agreement before hiring a lobbyist or lawyer.
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RobertBorchert
Frequent Contributor III
You wrote that none of the polygons overlap.  then you write that you need a line to divide planning jurisdiction equally between each city where they overlap.


Well you could simply create a new set of polygons where the overlap occurs and draw a line equidistant between the edges of the polygon.

I'm not authorized to upload my work, but I have four polygons, one for each city in my county; none of the polygons overlap.  I need to develop a line to divide planning jurisdiction equally between each city where jurisdicitons overlap (polygon).
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RichardFairhurst
MVP Honored Contributor
The only tool that might help you if you have an Advanced license is the Collapse Dual-lines to Centerline.  But I believe this tool will fail even on actual road casings when the casing lines have widely varying widths over the distance between the ends of the two side by side lines.  Increasing the tolerance to the levels that would be required for your problem would also be likely to produce very strange results even if a line was created.
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