My go-to source of map shape files is Natural Earth Data, which provides both vector and raster downloads with public domain licensing. I was an early user and found several bugs in their early vector maps, enough that I was listed as a contributor in the early release notes. By “bugs” I mostly mean places where the polygons didn’t conform to the SHP file requirements, such as winding in the wrong direction or intersecting themselves. I happened to be writing a SHP file parser at the time, so I had a lot of diagnostics active.
That was many years ago. Natural Earth Data has moved on quite well without me. I recently checked out the latest US county polygons. There are a few choices. I don’t know what “scale ranks” means here, so I went with the “without lakes” version which appears to also have greater detail based on the file size.
One visual diagnostic is to plot the coordinates of the points in the polygons (without drawing the edges) and color by the number of occurrences of that point. Two adjacent polygons should share exactly the same coordinates along the shared edges, so interior points should have at least two occurrences.
Here’s a scatter plot of all the points for the lower 48 states’ county border polygons. Those having a single occurrence are in blue.
The vast majority are on the boundary, but it looks like there are few stray singletons in the interior. Zooming in on the one in the northwest, with the polygon edges added:
It’s actually two singleton points where two county corners don’t quite coincide. I may need to file some new issues…
Update: Filed https://github.com/nvkelso/natural-earth-vector/issues/892 and https://github.com/nvkelso/natural-earth-vector/issues/893.
Having computed the occurrence counts, it’s also interesting to check out those points with high counts. Two (green) and three (yellow) occurrences are the norm, and there are a fair number of points with four occurrences or quadripoints, and there are even two quintipoints, in red here.
Being so rare, I should be able to confirm those.
The one in Florida was easy to confirm as five counties share a lake which contains the quintipoint. The other one was trickier to verify. I even consulted the Official Map of Louisiana PDF from the state’s web site, but it frustratingly had the place name “Hermitage” obscuring the critical intersection.
Google Maps generally shows one country border at a time, but I found someone who has added high-resolution county borders, and here is the junction in question.
So it’s not really a quintipoint, or even a quadripoint, but it’s not necessarily an error in the Natural Earth Data polygons. All map polygons have some limited resolution, and at their resolution, a quintipoint may be the most accurate representation.
Read more about map multi-points in the Wolfram Community post Beyond Four Corners, USA.
All this talk of “occurrence” reminds me I recently noticed this misspelling in the opening crawl for Dr. Strangelove.
