# Getting the coordinates for tripoints where three counties intersect

I'm trying to make a simplified triangulation of a US state (say Ohio) based on the counties. The way I accomplish this is to treat all boundaries, no matter how crooked, as straight lines whose vertices are all the points where three counties meet. How would I find the requisite coordinates from a shapefile for further processing?

RN I plan on getting the coordinates for use in Matlab for a personal algorithm that is based on Delaunay Triangulation, and I've attempted to use shapefiles describing said counties on Google Earth Engine and ArcGIS without much luck, unless I'm taking things in the wrong direction.

EDIT: The file is from http://ogrip-geohio.opendata.arcgis.com/datasets/7212b60cc5fc4949869995813628182c_12

and I am trying to use QGIS 2.18.14 to get the individual points. Is there an easy way to highlight and pinpoint all the places where at least 3 counties touch?

• Please Edit the question to specify what GIS software you are using and what you have tried. – Vince Jun 14 at 16:29
• @Vince got it, I'm planning on using these for Matlab – Sean Skyhawk Jun 14 at 16:39

I make a example for you:

I download, all polygons form ohio state in shapefile form: open in qgis like this:

I filter the information to select only 3 states:

1. right click
2. filter
3. coy this: "COUSUBFP" = '43554' OR "COUSUBFP" = '01000' OR "COUSUBFP" = '70898'

1. Know go to processing toolbox in the right and select centroids, to generate the points to make the delaunay triangulation

2. when i obtein the points. i run the next script in the console and obtain the middle point between the three countries.

``````layer = iface.activeLayer()
features = layer.getFeatures()

x = 0
y = 0

for f in features:
puntos = f.geometry().asPoint()
x = x + puntos.x()
y = y + puntos.y()

vlayer = QgsVectorLayer('Point?crs=epsg:4686&field=Punto:integer&index=yes', 'puntos' , 'memory')
points = []
points.append(QgsPointXY(x/3, y/3).asWkt())

prov = vlayer.dataProvider()

feats = [ QgsFeature() for i in range(len(points)) ]

for i, feat in enumerate(feats):
feat.setAttributes([i])
feat.setGeometry(QgsGeometry.fromWkt(points[i]))