Circle filling a polygon

teakplantation — Wed, 07 Dec 2022 15:50:36 GMT

For any given polygon in a feature class I would like to create the largest possible circle that fits within this polygon (see examples below); in case of the original polygon being a circle, the new circle would be identical to the original.

Is there a function in ArcGIS Pro to achieve this?

PS: the minimum bounding geometry tool can draw a minimum circle on the outside of each polygon (https://pro.arcgis.com/en/pro-app/latest/tool-reference/data-management/minimum-bounding-geometry.htm). I just need to achieve the circle within the polygon instead.

Re: Circle filling a polygon

JohannesLindner — Wed, 07 Dec 2022 16:18:08 GMT

AFAIK, there is no out of the box tool for that.

This thread lists a few algorithms the get an incircle: algorithm - Largest circle inside a non-convex polygon - Stack Overflow

I took one of the approaches:

tesselate the polygon with a Voronoi diagram (Thiessen polygons in ArcGIS)
find the node with the greates distance to the polygon's border, that's the center of the incircle

def create_incircle(polygon): add = arcpy.env.addOutputsToMap arcpy.env.addOutputsToMap = False # densify polygon to get rid of curves, which only have 2 vertices polygon = polygon.densify("DISTANCE", 10, 1) # extract vertices into a point fc vertices = arcpy.management.CreateFeatureclass("memory", "vertices", "POINT", spatial_reference=polygon.spatialReference) with arcpy.da.InsertCursor(vertices, ["SHAPE@"]) as cursor: for part in polygon: for v in part: cursor.insertRow([v]) # create Thiessen polygons thiessen = arcpy.analysis.CreateThiessenPolygons(vertices, "memory/thiessen") # intersect these with themselves to get candidate points test_points = arcpy.analysis.Intersect([thiessen], "memory/TestPoints", output_type="POINT") # get the point inside the polygon with the greatest distance to the polygon's boundary candidates = [] boundary = polygon.boundary() with arcpy.da.SearchCursor(test_points, ["SHAPE@"]) as cursor: for p, in cursor: if p.disjoint(polygon): continue candidates.append([p, p.distanceTo(boundary)]) center = sorted(candidates, key=lambda c: c[1])[-1] # buffer that point ith the distance to the boundary, return arcpy.env.addOutputsToMap = add return center[0].buffer(center[1]) # create the ouput fc incircles = arcpy.management.CreateFeatureclass("memory", "Incircles") arcpy.management.AddField(incircles, "FID", "LONG") # create the incircles with arcpy.da.InsertCursor(incircles, ["SHAPE@", "FID"]) as i_cursor: with arcpy.da.SearchCursor("TestPolygons", ["SHAPE@", "OID@"]) as s_cursor: for shp, oid in s_cursor: ic = create_incircle(shp) i_cursor.insertRow([ic, oid])

This is quite slow (1 - 2 seconds per feature), probably because the densification in line 5 adds lots of vertices. This can probably be optimized much, but it works as a quick-and-dirty approach. Sadly, it requires an Advanced license for the Thiessen polygons.

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Circle filling a polygon

Re: Circle filling a polygon