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I want to find how many of Polygon B can fit into Polygon A. I have a database of water bodies in the US as polygons of various unique shapes, 'Polygon A'. I have another layer with 'Polygon B' which is a circle.

Does ArcGIS have a tool to calculate how many times I could fill Polygon B into Polygon A? I would need there to be no overlap of Polygon B with itself and for there to be only complete Polygon B's within Polygon A (no half circles). A sample of the desired results in shown in the image below. Each circle is an individual object to quickly record how many objects fit in the waterbody polygon.

Right now, I have a process that utilizes the Intersect Analysis tool however, I am hoping there is a tool that would Fill all water body polygons with the maximum number of Polygon B. Polygon B is a simple circle and can be converted into a different layer type (polyline etc) if needed.

enter image description here

Vince
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Alvarado10
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  • It's bin packing problem I.e. https://gis.stackexchange.com/questions/185889/arcmap-fill-polygon-with-points-highest-possible-number-bin-packing-problem#186025 number of complete circles is objective function to maximize – FelixIP Nov 02 '23 at 00:01
  • You'd have to iterate, shifting and rotating the B polygons, like the circles generated from centroids a hexagon tessellation generated by Generate Tessellation, as in this Q&A, so no, an existing tool is unlikely. Not difficult, but possibly NP or NP-Hard https://gis.stackexchange.com/questions/461597/how-to-determine-the-number-of-circles-fitting-in-a-polygon-arcmap – Vince Nov 02 '23 at 00:19
  • I should note that it's easier to shift and rotate Polygon A over an oversize field of Polygon Bs, then, having found the optimal orientation with Select Layer by Location, shift and rotate the tessellation appropriately. – Vince Nov 02 '23 at 01:36

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