# Are tesselation patterns an effective way of covering a shape?

Facebook searches within a circle. Initially, I thought I would be able to get all the businesses within a given circle, so if I made the radius big enough (e.g. the size of New York City), I could get all the businesses (e.g. all the hair salons). The problem is, Facebook limits the number I can return to 100 businesses per search. So even if I am doing a large area, it will cap it off. Therefore, a single circle will not work.

My initial idea was that, for any given shape, one should be able to cover that shape with circles in a tessellation pattern. Here's an example of what I'm envisioning:

Now suppose I have a shape like this:

I assume people have confronted this issue before.

Would this methodology be effective to cover it in circles?

• To prevent your question asking two questions and being too broad I think you should research any QGIS implementation separately. The term that I think you should search on is circle packing but hex binning may also be relevant. – PolyGeo Sep 23 '17 at 6:42
• @PolyGeo I don't see how hex binning would be doable tho. The issue is Facebook uses circles. I have no way of implementing a hexagonal patterned search – Stan Shunpike Sep 23 '17 at 7:01
• The problem is how big to make your circles, because small circles are inefficient and large circles would get the "first 100 results" returned. Perhaps start with one big circle and then subdivide into four circles if it hits the 100 result limit, applied recursively. – Spacedman Sep 23 '17 at 7:34
• My thinking is that once you've packed with circles then if you remove any overlaps between the circles I think you are left with hexagons. Its not something that I've tried - just an idea that may or may not be worth exploring. – PolyGeo Sep 23 '17 at 9:14
• Suppose I use hexagons. Is there a QGIS tool that will do that? – Stan Shunpike Sep 23 '17 at 22:49