Creating circle-like area that encompasses original polygon

I'm starting with a caveat - I'm very new to this. I'm also using spectral tools in MS SQL Server, which probably isn't the best way either.

I'm attempting to make a polygon that represents an area where at any point along it's edge, a smaller polygon that is inside it is always fully encompassed by a radius of x. The reason I've used the term buffer is because that's kind of what I want, but instead of the buffer being to the nearest edge, I want it to the furthest edge.

I've explained that poorly I think. I want the smallest possible shape in which at any point inside it a radius of x would completely encompass a particular polygon.

So this is what I'm trying to get. The Blue area is my polygon, the Grey lines represent my desired radius (it's 150px in this case). I believe (but someone could prove me wrong) that at any point anywhere inside that dotted shape a Circle with a radius of 150px would completely encompass the blue shape.

But I can't work out how to draw that programmatically.

• can you draw a picture of what you want? Commented Aug 17, 2021 at 8:56
• Are you limited to spectral tools, or could you use another software-solution?` Commented Aug 17, 2021 at 15:38
• Are you looking for an algorithmic approach (step by step guide how to resolve this problem, software-indipendent) or for an actual implementation (code)? As an idea for a starting point: draw circles around each vertex of the polygon. Commented Aug 17, 2021 at 20:22

In QGIS, for this last step convert the circles to lines (`Menu Vector / Geometry Tools/Polygons to lines`), than use `Menu Processing / Toolbox / Split with lines`, splitting the circle-polygons with these lines.