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.