Creating circle-like area that encompasses original polygon

Question

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.

Answer 1

An algorithmic solution, to be used with QGIS or other software:

1. Extract vertices of your polygon (white dots).
2. Draw circles of the desired distance around these vertices (red lines).
3. Where all circles overlap is the area you're looking for (yellow area).

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.