I want to find out if one polygon is inside another by giving an array of points of each vertex. Is there any simple way to do that?
Edit: it’s not enough to check whether minimum point of inner is greater than outer and maximum point for outer is less then inner. It’s not the sufficient condition. Proof:

I want to find out if one polygon is inside another by giving an
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Once you’ve checked that the minimum bounding box for polygon A lies inside that for polygon B I think you’re going to have to check each edge of A for non-intersection with all the edges of B.
This is, I think, a simple approach, but I suspect you really want a clever approach which is more efficient.