Problem: You have a set of n ordered x,y points that form a contour of polygon A that may or may not be concave. You must create a new polygon B with m points such that:

1. all points in A are contained within B
2. m < n
3. B is the polygon with the smallest area
4. the algorithm must be reasonably fast and not overly complicated (i.e. no fast-fourier transforms lol!)

I'd like (3) to be the optimal solution but it doesn't have to be since I think this would make the problem NP-hard.

Have three solutions so far:

1. B is a square.
2. B is a circle with m points.
3. Construct B from A by removing concave points. Doesn't work with non-concave polygons however : /

Each solutions is terrible in its own way.