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I agree with you that what I want is a "smallest convex hull".
Looking at the other answers I'm not sure anymore. A convex hull means a banana shape would be represented as a semicircle. You seem to want a tight (not necessarily convex) vector graphic enclosing a sprite. I think you could achieve this by improving the convex hull (by replacing long edges with concave triangles until all edges are sufficiently "short" or "tight") Another problem I see are non-connected segments/territories . The shape of the USA would look very different if Alaska and Hawaii were included into just one hull ...
updatePointing to the next problem There is no unique solution for a concave polygon So starting from a convex hull and improving it till criteria are met is sensible.
Cheers Rolf
In reply to Re^3: Polygon Creation -- Request for Algorithm Suggestions (updated)
by LanX
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