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Smallest Quadrilateral around polygon
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Do you need a fast and analytically correct solution? There's always the brute force approximation approach. For every set of four vertices, consider "all" (for an approximation, "many") lines that pass through them without intersecting the polygon at any other point, to create many sets of four lines. If a set of four lines forms a closed quadrilateral which has a smaller area than any previously found quadrilateral, store it as the best. Optionally, take the best one you find (or a few of the best ones), and try similar ones to refine the approximation.
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