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Computational Geometry is the study of geometric problems from a computational perspective. Examples of problems include: computation of geometric objects such as convex hulls, dimensionality reduction, shortest path problems in metric spaces, or finding a small subset of points that approximates some measure of the whole set (i.e. a coreset).
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Recovering the slope of a digitized line
See Random Generation of Finite Sturmian Words by Berstel and Pocchiola for a proof that the feasible region of your LP has only three or four sides, as well as a simple algorithm for finding the poly …