Relative Convex Hull
In discrete geometry and computational geometry, the relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside a simple polygon or a Rectifiable set, rectifiable simple closed curve. Definition Let P be a simple polygon or a rectifiable simple closed curve, and let X be any set enclosed by P. A geodesic, ''geodesic'' between two points in P is a shortest path connecting those two points that stays entirely within P. A subset K of the points inside P is said to be ''relatively convex'', ''geodesically convex'', or ''P-convex'' if, for every two points of K, the geodesic between them in P stays within K. Then the ''relative convex hull'' of X can be defined as the intersection of all relatively convex sets containing X. Equivalently, the relative convex hull is the minimum-perimeter weakly simple polygon in P that encloses X. This was the original formulation of relative convex hulls, by . However this definition is complicated by the need t ...
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