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This does make sense under author's definition: convex hull is defined as the boundary of any convex set enclosing the set of points. But in standard terminolo
by chaoxu 12y ago
This does make sense under author's definition: convex hull is defined as the boundary of any convex set enclosing the set of points.
But in standard terminology, convex hull of a set S is the smallest convex set containing the set of points. The convex hull is always minimal because it's unique.
- darkmighty 12y agoIt actually makes sense to call it a minimal convex hull, since you can construct and envelope, or hull, for a set of points that is convex but not necessarily minimal: e.g. a large square with edges (min{xi},max{xi}) along each direction i.
- jlarocco 12y agoI guess the problem is that the author sounds less credible saying "minimal convex hull," because that's the only type anybody cares anything about. In the computational geometry literature the phrase "convex hull" almost always implies the minimal, unique convex hull. Using the phrase makes it sound like he googled the algorithms for half an hour and wrote up an article about it.
- aledalgrande 12y agoThat's what I thought about convex hull too. Nobody would use it or implement it, if not for the minimal case.