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I don't see which part the wikipedia is contradicting it self, could you point out? I see all 4 definition which are all equivalent. What is your domain? I be

by chaoxu 12y ago

I don't see which part the wikipedia is contradicting it self, could you point out? I see all 4 definition which are all equivalent. What is your domain? I be interested in seeing the motivation of defining convex hull that way. Because conic hull and linear hull(span) would have very strange definitions. "Since the author has very clearly defined the terminology, and uses it consistently in a way which makes sense and does not cause confusion." Certainly, the author clearly defined the terminology, but it is still confusing to people who already know the terminology. It would be really strange if I suddenly define "circle" to be a triangle. "I assume the author needs terminology for both of the listed cases, and it makes sense for case 2 to be defined as a subset of case 1." I would have less problem if this is the case, but I could still suggest better ways to describe this. However, "convex hull" (and it's variation) appeared without "minimal" exactly 3 times. 1. One is express interests in convex hull, in the introduction sentence. 2. One is to define "convex hull". 3. One is to define "minimal convex hull".

learnstats2 12y ago
>I be interested in seeing the motivation of defining convex hull that way. For example, to computationally identify the likely boundary of something - a microscopic cell, or submicroscopic cellular component. Perhaps you are not as knowledgeable about this field as you think. I found it rude of you to simply trash the author's article when they spent time preparing an extremely good resource - and I don't agree that your correction was useful. You did the author a disservice on that site and should consider an apology.
- chaoxu 12y ago
  "For example, to computationally identify the likely boundary of something - a microscopic cell, or submicroscopic cellular component." I still don't know which field you are from, thus I kindly request you to give me a definite reference where convex hull is defined that way. I'm cornered in the world of computational geometry, and doesn't know how other fields use the word. In fact, I don't even know what definition you are talking about. You said 'elastic band', but do you mean the 'elastic band' that bounds the points freely and somehow still convex(which is what the "convex hull" meant in the author's article), or do you mean the tightened 'elastic band'. Thus asking for seeing this definition is important for me to even understand what you are talking about. "Perhaps you are not as knowledgeable about this field as you think." Perhaps. This is why having definitive references help. This is the top 5 links that contains the definition of convex hull when I searched "convex hull" in google. (These exclude the wikipedia(wikibooks) pages because I have already use them) 1. http://mathworld.wolfram.com/ConvexHull.html http://mathworld.wolfram.com/ConvexHull.html (The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S.) 2. http://doc.cgal.org/latest/Convex_hull_2/ http://doc.cgal.org/latest/Convex_hull_2/ (A subset S⊆ℝ^2 is convex if for any two points p and q in the set the line segment with endpoints p and q is contained in S. The convex hull of a set S is the smallest convex set containing S. ) 3. http://www.cs.uu.nl/docs/vakken/ga/slides1.pdf http://www.cs.uu.nl/docs/vakken/ga/slides1.pdf (For any subset of the plane (set of points, rectangle, simple polygon), its convex hull is the smallest convex set that contains that subset) 4. http://www.cs.jhu.edu/~misha/Fall05/09.13.05.pdf http://www.cs.jhu.edu/~misha/Fall05/09.13.05.pdf (Given a finite set of points P={p1,…,pn}, the convex hull of P is the smallest convex set C such that P⊂C) 5. http://geomalgorithms.com/a10-_hull-1.html http://geomalgorithms.com/a10-_hull-1.html (The most common form of this algorithm involves determining the smallest convex set (called the "convex hull") containing a discrete set of points.) All of the definitions are not equivalent to the authors, but equivalent(or a special case when restricted to finite set/R^2) to each other. I also have book excerpts if you really need them. "I found it rude of you to simply trash the author's article when they spent time preparing an extremely good resource" I did not have object of their work, just particular terminology. I pointed out specific flaws in the article and constructively offered how to fix them. In fact it took out a huge amount of my time in order to come up with equivalent definition that also preserve the author's intuition. My definition is not obviously equivalent to the ones I presented above. It requires a proof, and I can only prove the case when there is only a finite number of points, which works great because that's the exact case the author is thinking about. " - and I don't agree that your correction was useful. " If you always take convex hull of a set of point S to mean "a convex curve that bounds a set of points S" then you won't think the correction is useful because my definition doesn't equal yours. "You did the author a disservice on that site and should consider an apology." I do not agree.

by chaoxu 12y ago

learnstats2 12y ago

>I be interested in seeing the motivation of defining convex hull that way. For example, to computationally identify the likely boundary of something - a microscopic cell, or submicroscopic cellular component. Perhaps you are not as knowledgeable about this field as you think. I found it rude of you to simply trash the author's article when they spent time preparing an extremely good resource - and I don't agree that your correction was useful. You did the author a disservice on that site and should consider an apology.

chaoxu 12y ago
"For example, to computationally identify the likely boundary of something - a microscopic cell, or submicroscopic cellular component." I still don't know which field you are from, thus I kindly request you to give me a definite reference where convex hull is defined that way. I'm cornered in the world of computational geometry, and doesn't know how other fields use the word. In fact, I don't even know what definition you are talking about. You said 'elastic band', but do you mean the 'elastic band' that bounds the points freely and somehow still convex(which is what the "convex hull" meant in the author's article), or do you mean the tightened 'elastic band'. Thus asking for seeing this definition is important for me to even understand what you are talking about. "Perhaps you are not as knowledgeable about this field as you think." Perhaps. This is why having definitive references help. This is the top 5 links that contains the definition of convex hull when I searched "convex hull" in google. (These exclude the wikipedia(wikibooks) pages because I have already use them) 1. http://mathworld.wolfram.com/ConvexHull.html http://mathworld.wolfram.com/ConvexHull.html (The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S.) 2. http://doc.cgal.org/latest/Convex_hull_2/ http://doc.cgal.org/latest/Convex_hull_2/ (A subset S⊆ℝ^2 is convex if for any two points p and q in the set the line segment with endpoints p and q is contained in S. The convex hull of a set S is the smallest convex set containing S. ) 3. http://www.cs.uu.nl/docs/vakken/ga/slides1.pdf http://www.cs.uu.nl/docs/vakken/ga/slides1.pdf (For any subset of the plane (set of points, rectangle, simple polygon), its convex hull is the smallest convex set that contains that subset) 4. http://www.cs.jhu.edu/~misha/Fall05/09.13.05.pdf http://www.cs.jhu.edu/~misha/Fall05/09.13.05.pdf (Given a finite set of points P={p1,…,pn}, the convex hull of P is the smallest convex set C such that P⊂C) 5. http://geomalgorithms.com/a10-_hull-1.html http://geomalgorithms.com/a10-_hull-1.html (The most common form of this algorithm involves determining the smallest convex set (called the "convex hull") containing a discrete set of points.) All of the definitions are not equivalent to the authors, but equivalent(or a special case when restricted to finite set/R^2) to each other. I also have book excerpts if you really need them. "I found it rude of you to simply trash the author's article when they spent time preparing an extremely good resource" I did not have object of their work, just particular terminology. I pointed out specific flaws in the article and constructively offered how to fix them. In fact it took out a huge amount of my time in order to come up with equivalent definition that also preserve the author's intuition. My definition is not obviously equivalent to the ones I presented above. It requires a proof, and I can only prove the case when there is only a finite number of points, which works great because that's the exact case the author is thinking about. " - and I don't agree that your correction was useful. " If you always take convex hull of a set of point S to mean "a convex curve that bounds a set of points S" then you won't think the correction is useful because my definition doesn't equal yours. "You did the author a disservice on that site and should consider an apology." I do not agree.