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POalgorithm like convex hull, but return the lower area polygon containing all points
 

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    1. PTQuestion
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    1. USAriel Larraburu
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    1. COWhat you ask is not simple. The issue is that there are a number of ways that you can get that result for the point set given, but each way may give different results. It might help to define what you mean by "smallest polygon", which could mean area, perimeter or something else. What you asking for is also likely to approach being NP-hard as the number of points desired that are not on the convex hull is increased. It is equivalent to the traveling salesman problem if all points are used and the perimeter is to be minimized.
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      1. POalgorithm like convex hull, but return the lower area polygon containing all points
      1. USNuclearman
    2. COHave you looked at [alpha shapes](http://doc.cgal.org/latest/Alpha_shapes_2/index.html)? But you'll need to provide an alpha parameter though. [Here](http://cgm.cs.mcgill.ca/~godfried/teaching/projects97/belair/alpha.html)'s perhaps, a better visual.
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      1. POalgorithm like convex hull, but return the lower area polygon containing all points
      1. USrrufai
    3. COAlpha shapes require that you provide a global alpha parameter to control the size of the alpha ball. This may not however be what you want. You might want to also look into conformal alpha shapes that take the local point distribution into account, so the alpha adjusts kind of to the local point distribution. [Here](http://rd.springer.com/article/10.1007%2Fs00371-006-0027-1)'s a reference.
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      1. POalgorithm like convex hull, but return the lower area polygon containing all points
      1. USrrufai
 

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