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I want to find the convex hull of a set of points so I have been trying to understand the output of the QHull program(http://www.qhull.org/). I gave the co-ordinates of a square 2 # dimension

4 # number of points

$ (-1 ,1),( 1, 1),(-1 -1),(1 ,-1) $ and the output that I got was

The first line : 4

Remaining lines: $(2,1,0),(2,2,0),(2,3,1),(2,3,2)$.

I am trying to do the same using Petricht's implementation of QHull(http://lpetrich.org/Science/ computational geometry section) in mathematica but I do not understand the output formats of the two. Petricht's implementation gives:

 CH2QuickHull[{{-1,-1},{-1,1},{1,-1},{1,1}}]

Output: {1,3,4,2}

Can somebody please explain the two outputs ?

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So anyway I just figured it out. QHull gives the list of vertices that correspond to the surface that is part of the convex hull of the set of points. It reports non-simplicial surfaces as well. Petricht's algorithm on the other hand reports the simplicial decomposition of the convex hull.

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  • $\begingroup$ But how does one get the surfaces from the simplex like we get in qhull? $\endgroup$
    – Abhishek Pal
    May 14, 2017 at 7:14

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