The convex hull of a point set is the outer boundary of the smallest convex set that encloses the point set entirely.

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Extract 3D lower hull from convex hull

For my problem I need to extract the lower convex hull of a set of 3D points (X,Y,Z). In Matlab, one can find the convex hull using the convhull function as follows: K = convhull(X,Y,Z). Could ...
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Extreme points from constraint expression of convex space

I'm looking for the extreme points of the convex set $S\subset [-1,1]^{n\times 3}$ with $r\in S$ such that \begin{equation} r_{i} \ge r_{k} \iff i\ge k, \end{equation} where the first inequality ...
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Concave polygon 'hull' finding

I implemented an algorithm to find the alpha shape of a set of points. The alpha shape is a concave hull for a set of points, whose shape depends on a parameter alpha deciding which points make up the ...
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Convex polytope volume and centroid calculation

I have troubles imagining how to compute a volume and centroid of an n-dimesional convex polytope. For a polygon (especially for convex polygon) the area and centroid are described in (wiki) by $$ ...
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Why is my lower convex hull extraction algorithm not working?

Recently, I wrote an algorithm to obtain a delaunay triangulation of a random point set in $I=[-10,10]$x$[-10,10] \subset R^2$ by projecting these points onto the 3 dimensional paraboloid $z=x^2+y^2$, ...