Containment algorithms and Convex hull algorithms to check if a point is inside the d dimensional convex hull spanned by n vectors

Asked Jul 21 '23 at 23:45

Active Jul 22 '23 at 00:12

Viewed 27 times

For n of d dimension vectors, I wanted to check if a d dimension point was inside the convex hall spanned by the d dimension vectors.

There are algorithms to compute the Convex hull algorithms, but they were slow, and mostly for the lower dimension. In fact, it's more convenient to address this as a "containment question", where, for 2D, we were able to reduce the question to a simple algorithm with the complexity of O(n).

However, our purpose was mainly at higher dimension, specifically, the 2,4,6,10,12... of even dimensions.

The Wikipedia's introductions to higher dimension convex hall algorithms were very brief, and it seemed to stopped at 2001.

Is there any papers and updates about the higher dimension convex hull algorithms, and specifically the higher dimension containment algorithms?

edited Jul 22 '23 at 00:12

Dave

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asked Jul 21 '23 at 23:45

ShoutOutAndCalculate

Probably easiest to use linear programming. – David Eisenstat Jul 22 '23 at 16:22
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If you speak R, there's a function `inHull` in the package `GMOIP`. – Stéphane Laurent Aug 11 '23 at 01:48
@StéphaneLaurent Thank you!! I do speak R, but I'm using an arbitrary precision package(mpmath) in python, so it's a bit complicated. How fast is inHull(with a few thousand points)? – ShoutOutAndCalculate Aug 11 '23 at 06:25

Containment algorithms and Convex hull algorithms to check if a point is inside the d dimensional convex hull spanned by n vectors

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