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?