🚀 go-pugleaf

I have received many answers referring to "Computational Geometry,
an introduction" by Preparata and Shamos. Thanks.
It looks to me that he methods proposed by this book can be applied
in R^2 only. Applying these methods in higher dimensions would 
increase the complexity of the algorithm (exponential complexity).
For instance, given n+1 points in R^m (n > m) and assume that the
origin is one of these points, the number of m-1 dimensional facets
of the convex hull is nCm which creates a combinatorial problem.
Is there a method that can check for the inclusion of a point in
a polytope in R^n that does not need an exponential time ? (I mean
methods that depend on ray shooting).
Thanks.
-Samer