convex-polygon

Suppose I have a point cloud given in 6-dimensional space, which I can make as dense as needed. These points turn out to lie on the surface of a lower-dimensional polytope (i.e. the point vectors (x1, x2, ... x6) appear to be coplanar). I would like to find the vertices of this unknown polytope and my current attempt makes use of the qhull algorithm, via the scipy interface in Python. In the beginning I would only get error messages, apparently caused by the lower dimensional input and/or the many degenerate points. I have tried a couple of brute-force methods to eliminate the degenerate

An O(n) algorithm to detect if a line intersects a convex polygon consists in checking if any edge of the polygon intersects the line, and look if the number of intersections is odd or even. Is there an asymptotically faster algorithm, e.g. an O(log n) one? lhf's answer is close to correct. Here is a version that should fix the problem with his. Let the polygon have vertices v0, v1, ..., vn in counterclockwise order. Let the points x0 and x1 be on the line. Note two things: First, finding the intersection of two lines (and determining its existence) can be done in constant time. Second,