Why quick hull algorithm works with farthest point in outside set of facet instead of working with point, which gives maximum volume for simplex, resultant from the facet and the point?
If points are uniformly distributed in space (general case), then largest volume point potentially provide greater amount of cutoff points (which is not above the newly created facets) on each step. Note, that N-dimensional oriented volume proportional to simple determinant, but 1-dimensional signed distance additionally requires calculation of (N-1)-dimensional oriented volume ("square") for the facet, wich, in turn, imply determinant calculation of two non-square matrices dot-product.
