To illustrate the method, we choose $ N=5$, and $ D=3$ so that $ N-D=2$ so that the data will always appear uniformly distributed when projected on a plane. Figure 5.8 shows the data as seen from the $ x_2,x_5$ plane after 4 and 20 iterations of the systematic method. The five facets of the valid region are caused by the manifold reaching the positivity limit of each of the five dimensions. Non-uniformity can be clearly seen for 4, but not for 20 iterations.
Figure: Visual uniformity test for $ N=5$, $ D=3$. The 2-D manifold as seen from the two dimensions $ x_2,x_5$ after 4 iteration (left) and 20 iterations (right).
\includegraphics[height=2.0in,width=2.0in]{tri2.eps} \includegraphics[height=2.0in,width=2.0in]{tri10.eps}
Later, we will discuss the difference between the systematic and the random-directions algorithm. But first, we must solve for the asymptotic mean.

Baggenstoss 2017-05-19