An algorithm is demonstrated that finds an ordinary intersection in an
arrangement of $n$ lines in $\mathbb{R}^2$, not all parallel and not all
passing through a common point, in time $O(n \log{n})$. The algorithm is then
extended to find an ordinary intersection among an arrangement of hyperplanes
in $\mathbb{R}^d$, no $d$ passing through a line and not all passing through
the same point, again, in time $O(n \log{n})$.

Two additional algorithms are provided that find an ordinary or monochromatic
intersection, respectively, in an arrangement of pseudolines in time $O(n^2)$.