Sort points into a collection of columns whose x-coordinates are similar within tolerance. This is most commonly used to reverse-engineer an orthogonal grid of points from a flat, unordered list.

The sorting happens in three stages. First, all points are projected onto the sorting plane to yield the $(xʹ,yʹ)$ coordinates in the plane on which the sorting occurs. Then, all those points whose $xʹ$ coordinates are closer together than the fuzz input number are considered to be part of the same column of points. Finally, the points within each column are sorted using their projected $yʹ$ coordinates.