Definition of projective transformation

It is defined as four * * * line points on a plane, and the ratio of the sum of two simple ratios is the intersection ratio or complex ratio of these four points, which is recorded as, where the sum is called the base point pair and the sum is called the equinox pair.

define that if the intersection ratio of four points is called the sum of point pairs and harmonic separation point pairs, or the harmonic yoke of point pairs, it is also called the fourth harmonic point, and the intersection ratio is called the harmonic ratio.