The routine returns A which is the harmonic conjugate of F with respect to B and C.

If A, B, C, F are four collinear points such that the cross-ratio(AF, BC) = -1 (so that B and C divide AF one internally and the other externally in the same numerical ratio), the segment AF is said to be divided harmonically by B and C. The points A and F are called harmonic conjugates of each other with respect to B and C, and the four points A, F, B, C are said to constitute a harmonic range.

The command with(geom3d,HarmonicConjugate) allows the use of the abbreviated form of this command.