8P-s-Tf1 9th point Tangent

Given the 8 reference points P1, …, P8 and a random point P.
8P-s-Tf1(P) is the tangent at P to the unique cubic defined by the nine points P, P1, …, P8.

See picture with description from Ref-63, p. 207 in the French language from Roger Cuppens.

8P s Tf1 9th point Tangent