Given a reference triangle Δ A B C, the trilinear vertex matrix of another triangle Δ A' B' C' is the 3×3 matrix whose rows are the trilinear coordinates of the vertices A', B', and C'. For example, Δ A B C has trilinear vertex matrix [1 | 0 | 0 0 | 1 | 0 0 | 0 | 1] and the orthic triangle has trilinear vertex matrix [0 | sec B | sec C sec A | 0 | sec C sec A | sec B | 0].

reference triangle | trilinear coordinates