Let each of f(a, b, c) and g(a, b, c) be a triangle center function or the zero function, and let one of the following three conditions hold. 1. The degree of homogeneity of g equals that of f. 2.f is the zero function and g is not the zero function. 3.g is the zero function and f is not the zero function. Also define three points with the following trilinear coordinates. A' | = | f(a, b, c):g(b, c, a):g(c, a, b) B' | = | g(a, b, c):f(b, c, a):g(c, a, b) C' | = | g(a, b, c):g(b, c, a):f(c, a, b).

reference triangle | trilinear coordinates