Creating a ternary plot from Cartesian coordinates

Question

I am trying something - I want to estimate contributions from sources via a mixing triangle.

I have all data points in the Cartesian system (2 tracers measured) Now I need to transform my coordinates into trilinear coordinates. I was looking for a pre-existing function for that or another way to compute it on my own. Can someone help me? Is there something existing already in R? ggtern needs those trilinear coordinates if I did not misunderstood the manual.

Thanks, Nadine