I have:
a triangle $ABC$
A linear function $f_0(X)$ where:
$f_0(A + s(B-A) + t(C-A)) = 1-s-t$
$s,t \in \mathbb{R}$
Can I express $\nabla f_0(x)$ as a linear combination of $A,B,C$?
I noticed that I can calculate the gradient by solving the system
$\nabla f_0(x) \cdot (B-A) = -1$
$\nabla f_0(x) \cdot (C-A) = -1$
.. but I'd like to avoid such a solution, as I was looking for something more immediate
Thanks.