Pictorial proof of Poincare-Hopf theorem

Question

Background

I was studying the proof of Poincare-Hopf theorem from Milnor's Topology from the differentiable viewpoint. In particular, I hope to see why the sum of indices of a vector field on a manifold $M$ equals the Euler number. In Milnor's book, however, he refered to Morse theory, which I am not familiar enough to see what's going on (I know the proof though).

What I have understood

1. I understand that all vector fields have the same sum of indices.
2. I understand that we can change the differential manifolds to some underlying simplex.

Based on my understandings 1 and 2, to prove Poincare-Hopf it suffices to construct a vector field on an underlying simplex with the sum of indices being the Euler characteristic.

Question

I would like to request a picture of such constructions (as simple as possible) for 2 dimensional simplices that show Poincare-Hopf theorem in dimension 2, where the Euler characteristic being interpretted as $V-E+F$. Hopf in his "Vector fields on n-dimensional manifolds" did not include any picture. I am sure such proof can be illustrated in some good pictures, and hope someone has seen some and would point them to me. Thank you very much in advance!