  In this note, we derive an approximation for the mean curvature normal vector
on vertices of triangulated surface meshes from the Young-Laplace equation and
the force balance principle. We then demonstrate that the approximation
expression from our physics-based derivation is equivalent to the discrete
Laplace-Beltrami operator approach in the literature. This work, in addition to
providing an alternative expression to calculate the mean curvature normal
vector, can be further extended to other mesh structures, including
non-triangular and heterogeneous meshes.
