  Soft interfaces can mediate interactions between particles bound to them. The
force transmitted through the surface geometry on a particle may be expressed
as a closed line integral of the surface stress tensor around that particle.
This contour may be deformed to exploit the symmetries present; for two
identical particles, one obtains an exact expression for the force between them
in terms of the local surface geometry of their mid-plane; in the case of a
fluid membrane the sign of the interaction is often evident. The approach, by
construction, is adapted directly to the surface and is independent of its
parameterization. Furthermore, it is applicable for arbitrarily large
deformations; in particular, it remains valid beyond the linear small-gradient
regime.
