We propose a mesh-based surface tracking method for fluid animation
that both preserves fine surface details and robustly adjusts the
topology of the surface in the presence of arbitrarily thin features
like sheets and strands. We replace traditional re-sampling methods
with a convex hull method for connecting surface features during
topological changes. This technique permits arbitrarily thin fluid
features with minimal re-sampling errors by reusing points from
the original surface. We further reduce re-sampling artifacts with
a subdivision-based mesh-stitching algorithm, and we use a higher
order interpolating subdivision scheme to determine the location
of any newly-created vertices. The resulting algorithm efficiently
produces detailed fluid surfaces with arbitrarily thin features while
maintaining a consistent topology with the underlying fluid simulation.