Above: A 1003 Houdini simulation up-resed to 8003 using our method. Mouse-over to see the original Houdini simulation.
We propose a method of increasing the apparent spatial resolution of an existing liquid simulation. Previous approaches to this
"up-resing" problem have focused on increasing the turbulence of the underlying velocity field. Motivated by measurements in the
free surface turbulence literature, we observe that past certain frequencies, it is sufficient to perform a wave simulation directly
on the liquid surface, and construct a reduced-dimensional surface-only simulation. We sidestep the considerable problem of generating
a surface parameterization by employing an embedding technique known as the Closest Point Method (CPM) that operates directly
on a 3D extension field. The CPM requires 3D operators, and we show that for surface operators with no natural 3D generalization,
it is possible to construct a viable operator using the inverse Abel transform. We additionally propose a fast, frozen core
closest point transform, and an advection method for the extension field that reduces smearing considerably. Finally, we propose two
turbulence coupling methods that seed the high resolution wave simulation in visually expected regions.