We present a novel method to interpolate smoke and liquid simulations in
order to perform data-driven fluid simulations. Our approach calculates a dense
space-time deformation using grid-based signed-distance functions of the
inputs. A key advantage of this implicit Eulerian representation is that it
allows us to use powerful techniques from the optical flow area. We employ a
five-dimensional optical flow solve. In combination with a projection
algorithm, and residual iterations, we achieve a robust matching of the inputs.
Once the match is computed, arbitrary in between variants can be created very
efficiently. To concatenate multiple long-range deformations, we propose a
novel alignment technique. Our approach has numerous advantages, including
automatic matches without user input, volumetric deformations that can be
applied to details around the surface, and the inherent handling of topology
changes. As a result, we can interpolate swirling smoke clouds, and splashing
liquid simulations. We can even match and interpolate phenomena with
fundamentally different physics: a drop of liquid, and a blob of heavy smoke