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Abstract
We present a simple and physically inspired method to animate realistically
looking fire directly in 2D instead of along a 3D simulation.
This naturally reduces the complexity of the animation from O(n3)
to O(n2). The fire is represented as a 2D scalar density field located
on a plane facing the camera, and is advected under a 2.5D velocity
field. In our method, the apparent motion of the fire on the viewing
axis is mimicked by introducing vibrations in the velocity field. We
model these rapid vibrations as pressure waves found in compressible
fluids and therefore consider the full Navier-Stokes equations.
The equations can be solved in a single pass and our method entirely
runs on the GPU. A natural extension is to make use of this
method directly in screen space: instead of filtering down the fire’s
simulation grid in world space, we rasterize the fire’s source, and
perform the simulation on a coarser grid directly in screen space.
The results are continuously renewed 3D-looking fires computed
solely in 2D.
1 Introduction
It was noted in [Horvath and Geiger 2009] that the motion of fire
on the viewing direction is less important than the motion spanning
the viewing plane. This observation led us to incorporate the motion
of the fire on the third dimensional axis into a visually compelling
2.5D velocity field. In a similar mindset, [Rasmussen et al. 2003]
obtained a three-dimensional incompressible flow by combining a
set of two-dimensional simulation grids along a Kolmogorov spectrum
turbulence model which provides coherence on the third dimension.
Our method keeps a two-dimensional representation for
the velocity, but attempts to consider the apparent motion of the fire
on the third dimensional axis directly into the 2D velocity field. We
do so by exaggerating the compressibility effects of a fluid in order
to create large pressure waves, which tend to break the flames during
advection and create the illusion of depth in the fire’s motion. |
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