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Figure 6.3. The choice of the grid cell size of a spatial hash has implications for the query
area of a fluid particle: larger cells (left) versus smaller cells (right). Smaller grid cell sizes
imply a smaller search volume, and thus a smaller amount of potential neighbors visited.
Note, however, that the amount of grid cells intersecting the volume increases, having a
negative impact on efficiency.
minimizes the chance of hash collisions. Choosing a larger number of hash buck-
ets is usually not a problem, as the memory footprint of the hash table is small
compared to the footprint of the list of fluid particles in the spatial hash.
The second choice pertains to the resolution of the spatial hash. The higher
the resolution of the spatial hash, the smaller the grid cells. This means the total
volume of grid cells intersecting the influence area of a particle decreases, so a
particle has a smaller volume to search for neighboring particles, as depicted in
Figure 6.3. For example, a grid cell size equal to 2 h means that 8 grid cells per
particle are queried for neighbors, with a total volume of (4 h ) 3 =64 h 3 , while
agridcellsizeequalto h implies that 27 grid cells have to be queried, with a
total volume of (3 h ) 3 =27 h 3 . The trade-off is that the amount of grid cells in-
tersecting the influence area of a particle increases, so the amount of hash indices
calculated per particle also increases. Whether the cost of calculating the extra
hash indices plus the associated cache misses of retrieving different hash buckets
is less than the efficiency gained by visiting a smaller number of potential neigh-
bors depends on the platform and characteristics of the simulated scenario, i.e.,
the average number of particles residing in a single hash bucket. Therefore, the
choice of spatial hash resolution should always be based on performance profiles
of the intended target platform.
The third choice that influences q is related to the fluid simulation itself. To
minimize q , we can increase the gas constant k used for determining the pres-
sure. This separates the fluid particles as much as possible. The fluid becomes
less compressible in central areas, which is beneficial for simulating water, but
it decreases the stability of particles on the fluid surface. Decreasing external
forces, like gravity pushing down on the fluid, may have a comparable effect, but
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