Image Processing Reference
In-Depth Information
50%, would be placed in each of the cells. Figure 13.4 shows a typical example of a
single stream of energy in a single cell being distributed to its neighbors. Excluding
any dampening factor or any new energy added from user interaction, the system
will retain exactly the same amount of energy over each timestep. The P
ARTIAL
and M
AKE
R
ECT
procedures in the code listing provided in the Appendix to this
chapter also describe how partials are created through this displacement process.
i
+
1
∑
j
1
∑
+
F
i
,
j
,
t
=
C
p
,
q
,
F
p
,
q
,
t
−
1
,
P
(
C
i
,
j
)
(13.6)
p
=
i
−
1
q
=
j
−
1
i
+
1
∑
j
1
∑
+
L
i
,
j
,
t
=
C
p
,
q
,
L
p
,
q
,
t
−
1
,
P
(
C
i
,
j
)
(13.7)
p
=
i
−
1
q
=
j
−
1
i
+
j
1
∑
+
1
∑
R
i
,
j
,
t
=
C
p
,
q
,
R
p
,
q
,
t
−
1
,
P
(
C
i
,
j
)
(13.8)
p
=
i
−
1
q
=
j
−
1
E
i
,
j
,
t
=
F
i
,
j
,
t
+
L
i
,
j
,
t
+
R
i
,
j
,
t
(13.9)
Other parameters can also be adjusted to create different characteristics for a par-
ticular fluid profile. These include: controlling the “jitter”, or randomness of the
system, and clamping the maximum outflow for the cells within the grid. I also
experimented with a toroidal representation of the system where fluid energy wraps
around the edges of the screen, instead of bouncing off the edges (that is,
x
max
+
1
=
x
0
and
x
min
−
1
x
max
). Setting a maximum outflow parameter interestingly creates the
sense of ice cracking and melting when a particular threshold is exceeded. Different
settings of
viscosity
and
angularity
can create more or less turbulent behaviors. The
iterative nature of the system does in fact create a wide variety of fluid-like struc-
tures, including the creation of eddies, vortices, and turbulence. Figure 13.1 and
Figure 13.6 show examples of fluid systems with different fluid profiles defined by
different settings for the
angularity
and
directionality
parameters. The Appendix to
this chapter provides a code listing that describes how a cell is updated via querying
its neighbors.
Just as simulations for realistic films and video games do not feel constrained by
a perfect representation of the physics of a visual effect, so to should media artists
not feel constrained by a perfect representation of existing algorithms and equations
for a particular kind of effect. By creating a custom fluid system with a wide range of
parameter adjustments I was able to extend the aesthetic applicability and variation
of the fluid system to capture unusual behaviors not normally depicted with fluid
representations. Although the system appears realistic, it in fact sacrifices physical
accuracy in order to emphasize interactivity, expressiveness, and experimentation.
=
13.3.2
Flow Visualization
The main image processing scheme in the Fluid Automata system is based on a
feedback loop whereby a high-resolution background image is perpetually blended
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