Digital Signal Processing Reference
In-Depth Information
(a) external force
(b) wave generation
(c) wave reflection
Fig. 4.
Wave reflection
Damping with Original Position.
The method proposed in this paper pro-
duces wave effect by keeping each cluster maintaining the original shape. How-
ever, the simple shape matching of each cluster produces long-lasting oscillation.
The actual water surfaces easily become calm when no more external forces
are exerted. In order to represent such property of water surface, we employed
damping with original shape. Each vertex are animated not only with the shape
matching force, but also with the restoration force back to the original position.
As shown in Fig. 5, the vertices are accelerated to move back to the original
position
x
0
i
, and the result animation shows plausible damping on the water sur-
face. Such behavior can be regarded a damping process that dissipates the wave
energy to restore the global water surface back to the energy equilibrium. The
restoration force is of course proportional to the deformation amount, and the
resulting behavior is naturally exponential function of the opposite direction of
the deformation. In our case, the deviation tendency of each particle was mea-
sured by the velocity of the particle, and the actual acceleration for each particle
i
is computed as
a
i
=(
x
0
i
− x
i
)exp(
−v
i
).
Fig. 5.
Damping with original shape: the deformed vertices
x
1
,x
2
,x
3
,x
4
incur restora-
tion force back to the original positions
x
1
,x
2
,x
3
,and
x
4
Wave Interference.
In order to produce realistic wave surface, interference of
different waves is very important. In the previous methods, the wave interference
was often ignored or required additional computation. However, our method
produces plausible wave interference without any additional consideration or
computation. figure to the left in Fig. 6 shows single wave while the figure to
the right shows the interference of two different waves. As shown in the figure,
the amplitude of the wave is computed by the average goal position of adjacent
clusters. This property easily enables the wavy interference.
Improved Cluster Shape.
The simple rectangular clusters cannot represent
various shape deformation so that the complex water surface cannot be produced.
