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4.6. Discussion
Cs 100 200 300 400 500 600 700 800 900 1000
IPs 0.017 0.033 0.051 0.067 0.088 0.100 0.120 0.136 0.159 0.177
Table 4.1: Interest point detection computational times in milliseconds per character and per
frame. Here the number of potential interest points is the same as the number of characters.
of view and farther than a threshold distance from it, this is greatly reduced and depends on
population density. For the previous example discussed in Section 4.5.2, the computational
time for the interest point detection, per character and per frame, was of 36.00 microseconds.
Table 4.1 shows the interest point detection computational times in milliseconds per frame
and per character for various numbers of characters. We can see that the automatic interest
point detection can be done for hundreds of characters in real-time (almost 500). However,
due to the complexity of our method, the computational times for 1000 characters are prohibitive.
Nevertheless, the attention behavior animation of 1000 characters is not a necessity
since users would only perceive those behaviors in the foreground.
We have also compared our dedicated IK solver with a typical Jacobian-based IK approach
[Peinado et al., 2007]. To perform this comparison, the same skeleton has been used
in both cases. The Jacobian-based approach takes a mean time of 20 milliseconds per iteration.
If we consider that this method needs about 15 iterations before converging, this
amounts to approximately 300 milliseconds to solve a constraint. Our method takes a mean
time of 300 microseconds to solve a constraint. Moreover, since it is an analytical approach,
we do not need more than one iteration to solve it. The complexity of our IK solver is
therefore in O(n) with n being the number of characters.
It is to be noted that all steps undertaken in our method are on a single thread. The multithreading
capabilities of the computer on which the simulations are conducted are left aside
for other tasks such as collision detection or rendering.
4.6 Discussion
Score computation. The most time consuming step in our method is the interest point
computation. An interesting thing to do would be to use levels of detail (LOD) to reduce
the complexity of this phase. Characters farther than a threshold distance from the camera
may be assigned random interest points or no interest points at all since it will hardly be
noticeable where or what they are looking at.
Motion continuity. An important aspect which should be mentioned is motion continuity,
which we do not specifically ensure. However, we compute the displacement map at each
frame from the motion captured postures. As long as this sequence is free from discontinuities,
there is little chance for our final motion to present some.
Character trajectories. It is not the purpose of our method to edit the trajectories or to
perform collision avoidance. These aspects therefore depend on the crowd animation engine
which has been used to create the trajectories in the first place.
Motion capture validation. The values we used to distribute the rotation on the joints are
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