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4.2. Walking Motion Reconstruction
follow and the eyes partially re-center with respect to the head. Indeed, when we look at
something, our eyes move before the head, which itself moves before the spine joints. The
motion of each character is thus adapted for him/her to attend to the automatically defined
interest points in a smooth and natural way.
However, since our method uses character trajectories only in order to remain generic,
our first step is to reconstruct the character walking motions from those trajectories and
motion captured walking cycles.
4.2 Walking Motion Reconstruction
As basis to the motion, we use a walking cycle which was recorded by motion capture. The
motion we use is of a person walking on a treadmill at 3 km/h. The trajectories obtained
from the crowd simulation engine are recorded at a sample rate of approximately 30 fps but
this amount varies slightly from one frame display to another. In order to solve this problem
for the reconstruction of the walking motion, we first proceed to a temporal normalization.
Moreover, during the simulation, the characters do not always walk around at the same speed.
Their pace varies throughout the simulation, in particular during collision avoidance. To
remedy to this problem, we thus proceed to a speed resolution.
4.2.1 Temporal normalization
In order to obtain the trajectories at exactly 30 fps, we first calculate the slope of the straight
line going from the first position in time to the next one for each of the coordinates (x, y, z).
We do the same for each of the orientation coordinates. By using the equation of the straight
line, we can then determine which would be the value of the second coordinate at a specific
time t (every 30 th of a second in our case).
xi = a(ti − ti−1)+xi−1
xi being the interpolated value to be found, a, the slope, ti, the next non-normalized time
value, ti−1, the previous normalized time value, and xi−1, the value at the previous normalized
time. We then repeat this process between each pair of consecutive points. The first
point being, in each case, the one which has just been calculated.
4.2.2 Speed resolution
The trajectories that we output from the crowd simulator vary in time in the matter of speed.
As an example, when a collision is to be avoided between two pedestrians, one can slow
down and the other speed up. Since we use a base motion of someone walking at 3 km/h,
the movement of the legs does not match with the displacement to be done. In order to solve
this, we have to determine, at each time step, at which speed the character is moving from
the trajectory values. Then, as we know the distance which is traveled within one walking
cycle at 3 km/h, we can determine the distance which should be traveled at the calculated
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