Game Development Reference
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etc.) synchronise these two loops. A multiprocessor hardware architecture is essential
in this type of approaches. There are several strategies to “copy'' the environment. It is
possible to extract a local force field, a local geometry from the environment or even
try, if possible, to reproduce this environment at a lower scale:
Approaches by force field
On the basis of a given position of the device, we canmark out a force field, i.e. associate
a force to every position taken by the interface around the initial position The first
approach consists of calculating the Jacobian of the force
J =
x (Cavusoglu &
Tendisk, 2000). Any difference
x ( t ) with respect to the initial position creates a force
F ( t )
= F 0 + J ×
x ( t ). It is also possible to use the temporal coherence by doing a
linear extrapolation in the course of time, on the basis of the last two forces F n and
F n 1 calculated by the simulation at the instants t n and t n 1 :
t n
F ( t )
= F n +
( F n F n 1 )
t n
t n 1
It is also possible to use spatial coherence by inspecting how the forces have changed
with respect to the last two positions and by extrapolating for the current position
(Picinbono & Lombardo, 1999). If P n 1 and P n are the two last positions taken into
account by the simulation and P ( t ) is the current measured position, then this position
is projected on P ( t ) on axis ( P n 1 P n ). Then the force returned is:
P ( t )
P n
F ( t )
= F n
( F n
F n 1 )
P n
P n 1
In general, the interpolations calculated on a spatial base are more stable than the
purely temporal interpolations. The calculations involved in these intermediate meth-
ods are moderate and the simulation does not provide additional information (except
in the case of Jacobian which needs to be calculated).
Geometric approaches
A simple model of the local geometry of the zone in which the avatar is located
is extracted from the environment. Adachi et al. (1995) use a plane tangent to the
point of collision, whereas Mark et al. (1996) suggest using several planes. Balaniuk
(1999) describes a general approach that makes it possible to approximate the local
geometry by a parameterised surface, and applies this formula in the case of a plane
and a sphere (see figure 16.9). These techniques being restricted to a convex geom-
etry, Mendoza and Laugier (2000) suggest recovering (using the graphics hardware
(Lombardo et al., 1999)) the triangle closest to the avatar as well as the adjacent tri-
angles from the environment. It is then sufficient to calculate the collisions with this
Multiresolution approaches
For deformable objects, certain models suggest creating a local model from a level of
lower resolution of a mechanical model (Astley &Hayward, 1997), or by reducing and
linearising a model (Cavusoglu & Tendisk, 2000). It is possible to counterbalance the
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