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suggested by (Colgate et al., 1995). In this perspective, one more interesting benefit of
the proxy method is the control of an object by an interface ... without force feedback.
In fact, the principle of decoupling allows zeroing out the force sent to the device,
while maintaining a control force in the simulation. This allows us to use a universal
control for any interface that determines positions (Meyer et al., 2002). Even without
force feedback, the operator can no longer disturb the virtual world with physically
impossible movements. 4 The difference in the positions of the device and the proxy
can be used to provide a feedback other than haptic (audio or visual) so as to indicate
that the movement is not allowed.
16.2.4 Modelling the environment for
haptic rendering
When an admittance type interface is used, the avatar is simulated physically because
its position is controlled by forces. When the virtual proxy technique is used, the posi-
tion of the avatar tries to minimise the distance from the position of the device by
dynamics or by optimisation. In both the cases, the collisions of the avatar are man-
aged, preferably, by contact methods. The geometrical definition of the environment
is enough for the calculation of haptic rendering. On the contrary, when a penalty
method is used during direct interfacing of a device in impedance mode, it is neces-
sary to add data such as penalty stiffness for all objects in order to characterise their
“hardness'' (or otherwise, use the same stiffness for all interactions). It should also
be noted that in case of a physical simulation of the environment, the avatar has an
imposed behaviour, whereas the other objects have a simulated behaviour. This implies
a specific management of this object.
To sum up, the use of geometric constraints coupled with dynamic equations is
sufficient for the algorithm of haptic rendering. Geometric modelling providing visual
rendering of an environment is used often. However, the result obtained generally
proves to be insufficient. In fact, as in the case of visual rendering, without the tech-
niques of normal-based shading or light incidence, the “facetisation'' of the object
becomes evident. If a rough geometric model is used, the rendering forces calculated
will be discontinuous at the borders of the polygons. For this purpose, we can draw
insight from the graphic shading techniques to create force shading. Similar to the
Phong shading technique, this involves interpolating the perpendicular from each inter-
nal point, as per the real perpendiculars of each vertex of the polygon (Ruspini et al.,
1997; Ho et al., 1999). The calculated forces of interaction are collinear to a perpen-
dicular line that develops progressively as per the position, which gives an impression
of a curve (see figure 16.7(a)). The forces felt at the angles are continuous, and the
surfaces are not felt to be completely even. Please note that this technique is specific to
point-based interactions and cannot be easily generalised for an avatar of any form.
Another solution consists of replacing the polygon-based models with implicit surfaces,
4 The idea of not considering the position of an interface and imposing another more coherent
position in the simulation is not new. The god-object was first proposed in a non-haptic context
(Dworkin et al., 1993) to transform an interface's discontinuous and unpredictable position into
a continuous movement that adjusts itself with the simulated environment.
 
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