Environmental Engineering Reference
In-Depth Information
Fig. 6. 3D trajectory in the action space.
Then the z position P
z
can be easily obtained as
M
P
P
(13)
z
x
where M is the vertical position of the pointer projected on the image plane.
With the 3D image features obtained, we can easily construct a virtual force function at both
directions. A virtual stroke force can be obtained as
2
2
FKa a
(14)
s
s
x
y
and a virtual push or pull can be considered as
(15)
FKa
p
p
z
where K
s
and K
p
are to be obtained from experiment and to be further adapted using self
learning algorithms,
a
x
and
a
y
are accelerations of pointer at x and y directions, while
a
z
is its
acceleration at the z direction. The variables
a
x
,
a
y
and
a
z
can all be calculated through second
order finite differentiation from P
x
, P
y
, and P
z
.
We should point out that a virtual force can be considered as a function of any subset of the
position variables and their derivatives. For example, a simple position based force feedback
can be obtained as
FKP
1
(16)
p
z
while a more sophiscated one may look like
3
ai
bi
F
KPKV
(17)
pi
i
vi
i
i
1
where K
pi
, P
i
, a
i
, K
vi
, V
i
, and b
i
should be determined by the specific program needs.
