Information Technology Reference
In-Depth Information
applications based on the use of an inner product
AB
where
a
1
a
2
a
p
b
1
b
2
b
q
.
B
:
q
A
:
p
×
2
=
and
×
2
=
(2.9)
Thus, we may plot the rows of
A
as the coordinates of a set of points and the rows of
B
give the directions of axes to be calibrated. Figure 2.6 shows the
i
th point
a
i
and the
k
th axis defined by
b
k
.
The inner product
a
i
b
k
is constant (
µ
, say) for all points on the line projecting
a
i
onto
b
k
. Therefore, the point of projection may be calibrated by labelling this point with
the value
µ
. This constant applies to the point of projection itself,
λ
b
k
. It follows that,
for the point
λ
b
k
to be calibrated
µ
, it must satisfy the inner product:
λ
b
k
b
k
=
µ
(2.10)
For fixed
b
k
, locus of all
points having the same
inner product
a
i
'
b
k
b
k
l
b
k
b
k
a
i
q
ik
a
i
O
λ
b
k
. The inner product has the value
Figure 2.6
The projection of
a
i
onto
b
k
is
µ
=
a
i
.
b
k
.cos
θ
ik
which is constant for all points on the line of projection. The
point
λ
b
k
may be given the calibration marker
µ
.
