Image Processing Reference
In-Depth Information
Fig. B.4
Right-angled
triangle
For this particular problem it might seem to be faster to do it by hand, as above,
instead of using Eq.
B.28
. This might also be true for such a simple problem, but
in general using Eq.
B.28
is definitely more efficient. Recall that you just have to
define the matrix and vectors, then the computer solves them for you—independent
of the number of equations and unknowns.
When implementing linear algebra in software, it is highly recommended to ap-
ply a built-in library as opposed to implementing the solution from scratch. This
is especially true for linear systems with more than three dimensions, since these
require iterative solutions.
B.8
Right-Angled Triangle
In Fig.
B.4
a right-angled triangle is shown. A right-angled triangle is defined as
θ
1
=
θ
2
. The three points
A
,
B
and
C
define the corners of the
triangle. The relationship between the lengths of the three edges is defined using
Pythagoras' theorem:
90° and
θ
3
=
90°
−
−
AB
+
−
AC
=
−
BC
2
2
2
(B.30)
From trigonometry we have
=
−
AC
=
−
AB
=
−
AC
−
BC
−
BC
−
AB
sin
(θ
2
)
,
cos
(θ
2
)
,
tan
(θ
2
)
(B.31)
B.9
Similar Triangles
In Fig.
B.5
two triangles are present. The outer triangle defined by the three points
ABC
and the inner triangle defined by the three points
DBE
. If the two triangles
have the same angles, i.e.,
θ
1
=
θ
4
,
θ
3
=
θ
5
, and
θ
2
=
θ
2
, then the triangles are said
to be
equiangular
or
similar
.
If we look at the outer triangle then we know from trigonometry that
−
BC
sin
(θ
1
)
=
−
CA
sin
(θ
2
)
=
−
AB
sin
(θ
3
)
(B.32)
