Image Processing Reference
In-Depth Information
Fig. B.5
Two similar
triangles, i.e., triangles with
the same angles
For the inner triangle we have
−
BE
sin
(θ
4
)
=
−
ED
sin
(θ
2
)
=
−
DB
sin
(θ
5
)
(B.33)
Combining the two equations we get the following relationships between the two
triangles:
sin
(θ
2
)
=
−
BC
=
−
BE
sin
(θ
1
)
sin
(θ
2
)
=
sin
(θ
4
)
−
CA
(B.34)
−
ED
sin
(θ
5
)
=
−
BC
=
−
BE
sin
(θ
1
)
sin
(θ
3
)
=
sin
(θ
4
)
(B.35)
−
AB
−
DB
sin
(θ
5
)
=
−
CA
−
AB
=
−
ED
−
DB
sin
(θ
2
)
sin
(θ
3
)
=
sin
(θ
2
)
(B.36)
−
BC
=
−
BE
−
DB
=
−
BE
⇔
(B.37)
−
AB
−
DB
−
AB
−
BC
−
DB
−
AB
=
−
BE
−
DB
−
AD
−
BE
−
BE
⇔
=
⇔
−
BC
+
−
DB
+
−
EC
−
DB
+
−
BE
−
DB
=
−
BE
+
1
=
1
⇔
(B.38)
−
AD
−
EC
−
AD
−
EC
−
BC
=
−
BE
−
BC
=
−
EC
−
AD
=
−
EC
−
BC
⇔
⇔
−
AB
−
DB
−
AB
−
AD
−
AB
(B.39)
