
24 Computing in Geographic Information Systems
FIGURE 2.2
Auxilary circle, the 2D projected ellipsoid
three variants of eccentricity of ellipse which has a value between [0,..,1]. The
formulae for first and second eccentricity ‘e’ of ellipse is given by
e
2
=
a
2
− b
2
a
2
(2.9)
⇒ a
2
e
2
= a
2
− b
2
(2.10)
⇒ b
2
= a
2
(1 − e
2
) (2.11)
The secondary eccentricity is denoted by e
0
and is given by
e
0
=
a
2
− b
2
b
2
(2.12)
Another computable geometric quantity of ellipse is flattening which is given
by the formulae first flattening ‘f’.
f =
a − b
a
(2.13)
The second flattening f
0
is given by the formula
f
0
=
a − b
b
(2.14)