Geography Reference
In-Depth Information
Fig. 1.18.
Special map projection of the sphere: the Hammer equiareal modified azimuthal projection. This map
projection is centered to the Greenwich meridian, with shorelines, 30
◦
longitude, 15
◦
latitude graticule, Tissot
ellipses of distortion, “the world in one chart”
A map projection which is worth studying with all the machinery of deformation measures is
the
Hammer equiareal modified azimuthal projection of the sphere
2
S
R
+
presented in Fig.
1.18
.The
ID card of this special map projection is shown in Table
1.2
.
Tab l e 1 . 2
ID card of Hammer equiareal modified azimuthal projection of the sphere
(i) Classification Modified azimuthal, transverse, rescaled equiareal. 1.0
(ii) Graticule Meridians: central meridian is straight, other meridians are
algebraic curves of fourth order. The limiting meridians
form an ellipse.
Parallels: curved. equator is straight, other parallels
are algebraic curves of fourth order.
Poles of the sphere: points.
Symmetry: about the central meridians.
(iii) Distortions Product of principal stretches is one, equiareal,
equidista
n
t
map of th
e equator.
(iv) Direct mapping equations
x
=
c
1
R
√
2
√
1
−
c
4
sin
2
Φ
sin(
c
3
Λ
)
,
1+
√
1
−c
4
sin
2
Φ
cos(
c
3
Λ
)
c
2
R
√
2
c
4
sin
Φ
y
=
,
1+
√
1
−c
4
sin
2
Φ
cos(
c
3
Λ
)
c
1
=2,
c
2
=1,
c
3
=
2
,
c
4
=1,
c
1
c
2
c
3
c
4
=1
.
(v) Usage
Atlas cartography.
(vi) Origins
Presented by E. Hammer (1858-1925) in 1892. The special
Hammer projection has been generalized from the sphere
S
2
R
+
to the ellipsoid-of-revolution
E
2
A
1
,A
1
,A
2
by
Grafarend and Syffus
(
1997e
).
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