Geography Reference
In-Depth Information
F
Mixed Cylindric Map Projections
Mixed cylindric map projections of the ellipsoid-of-revolution. Lambert projection and
Sanson-Flamsteed projection, generalized Lambert projection and generalized Sanson-
Flamsteed projection. The mapping equations and the conditions. Vertical coordinates and
horizontal coordinates, horizontal weighted mean and vertical weighted mean. Deforma-
tion analysis of vertically/horizontally averaged equiareal cylindric mappings. Cauchy-Green
deformation tensor and principal stretches.
The
mixed spherical map projections
of equiareal, cylindric type to be considered here are based
upon the
Lambert projection
and the sinusoidal
Sanson-Flamsteed projection
. These cylindric
and pseudo-cylindrical map projections of the sphere are generalized to the ellipsoid-of-revolution
(biaxial ellipsoid). They are used in consequence by two lemmas to generate a horizontal (a ver-
tical) weighted mean of equiareal cylindric map projections of the
ellipsoid-of-revolution
. Its left-
right deformation analysis via further results leads to the left-right principal stretches/eigenvalues
and left-right eigen-vectors/eigenspace as well as the maximal left-right angular distortion for
these new mixed cylindric map projections of ellipsoidal type. Detailed illustrations document
the cartographic synergy of mixed cylindric map projections.
Mixed cylindric map projections of the sphere are very popular projections, for instance, those
equiareal cylindric projections named after
Foucaut
(
1862
)or
Nell
(
1890
)and
Hammer
(
1900
).
The variants are the horizontal or vertical weighted means of the Lambert equiareal projections
and the equiareal pseudo-cylindrical mapping of sinusoidal type which is also known as Sanson-
Flamsteed projection of the sphere. In this chapter, let us exclusively aim at mixed cylindric map
projections of the ellipsoid-of-revolution.
Section F-1.
In Sect.
F-1
, we derive the conditions which must be fulfilled for a pseudo-cylindrical equiareal map
projection of a biaxial ellipsoid and the general form of ellipsoidal equiareal pseudo-cylindrical
mapping equations of Box
F.2
.
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