11 “Sphere to cylinder”: transverse aspect
Mapping the sphere to a cylinder: meta-cylindrical projections in the transverse aspect. Equidistant,
conformal, and equal area mappings.
Among cylindrical projections, mappings in the transverse aspect play the most important role. Although many worldwide adopted legal map projections use the ellipsoid-of-revolution as the reference
figure for the Earth, the spherical variant forms the basis for the Universal Transverse Mercator (UTM)
grid and projection. In the subsequent chapter, we first introduce the general concept of a cylindrical projection in the transverse aspect. Following this, three special map projections are presented:
(i) the equidistant mapping (transverse Plate Carr´ ee projection), (ii) the conformal mapping (transverse Mercator projection), and (iii) the equal area mapping (transverse Lambert projection). The
transverse Mercator projection is especially appropriate for regions with a predominant North-South
extent. As in previous chapters, the two possible cases of a tangent and a secant cylinder are treated
simultaneously by introducing the meta-latitude B = ±B 1 of a meta-parallel circle which is mapped
equidistantly. For a first impression, have a look at Fig. 11.1.
Fig. 11.1. Mapping the sphere to a (tangent) cylinder. Transverse aspect. Line-of-contact: Λ 0 = −60
◦ .
Mapping the sphere to a cylinder: meta-cylindrical projections in the transverse aspect. Equidistant,
conformal, and equal area mappings.
Among cylindrical projections, mappings in the transverse aspect play the most important role. Although many worldwide adopted legal map projections use the ellipsoid-of-revolution as the reference
figure for the Earth, the spherical variant forms the basis for the Universal Transverse Mercator (UTM)
grid and projection. In the subsequent chapter, we first introduce the general concept of a cylindrical projection in the transverse aspect. Following this, three special map projections are presented:
(i) the equidistant mapping (transverse Plate Carr´ ee projection), (ii) the conformal mapping (transverse Mercator projection), and (iii) the equal area mapping (transverse Lambert projection). The
transverse Mercator projection is especially appropriate for regions with a predominant North-South
extent. As in previous chapters, the two possible cases of a tangent and a secant cylinder are treated
simultaneously by introducing the meta-latitude B = ±B 1 of a meta-parallel circle which is mapped
equidistantly. For a first impression, have a look at Fig. 11.1.
Fig. 11.1. Mapping the sphere to a (tangent) cylinder. Transverse aspect. Line-of-contact: Λ 0 = −60
◦ .