“Ellipsoid-of-Revolution to Cylinder”: Oblique Aspect - Map Projections: Cartographic Information Systems - page 405

unknown coecients of the fundamental solution for the equations ( α ), ( β ), and ( γ )whichgovern
conformeomorphism by an equidistant map of the oblique meta-equator. In such a way, a boundary
value problem for the d'Alembert-Euler equations (Cauchy-Riemann equations) is defined and
solved. Finally, we show that special cases of the universal oblique Mercator projection for

2
A 1 ,A 2
are normal Mercator and transverse Mercator. In addition, we shortly outline the local reduction
of the universal oblique Mercator projection of

E

A 1 ,A 2 r giveninBox 16.1 and as an

E towards S

example plotted in Fig. 16.1 (Fig. 16.2 ).

S r , inclination i of a satellite orbit

Fig. 16.2. Universal Oblique Mercator Projection of the sphere

Box 16.1 (The universal oblique Mercator projection of the sphere

r . α,β : meta-longitude,
meta-latitude. L, B : longitude, latitude. Ω,i : longitude, inclination of the oblique meta-
equator).

S

x = rα =

(16.1)

= r arctan[cos i tan( L − Ω )+sin i tan B/ cos( L − Ω )] ,