In the context of Geographical Information Systems (GIS) the
book offers a timely review Map Projections. The first chapters are
of foundational type. We introduce the mapping from a left Riemann
manifold to a right one specified as conformal, equiaerial and
equidistant, perspective and geodetic. In particular, the mapping
from a Riemann manifold to a Euclidean manifold ("plane") and the
design of various coordinate systems are reviewed . A speciality is
the treatment of surfaces of Gaussian curvature zero. The largest
part is devoted for mapping the sphere and the
ellipsoid-of-revolution to tangential plane, cylinder and cone
(pseudo-cone) using the polar aspect, transverse as well as oblique
aspect. Various Geodetic Mappings as well as the Datum Problem sre
In the first extension we introduce optimal map projections by
variational calculus for the sphere, respectively the ellipsoid
generating harmonic maps. The second extension reviews alternative
maps for structures, namely torus (pneu), hyperboloid (cooling
tower), paraboloid (parabolic mirror), onion shape (church tower)
as well as clothoid (Hight Speed Railways) used in Project
Surveying. Third, we present the Datum Transformation described by
the Conformal Group C10
(3) in a threedimensional Euclidean space, a ten parameter
conformal transformation. It leaves infinitesimal angles and
distance ratios equivariant.
Numerical examples from classical and new map projections as
well as twelve appendices document the Wonderful World of Map
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