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 Projections.
Prof. Dr. Erik W. Grafarend, Stuttgart University, Stuttgart, Germany email: grafarend@gis.uni-stuttgart.de
Prof. Dr.-Ing. Rey-Jer You, National Cheng Kung University, Tainan, Taiwan Dipl.-Ing.
Rainer Syffus, ESG Elektroniksystem- und Logistik GmbH, Fuerstenfeldbruck, Germany