Map projections

More about the book

In the context of Geographical Information Systems (GIS), this book provides a comprehensive review of Map Projections. The initial chapters lay a foundational understanding of mapping from a left Riemann manifold to a right one, focusing on conformal, equiaerial, equidistant, perspective, and geodetic projections. It explores the transition from a Riemann manifold to a Euclidean manifold and discusses the design of various coordinate systems, with particular attention to surfaces of Gaussian curvature zero. A significant portion is dedicated to mapping the sphere and ellipsoid-of-revolution to tangential planes, cylinders, and cones using different aspects. The text also examines Geodetic Mappings and the Datum Problem. Subsequent sections introduce optimal map projections through variational calculus for the sphere and ellipsoid, generating harmonic maps. Alternative maps for various structures, such as torus, hyperboloid, paraboloid, onion shape, and clothoid, are presented, highlighting their applications in Project Surveying. Finally, the book discusses Datum Transformation using the Conformal Group C10 (3) in three-dimensional Euclidean space, a ten-parameter conformal transformation that preserves infinitesimal angles and distance ratios. Numerical examples from both classical and contemporary map projections, along with twelve appendices, further illustrate the diverse and intricate world of Map Projections.