Map Projections

Cartographic Information Systems

Author: Erik W. Grafarend,Rey-Jer You,Rainer Syffus

Publisher: Springer

ISBN: 3642364942

Category: Science

Page: 935

View: 2340

In the context of Geographical Information Systems (GIS) the book offers a timely review of 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 to the 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 are reviewed. 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.

Flattening the Earth

Two Thousand Years of Map Projections

Author: John P. Snyder

Publisher: University of Chicago Press

ISBN: 9780226767475

Category: History

Page: 365

View: 4946

As long as there have been maps, cartographers have grappled with the impossibility of portraying the earth in two dimensions. To solve this problem mapmakers have created hundreds of map projections - mathematical methods for drawing the round earth on a flat surface. Yet of the hundreds of existing projections, and the infinite number that are theoretically possible, none is perfectly accurate. Any projection inevitably distorts the geography it portrays. Flattening the Earth is the first detailed history of map projections since 1863. John P. Snyder discusses and illustrates the hundreds of known projections from before 500 B.C. to the present, emphasizing developments since the Renaissance - when the concept of a round earth gained acceptance - as mapmakers used increasingly sophisticated mathematical techniques to create ever more accurate projections. He closes with a look at the variety of projections, simple and complex, made possible today by the speed and power of computers. This book includes 170 illustrations, including outline maps from original sources and modern computerized reconstructions. The text is not mathematically based and is accessible to non-specialists, but a few equations are included to permit the more technical reader to plot some projections. Snyder also provides tables summarizing the features of nearly 200 different projections and listing those used in nineteenth- and twentieth-century atlases. As a survey of most known map projections, a discussion of cartographic technique, and a historical analysis of the development of map projections, this book will be an important resource for cartographers, geographers, and historians.

Datums and Map Projections for Remote Sensing, GIS, and Surveying

Author: Jonathan Iliffe

Publisher: CRC Press

ISBN: 9780849308840

Category: Science

Page: 150

View: 6403

A practical guide for those working with spatially referenced data and the problems that may be associated with datums and map projections. The book focuses on solving the problems encountered when combining data from different sources, and explores possible short cuts.

Cartographic Science

A Compendium of Map Projections, with Derivations

Author: Donald Fenna

Publisher: CRC Press

ISBN: 9780849381690

Category: Technology & Engineering

Page: 504

View: 3239

Geographic books routinely introduce map projections without providing mathematical explanations of projections and few delve into complex mathematical development or cover the breadth of projections. From basic projecting to advanced transformations, Cartographic Science: A Compendium of Map Projections, with Derivations is a comprehensive reference that offers an explanation of the science of cartography. The book is a compilation of more than a hundred map projections, from classic conics to contemporary transformations using complex variables. Starting from widely described geometric projecting onto flat paper, cylinder, and cone and then progressing through several layers of mathematics to reach modern projections, the author maximizes the application of one layer of complex mathematics before continuing on to the next. He also supplies numerous one-page tutorials that review terms and methodologies, helping minimize the challenges of unfamiliar mathematical territory. Divided into four parts, the first section examines the shape and size of the Earth, then proceeds to investigate the means for relating the curved surface to a flat surface, and addresses scaling. It goes on to cover pertinent principles of projection including literal projecting, true but synthetic projections, secantal projections, pseudocylindrical projections, and pseudoconical projections, as well as the other variants of more serious projections. The book concludes by looking at factors influencing Mean Sea Level and notes the cartographic aspects of current developments. Cartographic Science: A Compendium of Map Projections, with Derivations explains the mathematical development for a large range of projections within a framework of the different cartographic methodologies. This carefully paced book covers more projections, with gentle and progressive immersion in the mathematics involved, than any other book of its kind.

Map ProjectionsTheory and Applications

Author: Frederick Pearson, II

Publisher: CRC Press

ISBN: 9780849368882

Category: Technology & Engineering

Page: 384

View: 8376

About the Author: Frederick Pearson has extensive experience in teaching map projection at the Air Force Cartography School and Virginia Polytechnic Institute. He developed star charts, satellite trajectory programs, and a celestial navigation device for the Aeronautical Chart and Information Center. He is an expert in orbital analysis of satellites, and control and guidance systems. At McDonnell-Douglas, he worked on the guidance system for the space shuttle. This text develops the plotting equations for the major map projections. The emphasis is on obtaining usable algorithms for computed aided plotting and CRT display. The problem of map projection is stated, and the basic terminology is introduced. The required fundamental mathematics is reviewed, and transformation theory is developed. Theories from differential geometry are particularized for the transformation from a sphere or spheroid as the model of the earth onto a selected plotting surface. The most current parameters to describe the figure of the earth are given. Formulas are included to calculate meridian length, parallel length, geodetic and geocentric latitude, azimuth, and distances on the sphere or spheroid. Equal area, conformal, and conventional projection transformations are derived. All result in direct transformation from geographic to cartesian coordinates. For selected projections, inverse transformations from cartesian to geographic coordinates are given. Since the avoidance of distortion is important, the theory of distortion is explored. Formulas are developed to give a quantitative estimate of linear, area, and angular distortions. Extended examples are given for several mapping problems of interest. Computer applications, and efficient algorithms are presented. This book is an appropriate text for a course in the mathematical aspects of mapping and cartography. Map projections are of interest to workers in many fields. Some of these are mathematicians, engineers, surveyors, geodicests, geographers, astronomers, and military intelligence analysts and strategists.

Choosing a Map Projection

Author: Miljenko Lapaine,E. Lynn Usery

Publisher: Springer

ISBN: 3319518356

Category: Science

Page: 360

View: 7921

This book offers a much-needed critical approach to the intelligent use of the wide variety of map projections that are rapidly and inexpensively available today. It also discusses the distortions that are immanent in any map projection. A well-chosen map projection is one in which extreme distortions are smaller than those in any other projection used to map the same area and in which the map properties match its purpose. Written by leading experts in the field, including W. Tobler, F.C. Kessler, S.E. Battersby, M.P. Finn, K.C. Clarke, V.S. Tikunov, H. Hargitai, B. Jenny and N. Frančula. This book is designed for use by laymen. The book editors are M. Lapaine and E.L. Usery, Chair and Vice-Chair, respectively, of the ICA Commission on Map Projections for the period 2011-2015.

Map Projection Transformation

Principles and Applications

Author: Qihe Yang,John Snyder,Waldo Tobler

Publisher: CRC Press

ISBN: 9780748406678

Category: Technology & Engineering

Page: 384

View: 8430

With the advance of science and technology, there have been breakthroughs in the field of classical research and methods of map projection. Among these, computer science and space science have had the greater influence upon the field of research and the formation of a working body of map projection, developing them in breadth and depth. This book reflects several aspects of the development of modern mathematical cartography, especially the theory and methods of map projection transformation. Map projection transformation is an area of research in mathematical cartography newly developed over the last 25 years. It is widely used in surveying and computer-assisted cartography, data processing for information systems, and the transformation of data from space, remote sensing, and other space sciences. The development of map projection transformation not only expands new areas of research on mathematical cartography, but it also further develops the applied area with the creation and application of map projection transformation software and mapping mathematics bases on the computer.

An Introduction to the Mathematics of Map Projections

Author: R. K. Melluish

Publisher: Cambridge University Press

ISBN: 1107658489

Category: Mathematics

Page: 154

View: 4714

Originally published in 1931 as a guide for mathematically-minded geography students, this book addresses the mathematical theories underlying the construction of maps. Melluish reviews the problems inherent in depicting a sphere on a flat plane and the various ways in which these problems can be solved by varying projections. This book will be of value to anyone with an interest in the mathematical underpinnings of maps.

Small-Scale Map Projection Design

Author: Frank Canters

Publisher: CRC Press

ISBN: 9780203472095

Category: Technology & Engineering

Page: 352

View: 747

The use of computers in cartography has made it a lot easier for map makers to transform data from one map projection to another and experiment with alternative representations of geographical data. Yet this has also created new challenges and opportunities for map projection scientists. Small Scale Map Projection Design focuses on numerical map projection research, and is written from the perspective of the map projection user. It demonstrates how advances in the measurement of map projection distortion and in the development of low error map projections can help map makers decide what type of map projection is best for their purpose, and shows how they can eventually design their own tailor-made map projections. A number of significant contributions have been made to the subject over recent decades, and these are reviewed along with a substantial amount of original, unpublished material. This theoretical material is tied to practical applications and issues such as map projection use, optimization and selection, which are far too often carried out with simple rules-of-thumb methods.

Map Projections

A Working Manual

Author: John P. Snyder

Publisher: CUP Archive

ISBN: 9781001413013


Page: 383

View: 3679

Coordinate Systems and Map Projections

Author: D.H. Maling

Publisher: Elsevier

ISBN: 1483287076

Category: Science

Page: 505

View: 8868

A revised and expanded new edition of the definitive English work on map projections. The revisions take into account the huge advances in geometrical geodesy which have occurred since the early years of satellite geodesy. The detailed configuration of the geoid resulting from the GEOS and SEASAT altimetry measurements are now taken into consideration. Additionally, the chapter on computation of map projections is updated bearing in mind the availability of pocket calculators and microcomputers. Analytical derivation of some map projections including examples of pseudocylindrical and polyconic projections is also covered. Work undertaken in the USA and USSR on the creation of suitable map projections obtained through numerical analysis has been included. The book concludes with a chapter on the abuse and misrepresentation of map projections. An invaluable reference source for professional cartographers and all those interested in the fundamental problems of mapping the Earth.

Rhumb Lines and Map Wars

A Social History of the Mercator Projection

Author: Mark Monmonier

Publisher: University of Chicago Press

ISBN: 9780226534329

Category: Science

Page: 256

View: 1159

In Rhumb Lines and Map Wars, Mark Monmonier offers an insightful, richly illustrated account of the controversies surrounding Flemish cartographer Gerard Mercator's legacy. He takes us back to 1569, when Mercator announced a clever method of portraying the earth on a flat surface, creating the first projection to take into account the earth's roundness. As Monmonier shows, mariners benefited most from Mercator's projection, which allowed for easy navigation of the high seas with rhumb lines—clear-cut routes with a constant compass bearing—for true direction. But the projection's popularity among nineteenth-century sailors led to its overuse—often in inappropriate, non-navigational ways—for wall maps, world atlases, and geopolitical propaganda. Because it distorts the proportionate size of countries, the Mercator map was criticized for inflating Europe and North America in a promotion of colonialism. In 1974, German historian Arno Peters proffered his own map, on which countries were ostensibly drawn in true proportion to one another. In the ensuing "map wars" of the 1970s and 1980s, these dueling projections vied for public support—with varying degrees of success. Widely acclaimed for his accessible, intelligent books on maps and mapping, Monmonier here examines the uses and limitations of one of cartography's most significant innovations. With informed skepticism, he offers insightful interpretations of why well-intentioned clerics and development advocates rallied around the Peters projection, which flagrantly distorted the shape of Third World nations; why journalists covering the controversy ignored alternative world maps and other key issues; and how a few postmodern writers defended the Peters worldview with a self-serving overstatement of the power of maps. Rhumb Lines and Map Wars is vintage Monmonier: historically rich, beautifully written, and fully engaged with the issues of our time.