Handbook of Research on Geoinformatics

Handbook of Research on Geoinformatics Hassan A. Karimi University of Pittsburgh, USA INFORMATION SCIENCE REFERENCE Hershey • New York Director of Editorial Content: Kristin Klinger Director of Production: Jennifer Neidig Managing Editor: Jamie Snavely Assistant Managing Editor: Carole Coulson Typesetter: Jeff Ash Cover Design: Lisa Tosheff Printed at: Yurchak Printing Inc. Published in the United States of America by Information Science Reference (an imprint of IGI Global) 701 E. Chocolate Avenue, Suite 200 Hershey PA 17033 Tel: 717-533-8845 Fax: 717-533-8661 E-mail: [email protected] Web site: http://www.igi-global.com and in the United Kingdom by Information Science Reference (an imprint of IGI Global) 3 Henrietta Street Covent Garden London WC2E 8LU Tel: 44 20 7240 0856 Fax: 44 20 7379 0609 Web site: http://www.eurospanbookstore.com Copyright © 2009 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Handbook of research on geoinformatics / Hassan A. Karimi, editor. p. cm. Includes bibliographical references and index. Summary: "This book discusses the complete range of contemporary research topics such as computer modeling, geometry, geoprocessing, and geographic information systems"--Provided by publisher. ISBN 978-1-59904-995-3 (hardcover) -- ISBN 978-1-59140-996-0 (ebook) 1. Geographic information systems--Research--Handbooks, manuals, etc. I. Karimi, Hassan A. G70.212.H356 2009 910.285--dc22 2008030767 British Cataloguing in Publication Data A Cataloguing in Publication record for this book is available from the British Library. All work contributed to this book set is original material. The views expressed in this book are those of the authors, but not necessarily of the publisher. If a library purchased a print copy of this publication, please go to http://www.igi-global.com/agreement for information on activating the library's complimentary electronic access to this publication. Chapter XII Overview, Classification and Selection of Map Projections for Geospatial Applications Eric Delmelle University of North Carolina at Charlotte, USA Raymond Dezzani University of Idaho, USA ABSTRACT There has been a dramatic increase in the handling of geospatial information, and also in the production of maps. However, because the Earth is three-dimensional, geo-referenced data must be projected on a two-dimensional surface. Depending on the area being mapped, the projection process generates a varying amount of distortion, especially for continental and world maps. Geospatial users have a wide variety of projections too choose from; it is therefore important to understand distortion characteristics for each of them. This chapter reviews foundations of map projection, such as map projection families, distortion characteristics (areal, angular, shape and distance), geometric features and special properties. The chapter ends by a discussion on projection selection and current research trends." iNTRODUCTION Earth, continental areas and distances between points. Distortion, although less apparent on a Recent automation and increasing user-friendliness larger-scale map (because it covers a smaller area of geospatial systems (such as Geographical Infor- and the curvature of the Earth is less pronounced), mation Systems -GIS) has made the production misleads people in the way they visualize, cognize of maps easier, faster and more accurate. Cartog- or locate large geographic features (Snyder, 1993). raphers have at present an impressive number of Map projections have been devised to answer projections, but often lack a suitable classification some of the distortion issues, preserving selected and selection scheme for them, which significantly geometric properties (e.g., conformality, equiva- slow down the mapping process. Map projections lence, and equidistance) and special properties. generate distortion from the original shape of the Ignoring these distortion characteristics may lead Earth. They distort angles between locations on to an unconsidered choice of projection framework, Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited. Overview, Classification and Selection of Map Projections for Geospatial Applications resulting in a disastrous map, thereby devaluating three aforementioned families (Snyder, 1987; Lee, the message the map attempts to communicate. 1944). It is urgent for users of geospatial technologies to acquire a map projection expertise before interact- Conical Projection ing with any cartographic software. When a cone wrapped around the globe is cut along a meridian, a conical projection results. The cone THE MAP PROJECTION PROCESS has its peak -also called apex- above one of the two Earth’s poles and touches the sphere along one The Earth is essentially spherical, but is approxi- parallel of latitude (Figure 2a). When unwrapped, mated by a mathematical figure –a datum surface. meridians become straight lines converging to the For the purpose of world maps, a sphere with radius apex, and parallels are represented by arcs of circle. RE = 6371km is a satisfying approximation. For The pole is either represented as a point or as a line. large-scale maps however (i.e., at the continental When the cone is secant to the globe, it bisects the and country scale), the non-spherical shape of the surface at two lines of latitude (Figure 2b). Earth is represented by an ellipsoid with major axis a and minor axis b. The values of a and b Cylindrical Projection vary with the location of the area to be mapped and are calculated in such a way that the ellipsoid fits A cylinder is wrapped around the generating globe, the geoid almost perfectly. The full sized sphere so that its surface touches the Equator throughout is greatly reduced to an exact model called the its circumference. The meridians of longitude are generating globe (see Figure 1). Nevertheless, of equal length and perpendicular to the Equator. globes have many practical drawbacks: they are The parallels of latitude are marked off as lines difficult to reproduce, cumbersome for measuring distances, and less than the globe is visible at once. Those disadvantages are eliminated during the map Figure 1. The map projection process: the sphere, projection process, by converting the longitude approximated by a mathematical figure is reduced and latitude angles (λ,φ) to Cartesian coordinates to a generating globe that is projected on a flat (Canters and Decleir, 1989): surface. (after Canters and Decleir 1989) x f ( j,) l y g()j, l , (1) CLASSIFICATION OF MAP PROJECTIONS BY FAMILIES Three major projections classes are named after the developable surface onto which most of the map projections are at least partially geometrically projected. All three have either a linear or punctual contact with the sphere: they are the cylindrical, conical and azimuthal. The advantage of these shapes is that, because their curvature is in one dimension only, they can be flattened to a plane without any further distortion (Iliffe, 2000). The pseudocylindrical, pseudoconic, pseudoazimuthal and pseudoconical projections are based on the 0 Overview, Classification and Selection of Map Projections for Geospatial Applications parallel to the Equator, and spaced in such a way Azimuthal Projection to preserve specific properties, described further. The final process consists of cutting the cylinder An azimuthal projection results from the projec- along a specific meridian yielding acylindrical map tion of meridians and parallels at a point on a plane (Figure 2c). An example of a tangent projection tangent on one of the Earth’s poles. The meridians is the Plate Carrée projection with transformation become straight lines diverging from the center l l φ formulas x = R( – 0) and y = R , where λ0 is the of the projection. The parallels are portrayed as longitude of the prime meridian. A secant cylindri- concentric circles, centered on the chosen pole. cal projection is obtained when the cylinder bisects Azimuthal projections are widely used to portray the globe at two parallels (Figure 2d). The Behrman the polar areas (Figure 3). Three different kinds projection is a secant projection characterized by of azimuthal projection are possible: standard parallels at ±30º with transformation l l φ φ formulas x = R( – 0)cos 0, y Rj, where 0 denotes the standard latitude. Figure 2. Illustration of the tangent conical projection in (a) and a secant projection in (b). Illustration of the tangent cylindrical projection in (c) and its secant counterpart in (d). Distortion is minimum on the contact lines and increases away from those parallels of latitude. Figure 3. Illustration of the azimuthal projection and the three resulting cases Overview, Classification and Selection of Map Projections for Geospatial Applications 1. The orthographic case results from a per- curves. A polyconic projection results from project- spective projection from an infinite distance, ing the Earth on different cones tangent to each which gives a globe-like shape. Only one parallel of latitude. Both meridians

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