An album of map projections - USGS

262 Pages·2012·12.56 MB·English

U.S. Survey
~eological
Profes-sional- Paper 1453
.. ~ :. . ' ...

Department of the Interior
BRUCE BABBITT Secretary
U.S. Geological Survey
Gordon P. Eaton, Director
First printing 1989
Second printing 1994
Any use of trade names in this publication is for descriptive purposes
only and does not imply endorsement by the U.S. Geological Survey
Library of Congress Cataloging in Publication Data
Snyder, John Parr, 1926-
An album of map projections.
(U.S. Geological Survey professional paper; 1453)
Bibliography: p.
Includes index.
Supt. of Docs. no.: 119.16:1453
1. Map-projection. I. Voxland, Philip M. II. Title. Ill. Series.
GA110.S575 1989 526.8 86-600253
For sale by Superintendent of Documents,
U.S. Government Printing Office
Washington, DC 20401
United States Government Printing Office : 1989
CONTENTS
Preface vii
Introduction 1 McBryde·Thomas Flat-Polar Parabolic 72
Glossary 2 Quartic Authalic 74
Guide to selecting map projections 5 McBryde-Thomas Flat-Polar Quartic 76
Distortion diagrams 8 Putnii)S P 78
5
Cylindrical projections DeNoyer Semi-Elliptical 80
Mercator 10 Robinson 82
Transverse Mercator 12 Collignon 84
Oblique Mercator 14 Eckert I 86
Lambert Cylindrical Equal-Area 16 Eckert II 88
Behrmann Cylindrical Equal-Area 19 Loximuthal 90
Plate Carree 22 Conic projections
Equirectangular 24 Equidistant Conic 92
Cassini 26 Lambert Conformal Conic 95
Oblique Plate Carree 28 Bipolar Oblique Conic Conformal 99
Central Cylindrical 30 Albers Equal-Area Conic 100
Gall 33 Lambert Equal-Area Conic 102
Miller Cylindrical 35 Perspective Conic 104
Pseudocylindrical projections Polyconic 106
Sinusoidal 37 Rectangular Polyconic 110
McBryde·Thomas Flat-Polar Sinusoidal 44 Modified Polyconic, International Map of the World series 111
Eckert V 46 Bonne 112
Winkel! 48 Werner 114
Eckert VI 50 Azimuthal projections
McBryde 53 52 Perspective
Mollweide 54 Gnomonic 116
Eckert Ill 58 Stereographic 120
Eckert IV 60 Orthographic 124
Wagner IV 62 General Vertical Perspective 128
Hatano Asymmetrical Equal-Area 64 Nonperspective
Goode Homolosine 66 Azimuthal Equidistant 132
Boggs Eumorphic 68 Lambert Azimuthal Equal-Area 136
Craster Parabolic 70 Airy 140
iii
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CONTENTS
Modified Guyou 188
Two-Point Azimuthal 144 Peirce Quincuncial 190
Two-Point Equidistant 146 Adams Hemisphere in a Square 192
Miller Oblated Stereographic 148 Adams World in a Square 1 194
Wiechel 149 Adams World in a Square II 195
Craig Retroazimuthal 150 Lee Conformal World in a Triangle 196
Hammer Retroazimuthal 152 Conformal World in an Ellipse 198
Littrow 154 Vander Grinten I 200
Berghaus Star 156 Vander Grinten II 202
Aitoff 158 Van der Grinten Ill 203
Hammer 160 _ Van der Grinten IV 204
Briesemeister 162 Armadillo 206
Winkel Tripel 164 GSSO 208
Eckert-Greifendorff 166 Space Oblique Mercator 211
Wagner VII 168 Satellite Tracking 213
Chamberlin Trimetric 170 Appendix: Formulas for projections 216
Ti It ed Perspective · 172 Cylindrical projections 218
Miscellaneous Pseudocylindrical projections 220
Bacon Globular 174· Conic projections 224
Pseudoconic projections 225
Fournier Globular 175
Azimuthal projections
Nicolosi Globular 176
Perspective 226
Apian Globular I 177
Nonperspective 228
Ortelius Oval 178
Modified 230
Lagrange 180 Miscellaneous projections 234
Eisenlohr 184 Selected references 240
August Epicycloidal 186 Index 242
v

Preface
Every map must begin, either consciously or on a standardized basis, so that comparisons are
unconsciously, with the choice of a map projec more realistic. These maps have been plotted on
tion, the method of transforming the spherelike film as lines 0.005 in. wide by means of a photo
surface being mapped onto a flat plane. Because head computer-driven plotter and World Data
this transformation can become complicated, Bank I shoreline files (national boundaries
there is a tendency to choose the projection included where appropriate). Central meridians
that has been used for a suitable available base and other parameters have been given the same
map, even if it does not emphasize the desired values in so far as it was practical.
properties. Some smaller maps have been prepared with
This album has been prepared to acquaint the Dahlgren (Hershey) shoreline file. The map
those in the cartographic profession and other projection software for any given map consisted
cartophiles with the wide range of map projec of one of three programs. WORLD was developed
tions that have been developed during the past for a mainframe computer by Philip Voxland
few centuries. Because including all the hundreds at the University of Minnesota. CYLIND and
of known projection systems would be both diffi- AZIMUTH were developed for a personal micro
. cult and expensive, this volume presents some 90 computer and converted to mainframe computer
basic projections in over 130 different modifica programs at the U. S. Geological Survey (USGS)
tions and aspects. Dozens of other projections are by John Snyder, with the guidance of Michael K.
mentioned briefly. All the popular projections Linck, Jr., and John F. Waananen. The authors
have been included, along with many others thank Joel L. Morrison, past president of the Inter
that have interesting appearances or features, national Cartographic Association and Assistant
even if their usefulness for any serious mapping Division Chief for Research, National Mapping
is limited. Division, USGS, for writing the introduction to this
The most important question to raise about a book, as well as Tau Rho Alpha (USGS) and
map projection concerns distortion. How accu Arthur H. Robinson (University of Wisconsin/
rately does the flat projection show the desired Madison) for many constructive comments on the
portion of the spherelike Earth (or heavens or manuscript. The authors also thank Christopher J.
planetary body)? Since accuracy is desired in Cialek, Kathie R. Fraser, Carolyn S. Hulett, and
area, shape, and distance but cannot be achieved Ann Yaeger of the USGS for their assistance.
in all three simultaneously and since the region With this reprint, several corrections have been
mapped may vary in overall extent and shape, the incorporated. We thank Daniel Strebe for report
answer is not clear cut. Because this album ing most of the errors in the formulas.
emphasizes visual comparisons rather than tables
of scale variation, the Tissot indicatrix has been John P. Snyder
adopted as the most common means of compar
Philip M. Voxland
ing distortion on different parts of the same pro
jection and on different projections.
Computerized plotting has facilitated the
preparation of many outline map projections
vii