Map Projections--a Working Manual

Front Cover
U.S. Government Printing Office, 1987 - 383 pages
Supersedes USGS Bulletin 1532.
 

Contents

Lengths of 1 of latitude and longitude on two ellipsoids of reference
25
Ellipsoidal correction factors to apply to spherical projections based on Clarke 1866 ellipsoid
27
Spherical triangle
30
Rotation of a graticule for transformation of projection
31
Cylindrical map projections
37
Gerardus Mercator
39
The Mercator projection
40
Map projections used for extraterrestrial mapping 42
42
Rectangular coordinates
45
Johann Heinrich Lambert
49
The Transverse Mercator projection
50
U S State plane coordinate systems 5256
52
Universal Transverse Mercator grid coordinates
59
Rectangular coordinates for the sphere 60
60
Universal Transverse Mercator grid zone designations for the world
62
Location of points with given scale factor
63
Oblique Mercator projection
67
Hotine Oblique Mercator projection parameters used for Landsat 1 2 and 3 imagery
68
Coordinate system for the Hotine Oblique Mercator projection
73
Lambert Cylindrical EqualArea projection
78
Transverse Cylindrical EqualArea projection
79
Page
81
Fourier coefficients for oblique and transverse Cylindrical EqualArea projection of the ellipsoid
83
The Miller Cylindrical projection
87
65
89
The Cassini projection
92
Albers EqualArea Conic projection
99
Polar coordinates
103
Lambert Conformal Conic projection
104
Polar coordinates
110
Equidistant Conic projection
112
Polar coordinates
115
Bipolar Oblique Conic Conformal projection
121
Rectangular coordinates 122
122
Ferdinand Rudolph Hassler
125
North America on a Polyconic projection grid
126
Rectangular coordinates for the Clarke 1866 ellipsoid 132
132
Rectangular coordinates for the International ellipsoid
136
Typical IMW quadrangle graticulemodified Polyconic projection
137
Bonne projection
139
Comparison of major azimuthal projections 142144
142
Geometric projection of the parallels of the polar Orthographic projection
146
Geometric projection of the parallels of the polar Gnomonic projection
164
A polar aspect B equatorial aspect C oblique aspect
166
Rectangular coordinates for equatorial aspect
168
Geometric projection of the parallels of the polar Perspective projections Vertical and Tilted
170
A polar aspect B equatorial aspect C oblique aspect
171
Tilted Perspective projection
172
Rectangular coordinates for equatorial aspect from geosynchronous satellite
174
Coordinate system for Tilted Perspective projection
176
V
177
A polar aspect B equatorial aspect C oblique aspect
183
Geometric construction of polar Lambert Azimuthal EqualArea projection
185
Rectangular coordinates for equatorial aspect 188
188
Ellipsoidal polar Lambert Azimuthal EqualArea projection
190
A polar aspect B equatorial aspect C oblique aspect
193
Rectangular coordinates for equatorial aspect 196
196
Ellipsoidal Azimuthal Equidistant projectionpolar aspect
198
Plane coordinate systems for Micronesia
200
145
204
50State map
205
ModifiedStereographic Conformal projection of 48 United States bounded by a nearrectangle of constant scale
206
Coefficients for specific forms 209
209
Rectangular coordinates for Clarke 1866 ellipsoid
212
Two orbits of the Space Oblique Mercator projection
216
One quadrant of the Space Oblique Mercator projection
217
Scale factors for the spherical Space Oblique Mercator projection using Landsat constants
221
Scale factors for the ellipsoidal Space Oblique Mercator projection using Landsat constants
226
Cylindrical SatelliteTracking projection
232
Conic SatelliteTracking projection conformality at lats 45 and 70 N
233
Conic SatelliteTracking projection conformality at lats 45 and 80 9 N
234
Conic SatelliteTracking projection standard parallel 80 9 N
235
Rectangular coordinates
238
Van der Grinten projection
240
Geometric construction of the Van der Grinten projection
241
Rectangular coordinates 244
244
Interrupted Sinusoidal projection
246
Mollweide projection
250
Rectangular coordinates for 90th meridian
252
Eckert IV projection
254
Eckert VI projection
255
Rectangular coordinates for 90th meridian
258
great circle distance as an arc of a circle ୧ eccentricity of the ellipsoid 1 ba
259
flattening of the ellipsoid
261

Other editions - View all

Common terms and phrases

Popular passages

Page 9 - That the Conference proposes to the Governments here represented the adoption of the meridian passing through the centre of the transit instrument at the Observatory of Greenwich as the initial meridian for longitude.
Page 9 - III. That from this meridian longitude shall be counted in two directions up to 180 degrees, east longitude being plus and west longitude minus.
Page 122 - This distribution of the projection, in an assemblage of sections of surfaces of successive cones, tangents to or cutting a regular succession of parallels, and upon regularly changing central meridians, appeared to me the only one applicable to the coast of the United States.
Page 216 - The angle between the plane of the earth's equator and the plane of the ecliptic (the plane of the earth's orbit) is 23?5 (the latitude of the tropic of Cancer).
Page 162 - It is important to remember that the shortest distance between any two points on the surface of a sphere is the arc of a great circle joining these points (see Fig.
Page 103 - This yields the greatest similarity that any plane figure can have with one drawn on the surface of a sphere. The question has not been asked whether this property occurs only in the two methods of representation mentioned or whether these two representations, so different in appearances, can be made to approach each other through intermediate stages. ... if there are stages intermediate to these two representations, they must be sought by allowing the angle of intersection of the meridians to be...
Page 3 - Earth is essentially a sphere, although a number of intellectuals nearly 2,000 years earlier were convinced of this. Even to the scholars who considered the Earth flat, the skies appeared hemispherical, however. It was established at an early date that attempts to prepare a flat map of a surface curving in all directions leads to distortion of one form or another. A map projection is a systematic representation of all or part of the surface of a round body, especially the Earth, on a plane.
Page 125 - States, in which the 1° quadrangle is the largest unit * * * and the 15' quadrangle is the average unit. * * * Misuse of this projection in attempts to spread it over large areas -that is, to construct a single map of a large area -has developed serious errors and gross exaggeration of details. For example, the polyconic projection is not at all suitable for a singlesheet map of the United States or of a large State, although it has been so employed.
Page 212 - PROJECTION 2.11.1 Space oblique Mercator projection The launching of an Earth-sensing satellite by the National Aeronautics and Space Administration (NASA) in 1972 led to a new era of continuing mapping from space. This satellite, first called ER.TS-1 and then renamed Landsat 1 in 1975, was followed by two others, all of which circled the Earth in a nearly circular orbit inclined about 99° to the Equator and scanning a swath about 185 km (officially 100 nautical miles) from an altitude of about...
Page 8 - Each degree is sub-divided into 60 minutes, and each minute into 60 seconds.

Bibliographic information