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Some projections treat the Earth only as a sphere, others as either ellipsoid or sphere. Some newer projections are spe- CIal Iy de SIgned for satell Ite mapping. When the c linder is cut alon som meridian and unrolled, a cylindrical projection with straight meridians and straight . A plane tangent to one of the Earth's poles is the basis for polar azimuthal projections. ' A developable surface is one that can be transformed to a plane without distortion.

The USGS has also conceived and designed several new projections, including the Space Oblique Mercator, the first map projection designed to permit mapping of the Earth continuously from a satellite with low distortion. 1987, Map projections--a working manual / by John P. Less useful but mathemat Ically intriguing projections have been designed to fit the sphere conformally into a square, an ellipse, a triangle, or some other geometric figure. Method of construction.-In the days before ready access to computers and plotters, ease of construction was of greater importance. In this case, the group of projections is named for the function, not the plane, since all common tangent-plane projections of the sphere are azimuthal. The parallels of latitude are complete circles, centered on the pole. 6 MAP PROJECTION~A WORKING MANUAL Regular Cylindrical Regula r Conic (plane) Oblique Azimuthal (planei FIGURE I.-Projection of the Earth onto the three major surfaces. The axis of the cylinder or cone can have a direction different from that of the Earth's axis, while the plane may be tangent to a point other than a pole (fig. Th IS type of mod If Icat IOn leads to Important obhque, transverse, and equatorial projections, in which most meridians and parallels are no longer straight lines or arcs of circles.

Equal-area and equidistant projections appear in the National Atlas. On the Gnomonic projection, all great circle paths-the shortest routes between points on a sphereare shown as straight lines. 1), so that its surface touches the Equator throughout its circumference, the meridians of longitude may be projected onto the cylinder as equidistant straight lines perpendicular to the Equator, and the parallels of latitude marked as lines parallel to the Equator, around the circumference of the cylinder and mathematically spaced for certain characteristics. When the cone is cut along a meridian, unrolled, and laid flat, the meridians remain straight radiating lines, but the parallels are now circular arcs centered on the apex. This conceptually provides two standard parallels; but for most conic projections this construction is not geometrically correct.

Other projections, such as the Miller Cylindrical and the Van der Grinten, are chosen occasionally for convenience, sometimes making use of existing base maps prepared by others. On the Stereographic, all small circles, as well as great circles, are shown as circles on the map. For some cases, the parallels may also be projected geometrically from a common point onto the cylinder, but in the most common cases th are not ers ecti e. The angles between meridians are shown smaller than the true angles. , parallels are geometrically projected from a common point of perspective; on The concepts outlined above may be modified in two ways, which still provide . The plane may likewise cut through the globe at any parallel instead of touching a pole, but this is only useful for the Stereographic and some other perspective projections.

Snyder After decades of using only one map projection, the Polyconic, for its mapping program, the U. Geological Survey (USGS) now uses several of the more common projections for its published maps. of Docs Washington , , I I , , I , , , , I , I I , I- I I ~ i , I I I : , I , , , I , I I I , I , , , , , I I I I I r I , : : : I , r I I I , 1 , I W·.st~rn Field Operation Center . GEOLOGICAL SURVEY PROFESSIONAL PAPER 1395 Supersedes USGS Bulletin 1532 DEPARTMENT OF THE INTERIOR DONALD PAUL HODI eral map p I oj ections pro v ide special char acteris- tics that no other projection provides. , the meridians are projected onto the cone as equidistant straight lines radiating , the cone in planes perpendicular to the Earth's axis, spaced for the desired characteristics.

For larger scale maps, including topographic quadrangles and the State Base Map Series, conformal projections such as the Transverse Mercator and the Lambert Conformal Conic are used. LIBRARY V 12 1987 Spohne, Washington 99201 Map Projections A Working Manual By JOHN P. On the Mercator projection, all rhumb lines, or lines of constant direction, are shown as straight lines. A cylinder is a limiting form of a cone with an increasingly sharp point or apex. If a cylinder is wrapped around the globe representing the Earth (see fig. , the Earth and with the surface of the cone touching the globe along some particu- . The parallels may not be projected geometrically for any useful conic projections. e cy In er or cone may e secan 0 or cu ego e a wo para e s ins ea of being tangent to just one.

PDF documents opened from your browser may not display or print as intended. More information about viewing, downloading, and printing report files can be found . Still others are more remotely related to cylindrical, conic, or azimuthal projections, if at all 8 MAP PROJECTIONS--A WORKING MANUAL 2.

Sorry, we just need to make sure you're not a robot. LONGITUDE AND LATITUDE To identify the location of points on the Earth, a graticule or network of longitude and latitude lines has been superimposed on the surface.

For best results, please make sure your browser is accepting cookies. They are commonly referred to as meridians and parallels, respectively.

Sorry, we just need to make sure you're not a robot. The concept of latitudes and longitl Jdes was originated early in recorded history by Greek and Egyptian scientists, especially the Greek astronomer Hipparchus (2nd century, B. Claudius Ptolemy further formalized the concept (Brown, 1949, p. PARALLELS OF LATITUDE Given the North and South Poles, which are approximately the ends of the axis about which the Earth rotates, and the Equator, an imaginary line halfway between the two poles, the parallels of latitude are formed by circles surrounding the Earth and in planes parallel with that of the Equator.

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