Projections
Map projections are controlled deformations of the geographic grid of the model spheroid. Since shape and area cannot be maintained in the transformation from the allside curve to the plane of the map sheet, projections favour one or the other of these geometric properties, though some success can be achieved in representing both tolerably well for some mapping purposes.
A "Conformal" or "Orthomorphic" (correct shape) projection retains shape in that distortion is made equal in all directions from a point so that angular direction from a point is true, i.e. the cardinal directions are 90 degrees apart. However, true shape cannot be preserved over large areas because area now varies across the surface.
An "Equivalent" or "Equal-Area" projection retains area of regions in correct relative size, but in doing so cannot retain corret shape.
Scale requirements for Conformal and Equivalent are contradictory, no projection can be both. Conformal projection will represent similar Earth regions of unequal size, and Equivalent projections will represent most regions as deformed angular shape.
Two other types of projections are the Equidistant, one which maintains scale in all directions from one or two points, but only those points and the "Azmuthul" projection which show great circle arcs as straight lines for all directions from one, and at the most, two points only.
There are 3 main groups projections:
1. Perspective projections are derived directly from the spheroid model and can be simulated using a light source, model globe and projection screen.
2.Non-perspective projections are mathematically derived, but are closely related to perspective projections of which they are modifications made for better preservation of one or another property.
3.Conventional (i.e.miscellaneous) projections are mathematically derived on arbitrary assumptions and include world projections which as 'impossible' as projections of any model.
Images from the University of Texas Map Library
Perspective Projections
These are of three types, a light source being imagined as the globe centre (gnomonic), on its surface (stereographic), or out in space at 'infinity' (orthographic). Three projection surfaces can be used, a plane surface (zenithal) a cylinder (cylindrical) or a cone (conic). These can be oriented on a model so as to be of polar, equitorial or oblique case. the Zenithal projection touches the globe as a point, the Cylindrical and Conic projections touch along a circumference and a small circle respectively. At such junctions the projection retains the geometric properties of the globe, but elsewhere the projection will result in exaggeration or diminution of true scale. To spread the inherent errors, the cylinder and cone can be imagined as cutting the model globe, thus giving two 'standard parallels' between which scale changes are lessened. Common perspective projections are the Zenithal gnomonic polar case, Zenithal stereographic polar case, Zenithal orthographic polar case and Equitorial cases, Zenithal appoximated equidistant; Zenithal apporximate equal area, simple perspective cylindrical gnomonic case, Galls projection, Conic perspective gnomonic polar case.
Non-Perspective Projections
Derived from the Zenithal projections are the Zenithal Equidistant and Zenithal Equal Area projections, most commonly polar case. Derived from simple perspective cylindrical are the Plate Carree, Cassini's projection, Mercator's projection, and Lamberts' Equal Area projection. Derived from the Conic, Polyconic, Bonnes projection, Two Standard Equal Area projection and One and Two Standard Orthomorphic projections.
Conventional Projections
These are typically equal area and allow the whole world to be shown. They are mathematical devices. Well used ones are the Sanson-Flamsteed (Sinusoidal) projection, Mollweide projection and Aitoffs Equal Area projection. Any of these can be adjusted to a Recentred Globe projection in which shape and area are both moderately preserved.
Examples of Various Projections
 | Azimuthal Equidistant - Distances measured from the center are true. The center of the projection is the only point without distortion. (Known by the Egyptians 2000 years ago, but they didn't have a GIF animator) |
 | Bonne - Scale is true along the central meridian and along all parallels. (Rigober Bonne, mid-1700's. The worlds only true romantic cartographer. Created the projection as a box cover design for his other invention - chocolate covered Bonne-Bonnes). Cries out for a slogan, like "Love makes the world go 'round" or "Love it or leave it". |
 | Oblique Mercator - This is your projection. And this is your projection on drugs. Any questions? (Rosenmund, Laborde, Hotine, and others, 1900-1950) |
 | Polyconic - Free of distortion only along the central meridian. (Ferdinand
R. Hassler, 1820). Slogan - "Kiss my world". |
 | Stereographic - Scale increases away from the center of the projection. Mainly
used for polar maps. (Hipparchus, 2nd century B.C., who died penniless because no one
understood it. ...that, and because pennies weren't invented yet) |
Table created by: Jim Padykula.
|
