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The sphere is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. For maps of smaller regions, an ellipsoidal model must be chosen if greater accuracy is required. [1] The ellipsoidal form of the polar ellipsoidal projection uses conformal latitude. There are ...
The Dymaxion map projection, also called the Fuller projection, is a kind of polyhedral map projection of the Earth's surface onto the unfolded net of an icosahedron.The resulting map is heavily interrupted in order to reduce shape and size distortion compared to other world maps, but the interruptions are chosen to lie in the ocean.
Because the infinitesimal circles represented by the ellipses on the map all have the same area on the underlying curved geometric model, the distortion imposed by the map projection is evident. There is a one-to-one correspondence between the Tissot indicatrix and the metric tensor of the map projection coordinate conversion. [1]
However, by uniformly shrinking the resulting flat map, as a final step, any pair of circles parallel to and equidistant from the contact circle can be chosen to have their scale preserved, called the standard parallels; then the region between chosen circles will have its scale smaller than on the sphere, reaching a minimum at the contact circle.
Use BlankMap-World.svg for that purpose. This is a purely technical illustration created for the purpose of being used in the documentation for the main image, from which this file was derived: BlankMap-World.svg. As such, this map is not making any political statements – it simply shows hidden elements in the main image.
Cartographic symbology encodes information on the map in ways intended to convey information to the map reader efficiently, taking into consideration the limited space on the map, models of human understanding through visual means, and the likely cultural background and education of the map reader. Symbology may be implicit, using universal ...
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Here there is one exception: the Hopf circle containing the projection point maps to a straight line in R 3 — a "circle through infinity". The fibers over a circle of latitude on S 2 form a torus in S 3 (topologically, a torus is the product of two circles) and these project to nested toruses in R 3 which also fill space.