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Snyder [6] describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a spherical datum can be transformed into Albers equal-area conic projection coordinates with the following formulas, where is the radius, is the longitude, the reference longitude, the latitude, the reference latitude and and the standard parallels:
c. 150 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres. Maps all small circles to circles, which is useful for planetary mapping to preserve the shapes of craters. c. 150 BC: Orthographic: Azimuthal Perspective Hipparchos*
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
The reference point (λ 0, φ 0) with longitude λ 0 and latitude φ 0, transforms to the x,y origin at (0,0) in the rectangular coordinate system. [5] The Y axis maps the central meridian λ 0, with y increasing northwards, which is orthogonal to the X axis mapping the central parallel φ 0, with x increasing eastwards. [5]
When a coordinate system is chosen in the Euclidean space, this defines coordinates on : the coordinates of a point of are defined as the coordinates of (). The pair formed by a chart and such a coordinate system is called a local coordinate system , coordinate chart , coordinate patch , coordinate map , or local frame .
The international standard convention —that east is positive—is consistent with a right-handed Cartesian coordinate system, with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the northern hemisphere ) to give a precise position on the Earth's surface.
Stereographic projection of the world north of 30°S. 15° graticule. The stereographic projection with Tissot's indicatrix of deformation.. The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity.
Equirectangular projection of the world; the standard parallel is the equator (plate carrée projection). Equirectangular projection with Tissot's indicatrix of deformation and with the standard parallels lying on the equator True-colour satellite image of Earth in equirectangular projection Height map of planet Earth at 2km per pixel, including oceanic bathymetry information, normalized as 8 ...