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The figure below shows a point P at latitude φ and longitude λ on the globe and a nearby point Q at latitude φ + δφ and longitude λ + δλ. The vertical lines PK and MQ are arcs of meridians of length Rδφ. [d] The horizontal lines PM and KQ are arcs of parallels of length R(cos φ)δλ.
Geodesy. The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, which means it ignores altitude and treats the earth surface as a perfect ellipsoid.
They are written in terms of longitude (λ) and latitude (φ) on the sphere. Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0). The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following: [1]
The Mollweide is a pseudocylindrical projection in which the equator is represented as a straight horizontal line perpendicular to a central meridian that is one-half the equator's length. The other parallels compress near the poles, while the other meridians are equally spaced at the equator. The meridians at 90 degrees east and west form a ...
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 ...
(On the sphere it depends on both latitude and longitude.) The scale is true on the central meridian. • The projection is reasonably accurate near the equator. Scale at an angular distance of 5° (in latitude) away from the equator is less than 0.4% greater than scale at the equator, and is about 1.54% greater at an angular distance of 10°. •
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the ...
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...