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The universal polar stereographic (UPS) coordinate system is used in conjunction with the universal transverse Mercator (UTM) coordinate system to locate positions on the surface of the Earth. Like the UTM coordinate system, the UPS coordinate system uses a metric-based cartesian grid laid out on a conformally projected surface.
A two-dimensional coordinate system on the stereographic plane is an alternative setting for spherical analytic geometry instead of spherical polar coordinates or three-dimensional cartesian coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane.
On an ellipsoid, the perspective definition of the stereographic projection is not conformal, and adjustments must be made to preserve its azimuthal and conformal properties. The universal polar stereographic coordinate system uses one such ellipsoidal implementation.
This transverse, ellipsoidal form of the Mercator is finite, unlike the equatorial Mercator. Forms the basis of the Universal Transverse Mercator coordinate system. 1922 Roussilhe oblique stereographic: Henri Roussilhe 1903 Hotine oblique Mercator Cylindrical Conformal M. Rosenmund, J. Laborde, Martin Hotine 1855 Gall stereographic: Cylindrical
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are
Every pair of nodes having a common parent can be converted from a mixed polar–Cartesian coordinate system to a Cartesian coordinate system using the above formulas for a splitting. Polyspherical coordinates also have an interpretation in terms of the special orthogonal group .
[1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. [4] [5] Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography.
Hyperspherical coordinates. Sphere S 2: Spherical coordinates. Stereographic chart Central projection chart Axial projection chart Mercator chart. 3-sphere S 3: Polar chart. Stereographic chart Mercator chart. Euclidean spaces: n-dimensional Euclidean space E n: Cartesian chart: Euclidean plane E 2: Bipolar coordinates. Biangular coordinates ...