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A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
The coordinates of a point P may change due to either a rotation of the coordinate system CS , or a rotation of the point P . In the latter case, the rotation of P also produces a rotation of the vector v representing P. In other words, either P and v are fixed while CS rotates (alias), or CS is fixed while P and v rotate (alibi). Any given ...
Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems. In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. [1] A geographic coordinate transformation is a ...
This is the convention followed in this article. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distance r along the radial line connecting the point to the fixed point of origin; the polar angle θ ...
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 ...
Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator[1] or WGS 84/Pseudo-Mercator is a variant of the Mercator map projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted it in 2005. [2] It is used by virtually all major online map providers, including Google ...
Let P be the point on the lower unit hemisphere whose spherical coordinates are (140°, 60°) and whose Cartesian coordinates are (0.321, 0.557, −0.766). This point lies on a line oriented 60° counterclockwise from the positive x -axis (or 30° clockwise from the positive y -axis) and 50° below the horizontal plane z = 0 .
The galactic longitude (l) runs from the Sun upwards in the image through the center of the galaxy. The galactic latitude (b) is perpendicular to the image (i.e. coming out of the image) and also centered on the Sun. The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary ...