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In geometry, a Cartesian coordinate system (UK: / k ɑːr ˈ t iː zj ə n /, US: / k ɑːr ˈ t iː ʒ ə n /) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines ...
If points in the real projective plane are represented by homogeneous coordinates (x, y, z), the equation of the line is lx + my + nz = 0, provided (l, m, n) ≠ (0,0,0) . In particular, line coordinate (0, 0, 1) represents the line z = 0, which is the line at infinity in the projective plane.
Thus the state plane coordinate system is still useful. Originally, the state plane coordinate systems were based on the North American Datum of 1927 (NAD27). Later, the more accurate North American Datum of 1983 (NAD83) became the standard (a geodetic datum is the way a coordinate system is linked to the physical Earth). More recently there ...
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
Local tangent plane coordinates (LTP) are part of a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. They are also known as local ellipsoidal system , [ 1 ] [ 2 ] local geodetic coordinate system , [ 3 ] local vertical, local horizontal coordinates ( LVLH ), or ...
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .