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Trilinear coordinates. In geometry, the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates. The ratio x : y is the ratio of the perpendicular distances from the point to the ...
A normal neighborhood U is an open subset of M such that there is a proper neighborhood V of the origin in the tangent space T p M, and exp p acts as a diffeomorphism between U and V. On a normal neighborhood U of p in M, the chart is given by: :=: The isomorphism E, and therefore the chart, is in no way unique. A convex normal neighborhood U ...
The azimuthal angle is denoted by. φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane. The function atan2 (y, x) can be used instead of the mathematical function arctan (y/x) owing to its domain and image. The classical arctan function has an ...
Geodesy. 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.
The Cassini Grid was a grid coordinate system used on British military maps during the first half of the twentieth century, particularly during World War II. The referencing consists of square grids drawn on a Cassini projection. For a period after the war, the maps were also used by the general public. The system has been superseded by the ...
CIE 1964 color space. The CIE 1964 (U*, V*, W*) color space, also known as CIEUVW, is based on the CIE 1960 UCS: [1] where (u0, v0) is the white point and Y is the luminous tristimulus value of the object. The asterisks in the exponent indicates that the variable represent a more perceptually uniform color space than its predecessor (compare ...
The parabolic cylindrical coordinates (σ, τ, z) are defined in terms of the Cartesian coordinates (x, y, z) by: The surfaces of constant σ form confocal parabolic cylinders. that open towards +y, whereas the surfaces of constant τ form confocal parabolic cylinders. that open in the opposite direction, i.e., towards −y.
The Swedish grid (in Swedish Rikets Nät, RT 90) is a coordinate system that was previously used for government maps in Sweden. RT 90 is a slightly modified version of the RT 38 from 1938. RT 90 has been replaced with SWEREF 99 as the official Swedish spatial reference system. While the system could be used with negative numbers to represent ...