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The Cartesian (x′,y′) axes are related to the rotated graticule in the same way that the axes (x,y) axes are related to the standard graticule. The tangent transverse Mercator projection defines the coordinates (x′,y′) in terms of −λ′ and φ′ by the transformation formulae of the tangent Normal Mercator projection:
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
Selection of a model for the shape of the Earth or planetary body (usually choosing between a sphere or ellipsoid). Because the Earth's actual shape is irregular, information is lost in this step. Transformation of geographic coordinates (longitude and latitude) to Cartesian (x,y) or polar (r, θ) plane coordinates.
A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of Earth as coordinates.It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space.
A birational map from X to Y is a rational map f : X ⇢ Y such that there is a rational map Y ⇢ X inverse to f. A birational map induces an isomorphism from a nonempty open subset of X to a nonempty open subset of Y, and vice versa: an isomorphism between nonempty open subsets of X, Y by definition gives a birational map f : X ⇢ Y. In this ...
Cassini projection of the world Cassini projection with 1,000 km indicatrices Cassini projection of the world modeled as a highly oblate ellipsoid with flattening 1:2 (= eccentricity √ 3 ⁄ 2) The Cassini projection (also sometimes known as the Cassini–Soldner projection or Soldner projection [ 1 ] ) is a map projection first described in ...
Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where
The X column is the ratio of the length of the parallel to the length of the equator; the Y column can be multiplied by 0.2536 [11] to obtain the ratio of the distance of that parallel from the equator to the length of the equator. [7] [9] Coordinates of points on a map are computed as follows: [7] [9]