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For the transverse Mercator, the axis of the cylinder lies in the equatorial plane, and the line of tangency is any chosen meridian, thereby designated the central meridian. Both projections may be modified to secant forms, which means the scale has been reduced so that the cylinder slices through the model globe.
The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.
To convert Transverse Mercator coordinates to lat-lon, first calculate ′, the footprint latitude— i.e. the latitude of the point on the central meridian that has the same N as the point to be converted; i.e. the latitude that has a meridian distance on the spheroid equal to N/. Bowring's formulas below seem quickest, but traditional ...
Since both the transverse axis and the conjugate axis are axes of symmetry, the symmetry group of a hyperbola is the Klein four-group. The rectangular hyperbolas xy = constant admit group actions by squeeze mappings which have the hyperbolas as invariant sets .
The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude , it is a horizontal position representation , which means it ignores altitude and treats the earth surface as a perfect ellipsoid .
The transverse Mercator projection in Eire and Northern Ireland (an international implementation spanning one country and part of another) is currently implemented in two ways: Irish grid reference system. datum: Ireland 1965 ellipsoid: Airy 1830 modified major axis: 6 377 340.189 minor axis: 6 356 034.447 central meridian scale factor: 1.000035
Transverse axis refers to an axis that is transverse (side to side, relative to some defined "forward" direction). In particular: Transverse axis (aircraft) Transverse axis of a hyperbola, coincides with the semi-major axis
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...