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A conformal map has an isotropic scale factor. Conversely isotropic scale factors across the map imply a conformal projection. Isotropy of scale implies that small elements are stretched equally in all directions, that is the shape of a small element is preserved. This is the property of orthomorphism (from Greek 'right shape'). The ...
Map layout, also called map composition or (cartographic) page layout, is the part of cartographic design that involves assembling various map elements on a page. This may include the map image itself, along with titles, legends, scale indicators, inset maps, and other elements.
The vertical exaggeration is given by: = where VS is the vertical scale and HS is the horizontal scale, both given as representative fractions.. For example, if 1 centimetre (0.39 in) vertically represents 200 metres (660 ft) and 1 centimetre (0.39 in) horizontally represents 4,000 metres (13,000 ft), the vertical exaggeration, 20×, is given by:
μ – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. R – rotation matrix. Consists of three axes (small [clarification needed] rotations around each of the three coordinate axes) r x, r y, r z. The rotation matrix is an orthogonal matrix. The angles are given in either degrees or radians.
This implies that the vertical scale factor, h, equals the horizontal scale factor, k. Since k = sec φ, so must h. The graph shows the variation of this scale factor with latitude. Some numerical values are listed below. at latitude 30° the scale factor is k = sec 30° = 1.15, at latitude 45° the scale factor is k = sec 45° = 1.41,
In most European countries, the largest scale topographic map series is a 1:25.000 scale series. Notable exceptions are Austria (1:50,000) and Finland (1:20,000). Many non-European states limit the largest scale of their map series, usually to 1:50,000 scale, frequently due to the large size of the country covered (and hence for financial reasons).
Such a scaling changes the diameter of an object by a factor between the scale factors, the area by a factor between the smallest and the largest product of two scale factors, and the volume by the product of all three. The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors ...
In each zone the scale factor of the central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines, or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard ...