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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 ...
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, at latitude 60° the scale factor is k = sec 60° = 2,
In an orthogonal coordinate system the lengths of the basis vectors are known as scale factors. The scale factors for the elliptic coordinates ( μ , ν ) {\displaystyle (\mu ,\nu )} are equal to h μ = h ν = a sinh 2 μ + sin 2 ν = a cosh 2 μ − cos 2 ν . {\displaystyle h_{\mu }=h_{\nu }=a{\sqrt {\sinh ^{2}\mu +\sin ^{2 ...
The graph shows the variation of the scale factors for the above three examples. The top plot shows the isotropic Mercator scale function: the scale on the parallel is the same as the scale on the meridian. The other plots show the meridian scale factor for the Equirectangular projection (h=1) and for the Lambert equal area projection.
The scale factors for (,,) are: = + + = + = (+) () Knowing the scale factors, various functions of the coordinates can be calculated by the general method outlined in the orthogonal coordinates article.
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Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR (visual flight rules) sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45 ...
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1]