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For example, a Mercator map printed in a book might have an equatorial width of 13.4 cm corresponding to a globe radius of 2.13 cm and an RF of approximately 1 / 300M (M is used as an abbreviation for 1,000,000 in writing an RF) whereas Mercator's original 1569 map has a width of 198 cm corresponding to a globe radius of 31.5 cm and an ...
Miller projection with 1,000 km indicatrices of distortion. The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4 ⁄ 5, projected according to Mercator, and then the result is multiplied by 5 ⁄ 4 to retain scale along the equator. [1] Hence:
Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map. The oblique Mercator projection, on the other ...
On a Mercator projection map, any rhumb line is a straight line; a rhumb line can be drawn on such a map between any two points on Earth without going off the edge of the map. But theoretically a loxodrome can extend beyond the right edge of the map, where it then continues at the left edge with the same slope (assuming that the map covers ...
With no distortion along the central meridian and the equator, distances along those lines are correct, as are the angles of intersection of other lines with those two lines. Distortion is lowest throughout the region of the map close to those lines. A sinusoidal projection shows relative sizes accurately, but distorts shapes and directions.
This document from the U.S. National Geodetic Survey describes the State Plane Coordinate System of 1983, including details on the equations used to perform the Lambert Conformal Conic and Mercator map projections of CCS83; Lambert Conformal Conic to Geographic Transformation Formulae from Land Information New Zealand
These last three equations can be used as the starting point for the derivation of an equation of motion in General Relativity, instead of assuming that acceleration is zero in free fall. [2] Because the Minkowski tensor is involved here, it becomes necessary to introduce something called the metric tensor in General Relativity.
The formulas for the spherical orthographic projection are derived using trigonometry.They are written in terms of longitude (λ) and latitude (φ) on the sphere.Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0).