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The Lambert projection is relatively easy to use: conversions from geodetic (latitude/longitude) to State Plane Grid coordinates involve trigonometric equations that are fairly straightforward and which can be solved on most scientific calculators, especially programmable models. [9]
Most state plane zones are based on either a transverse Mercator projection or a Lambert conformal conic projection. The choice between the two map projections is based on the shape of the state and its zones. States that are long in the east–west direction are typically divided into zones that are also long east–west.
The invention of the Lambert cylindrical equal-area projection is attributed to the Swiss mathematician Johann Heinrich Lambert in 1772. [1] Variations of it appeared over the years by inventors who stretched the height of the Lambert and compressed the width commensurately in various ratios.
There are several projections used in maps carrying the name of Johann Heinrich Lambert: Lambert cylindrical equal-area projection (preserves areas) Lambert azimuthal equal-area projection (preserves areas) Lambert conformal conic projection (preserves angles, commonly used in aviation navigation maps) Lambert equal-area conic projection ...
Lambert's projection is the basis for the cylindrical equal-area projection family. Lambert chose the equator as the parallel of no distortion. [2] By multiplying the projection's height by some factor and dividing the width by the same factor, the regions of no distortion can be moved to any desired pair of parallels north and south of the ...
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection; that is, the projection is a conformal map in the mathematical sense. For example, if two roads cross each other at a 39° angle, their images on a map ...
Lambert azimuthal equal-area projection of the world. The center is 0° N 0° E. The antipode is 0° N 180° E, near Kiribati in the Pacific Ocean.That point is represented by the entire circular boundary of the map, and the ocean around that point appears along the entire boundary.
The inverse projection for φ and λ are sixth order expansions in terms of the ratio x / a , with coefficients expressed in terms of y, a and e. (See Transverse Mercator: Redfearn series.) The Krüger–λ series were the first to be implemented, possibly because they were much easier to evaluate on the hand calculators of the mid ...