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Orthographic projection in cartography has been used since antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance.
Orthographic projection (also orthogonal projection and analemma) [a] is a means of representing three-dimensional objects in two dimensions.Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, [2] resulting in every plane of the scene appearing in affine transformation on the viewing surface.
They map parallels to complex curves bowing away from the equator, and meridians to complex curves bowing in toward the central meridian. Listed here after pseudocylindrical as generally similar to them in shape and purpose. Other Typically calculated from formula, and not based on a particular projection Polyhedral maps
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
Therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane. [citation needed] The most well-known map projection is the Mercator projection. [7]: 45 This map projection has the property of being conformal. However, it has been criticized throughout the 20th century for enlarging regions ...
In the 16th and 17th century, the equatorial aspect of the stereographic projection was commonly used for maps of the Eastern and Western Hemispheres. It is believed that already the map created in 1507 by Gualterius Lud [6] was in stereographic projection, as were later the maps of Jean Roze (1542), Rumold Mercator (1595), and many others. [7]
The Lambert azimuthal projection is used as a map projection in cartography. For example, the National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, [3] and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. [4]
The map has area 4 π R 2, conforming to the surface area of the generating globe. The x-coordinate has a range of [−2R √ 2, 2R √ 2], and the y-coordinate has a range of [−R √ 2, R √ 2]. Equation (1) may be solved with rapid convergence (but slow near the poles) using Newton–Raphson iteration: [5]