#Parallels map how to#

Map projection equations have a significant role in projection change Using the forward mapping equation of the north polar stereographic projection, the values found for the Cartesian coordinates are for x = -2615435m and for y = 2194610m. Suppose the same point, located at 60 oN and 130 oW, is projected on a map that uses the stereographic projection (where the reference surface is a sphere with a radius of 6371000 m., the centre of the projection is located on the North pole and the longitude of the centre ( l o) is 0 o).

Where R is the radius of the spherical reference surface l o is the longitude of the projection cen tre.

The second example is the mapping equations used for the north polar stereographic projection:.

Using the forward mapping equation of the Mercator projection, the values found for the Cartesian coordinates are for x = -14,455,340m and for y = 8,390,339m. and the central meridian ( l o) is 0 o, equal to the Greenwich meridian). Suppose a point, located at 60 oN and 130 oW, is projected on a map that uses the Mercator projection (where the reference surface is a sphere with a radius of 6371000 m. Where R is the radius of the spherical reference surface f and l are given in radians l o is the central meridian of the projection e = 2.7182818, the base of the natural logarithms, not the eccentricity.

The first example are the mapping equations used for the Mercator projection:.

The corresponding inverse mapping equation transforms mathematically the planar Cartesian coordinates ( x,y) of a point on the map plane to a set of geographic coordinates ( f, l ) on the curved reference surface:ДЇollowing are two examples of mapping equations for the sphere (equations for the ellipsoid are generally more complex). A forward mapping equation transforms the geographic coordinates ( f, l ) of a point on the curved reference surface to a set of planar Cartesian coordinates ( x, y), representing the position of the same point on the map plane: This is mostly achieved through mapping equations. The actual mapping cannot usually be visualized as a true geometric projection, directly onto the mapping plane as illustrated in the figure above. Mapping onto a 2D mapping plane means transforming each point on the reference surface with geographic coordinates ( f, l ) to a set of Cartesian coordinates ( x, y) representing positions on the map plane (figure below).Д®xample of a map projection where the reference surface with geographic coordinates ( f, l ) is projected onto the 2D mapping plane with 2D Cartesian coordinates (x, y).

The reference surface for large-scale mapping is usually an oblate ellipsoid, and for small-scale mapping, a sphere. To represent parts of the surface of the Earth on a flat paper map or on a computer screen, the curved horizontal reference surface must be mapped onto the 2D mapping plane.

#Parallels map how to#

The field of map projections concerns itself with the ways of translating the curved surface of the Earth into a flat map.ДЄ map projection is a mathematically described technique of how to represent the EarthвЂ™s curved surface on a flat map. Now that we know that the EarthвЂ™s surface is curved in a specific way, we know that a map is in fact a flattened representation of some part of the planet. For quite some time it was thought that our planet was flat, and during those days, a map simply was a miniature representation of a part of the world. Maps are one of the worldвЂ™s oldest types of document.

Geometric aspects of mapping: map projections

2022.03

Parallels map