Map Projection Series Introduction (iii)----map projection

4. Map projection

4.1 Projection Essence

A method of mapping points on the Earth's ellipsoid to a plane, called a map projection .

Why do you want to project?
– Geographical coordinates are spherical coordinates, which are not convenient for acreage of parameters such as distance, azimuth and area.
– The Earth ellipsoid is a non-developable surface.
– The map is planar, meets visual psychology, and is easy to distance, azimuth, area isometric and various spatial analyses.

The essence of projection: Cartesian plane right angle coordinate system by latitude coordinate

Establish the mathematical basis of the corresponding longitude network on the longitude Network on the Earth's ellipsoid, that is, the function relationship between the geographical coordinates (λ,φ) of the points on the Earth's ellipsoid and the plane coordinates (x, y) of the corresponding points on the plane. When different specific conditions are given, different types of projection are obtained.

4.2 Projection classification

The surface of the Earth's ellipsoid is an impossible surface to be unfolded, and cracks or folds will occur if such a surface is to be represented on a plane. On the projection surface, it can be avoided by using the longitude "stretch" or "compression" (mathematically) to form a complete map. But inevitably it will deform.

The deformation of a map projection is usually: length deformation , area deformation , and angular deformation . In the actual application, according to the purpose of using the map, to limit some kind of deformation.

Classification by deformation properties:
– Conformal projection: angular distortion of 0 (Mercator)
– Equal product projection: area deformation of 0 (Albers)
– Arbitrary projection: distortion of length, angle and area
Among them, various kinds of deformation and mutual influence: equal product and conformal mutual exclusion, equal product projection angle deformation is large, conformal projection area deformation.
from the projection surface type:
– Horizontal cylindrical projection: The projection surface is a horizontal cylinder
– conic projection: The projection surface is a cone
– Azimuth projection: Plane of projection plane
The relationship between the projection surface and the earth position is divided into:
– Positive axis projection: the center axis of the projection surface is coincident with the axis
– Oblique axis projection: The center axis of the projection surface intersects the axis
– Transverse projection: The center axis of the projection surface is perpendicular to the axis
– Tangent projection: Tangent of the projection surface to the ellipsoid
– Phase Cut projection: projection surface and ellipsoid

4.3 Projection selection

Key Considerations When choosing a map projection
– Extent, shape, and geographic location of the cartographic area (main factor)
– Use of maps, publication methods and other special requirements

          Projection selection instance
           – world map, The main use is positive cylinder, pseudo-cylinder and multi-conic projection. Mercator is also used to map world routes, world traffic maps, and world time zones.
           – the world map published in China is a multi-conic projection with equal differential parallels.
           – for hemisphere maps, the east and the Western Hemisphere are often selected by the transverse azimuth projection, and the north and the northern hemisphere are often selected with a positive-axis azimuth projection;
           – in the mid-latitude region of the east-west, normal-axis conic projections are commonly used, such as China and the United States.
           – in areas that extend north and south, they generally use horizontal cylindrical projections or multi-conic projections, such as Chile and Argentina.

projection Parameters:
 Standard line
– Concept: Tangent or secant of the projection plane and the reference ellipsoid. Divided into standard parallels and standard meridians.
– Features: No deformation, also known as the main scale.
 Center Line
– Concept: Refers to the Central meridian (the Origin meridian) and the central latitude (the origin parallels), which defines the center or origin of the projection of the graph.
– Features: Generally there will be deformation.

"Summary":
– The projection that achieves isometric, equal area, equidistant at the same time does not exist.
– The projection method is varied, and a country or region can choose the projection method according to its latitude and longitude, size and use of the map.
– In large-scale drawings larger than 1:100,000, the deformation caused by various projections can be ignored.

4.4 Common map projection in China (see next article)

Map Projection Series Introduction (iii)----map projection