Knowledge of common map projection (III.)---map projection in China

1. Gauss-gram Gauss–krüger projection

Gauss-gram Gauss–krüger projection This projection is by the German mathematician, physicist, astronomer Gauss in the 1820s, after the German geodesy home Crugge in 1912 to complement the projection formula, it is called Gauss-gram Gauss–krüger projection. Also known as transverse Mercator projection, tangent cylindrical projection, is a variant of the Mercator projection.

On the projection plane, the central meridian and the equatorial projection are straight lines, and with the central meridian and the equator intersection 0 as the coordinate origin, the central meridian is projected as a longitudinal axis, the equator is projected as a horizontal axis, thus forming a Gaussian plane Cartesian coordinate system.

(1) Concept: The elliptical cylinder is a projection surface, so that it is tangent to a certain meridian of the Earth's ellipsoid (the central meridian of the projection belt), and then, according to the isometric conditions, the central meridian is projected on both sides of a certain range onto the elliptical cylinder, and then projected into a planar projection, as shown in the following:

The central Meridian and the equatorial projection are straight lines perpendicular to each other, the other meridians are symmetrical to the central meridian, converging to the two-level concave curve, and the parallels are symmetric to the equator and bent to a two-level convex curve, longitude at right angles.

Gauskruge projection without angular deformation, that is, w=0, there is no deformation on the central meridian, that is, m0=1, the length of the other meridians is greater than 1, the farther away from the central meridian deformation greater.

(2) method of strip

Our provisions,1:25,000-1:500,000 of the topographic map using 6-degree sub-belt projection, that is, by the difference of 6 degrees, starting from the Zero Meridian, from west to east each through the difference of 6 degrees for a projection belt, the global total of 60 bands, with 1,2,3,4,5, ... Said. The relationship between the central Meridian and the band number is:l=n*6°-3°, China is in 13-23 belt, a total of 11 bands;

1:5000,1:1 's topographic map uses 3 degrees, starting from longitude 1.5 degrees, every 3 degrees for the area, with ... said that the global division of 120 projection belt, the central meridian and the relationship between the number:l=n*3°, China is in 23-45, a total of 22 bands;

How to Express in ArcGIS 10.2:

For example: National 2000 coordinate system, 6° zone, 13 bands are represented by: CGCS2000 GK Zone 13 (with code) CGCS2000 GK CM 75E (no band number, 75=13*6°-3°) For example: National 2000 coordinate system, 3° belt, 25 bands are represented by: CGCS2000 3 degree GK Zone 25 (with code) CGCS2000 3 degree GK CM 75E (no band number, 75=25*3°)

(3) Projection plane right angle coordinate system and coordinate network stipulation

1) projection plane Right angle coordinate system stipulation

in order to facilitate the measurement of the topographic map, a rectangular coordinate system is established in the Gaussian projection zone, which specifies that a central meridian is the x-axis and the equator is the y-axis, and its intersection point is the Origin o. The x values are positive in the northern hemisphere, negative in the southern hemisphere, and Y values are positive east of the central Meridian and negative to the West. I am over in the Northern hemisphere, the X value is all positive, in order to avoid negative values of Y, but also the x-axis to move westward 500km.

2) The plane rectangular coordinate (FANGRI) NET stipulation

3) geographical coordinates (latitude and longitude) net stipulation

4) adjacent belt supplementary Coordinate network and its regulations

2. Universal Transverse Mercator (Universal transverse Mercator projection,utm) projection

similar to the Gauskruge projection, the world is divided into 60 projection bands, each with a deviation of 6°, longitude from 180°w and 174°w as the starting band, and continuous eastward calculation, with the numbering system and 1:1 million scale map relevant provisions are consistent. the data of satellite imagery in China is usually based on UTM projection .

The difference between a Gauskruge projection and a UTM projection:

Gaussian-gram gauss–krüger projections and UTM projections are variants of the transverse Mercator projection, and currently some foreign software or supporting software for foreign imported instruments often does not support Gaussian-gram gauss–krüger projections, but supports UTM projections, Therefore, the UTM projection is often used as the Gaussian-gram gauss–krüger projection phenomenon.

from the projection geometry, the Gaussian-gram gauss–krüger projection is "conformal transverse elliptic column projection", the central meridian remains unchanged after projection, that is, the scale coefficient of 1;utm projection is "conformal transverse cylindrical projection", cylindrical cut the earth in the latitude 80 degrees, latitude 84 degrees two, such as High circle, After projection, there is no deformation on the two secant lines, and the length of the central meridian is 0.9996.

from the calculation results, the main difference between the two is the proportional factor, the Gaussian-gram gauss–krüger projection on the central meridian of the scale coefficient of 1,utm projection is 0.9996, Gaussian-gram gauss–krüger projection and UTM projection can be approximated x[utm]=0.9996 * x[Gauss],y[utm]= 0.9996 * y[Gauss], coordinate conversion (note: If the coordinate axis is shifted westward by 500000 meters, the conversion must be converted with the Y value minus 500000 multiplied by the scale factor plus 500000). From the point of view of the band, the beginning of the difference between the two, Gauss-gram Gauss–krüger projection from 0 degrees from the meridian every 6 degrees from the west to the east, the 1th with the central longitude of the 3°;utm projection from the longitude of the west of the 6 degrees from the western east of the belt, the 1th band of the central longitude of -177°, So the 1th band of the Gaussian-gram Gauss–krüger projection is the 31st band of UTM. In addition, the East Pseudo-offset (false_easting) of the two projections is 500 km, the Gaussian-gram Gauss–krüger projection North Pseudo-offset (false_northing) is zero, the UTM northern projection North Pseudo-offset (false_northing) is zero, and the southern hemisphere is 10000 km.

3. Lambert (Lambert) projection

Lambert projection It is a positive conic projection drawn up by the German mathematician Lambert (J.h.lambert). There are two kinds: ① conformal conic projection. It is envisaged to cut or cut the spherical surface with a positive cone, and apply the conformal condition to project the face of the earth onto the cone surface and then expand it into a plane along a busbar. After projection, the parallels are concentric circular arcs, and the meridians are concentric circle radii. There is no angular distortion, and the warp length is equal to the length of the parallels. It is suitable for middle and small scale map of mid-latitude region distributed along latitude. The international use of this projection 1:1 million topographic maps and aerial maps; ② azimuth projection. It is envisaged that the sphere and plane are tangent to a point, and the longitude is projected on the plane by the equal product condition.

In ArcGIS 10.2:

(1) Lambert_azimuthal_equal_area (equal product azimuth projection)

(2) Lambert_conformal_conic (conformal conic projection)

<span style= "FONT-SIZE:14PX;" >asia_lambert_conformal_conicwkid:102012 Authority:ESRIProjection:Lambert_Conformal_ConicFalse_Easting: 0.0false_northing:0.0central_meridian:105.0standard_parallel_1:30.0standard_parallel_2:62.0latitude_of_origin: 0.0Linear Unit:meter (1.0) Geographic coordinate system:gcs_wgs_1984angular unit:degree (0.0174532925199433) Prime Meridian:greenwich (0.0) Datum:D_WGS_1984Spheroid:WGS_1984Semimajor Axis:6378137.0semiminor Axis: 6356752.314245179Inverse flattening:298.257223563</span>

(3)lambert_azimuthal_equal_area_auxiliary

Deformation distribution Law:

① No angular distortion

② two standard parallels without any distortion.

③ and other deformation lines consistent with the parallels, that is, the same latitude on the deformation everywhere equal

④ on the same meridian, the outer side of the two standard parallels is a positive deformation (the length ratio is greater than 1), while the two standard parallels are negative variants (length ratio less than 1). Deformation is more uniform, the absolute value of deformation is also relatively small.

⑤ the line length of the same parallel lines is equal, and the length of the longitude between the two parallels is equal everywhere.

China 1: The 1 million topographic map uses the Lambert projection, and its principle of distribution is consistent with the global Unified International one out of 10,000 mapping projection stipulated by the International Geographic Society.

4. Albers (Albers) projection

Equal area cut conic projection, and Lambert projection input the same projection family, by Albers and 1805 years, most of China's provinces and most of this scale map use Albers and Lambert projection, commonly used to compile administrative divisions, population density map and socio-economic map, etc. .

Albers China Regional parameters: (25,47,105,0), for a custom Albers projection system, geodetic coordinates are CGCS2000:

Knowledge of common map projection (III.)---map projection in China