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Community Blog An Overview of Geographic and Projected Coordinate Systems

An Overview of Geographic and Projected Coordinate Systems

In this article, the author discusses geographic and projected coordinate systems and explores projecting a spherical object onto a planar surface.

By Digoal

First, let's talk about geographic coordinate systems. A geographic coordinate system describes a geographic location's position on the Earth's surface using spherical measures of latitude and longitude.

A geographic coordinate system is a spherical coordinate system. How to store digital information on Earth in a spherical coordinate system? As the Earth is an irregular spheroid, how to store data on such a spheroid scientifically?

Let's create a spheroid that supports quantitative calculations and has a long axis, a short axis, and an eccentricity.

The following rows list the parameters in the Krasovsky 1940 spheroid.

Spheroid: Krasovsky_1940
Semimajor Axis: 6378245.000000000000000000
Semiminor Axis: 6356863.018773047300000000
Inverse Flattening（扁率）: 298.300000000000010000

After determining the spheroid, we need a datum to pinpoint the spheroid. We can find the following row in the description of the coordinate system:

Datum: D_Beijing_1954

The preceding row indicates that the datum is D_Beijing_1954.

When the spheroid and datum are complete, a geographic coordinate system is ready for use.

Complete parameters:

Alias:
Abbreviation:
Remarks:
Angular Unit: Degree (0.017453292519943299)
Prime Meridian（起始经度）: Greenwich (0.000000000000000000)
Datum（大地基准面）: D_Beijing_1954
Spheroid（参考椭球体）: Krasovsky_1940
Semimajor Axis: 6378245.000000000000000000
Semiminor Axis: 6356863.018773047300000000
Inverse Flattening: 298.300000000000010000

Let's learn about projected coordinate systems from the following parameters:

Projection: Gauss_Kruger
Parameters:
False_Easting: 500000.000000
False_Northing: 0.000000
Central_Meridian: 117.000000
Scale_Factor: 1.000000
Latitude_Of_Origin: 0.000000
Linear Unit: Meter (1.000000)
Geographic Coordinate System:
Name: GCS_Beijing_1954
Alias:
Abbreviation:
Remarks:
Angular Unit: Degree (0.017453292519943299)
Prime Meridian: Greenwich (0.000000000000000000)
Datum: D_Beijing_1954
Spheroid: Krasovsky_1940
Semimajor Axis: 6378245.000000000000000000
Semiminor Axis: 6356863.018773047300000000
Inverse Flattening: 298.300000000000010000

According to these parameters, each projected coordinate system has a geographic coordinate system.

Projected coordinate systems are essentially planar coordinate systems, which store maps in meters.

Why does a projected coordinate system use parameters of a geographic coordinate system?

Here, we need to understand what projection is. Projection is a process of converting spherical coordinates into planar coordinates.

Then we can understand what is required to project a spherical object onto a planar surface:

1) Spherical coordinates

2) Conversion process (algorithm)

In other words, a spherical coordinate must be available for projection using an algorithm in order to obtain a projected coordinate. Therefore, every projected coordinate system must have parameters of a geographic coordinate system.

We can find various names of coordinate systems in textbooks. Projections in all these coordinate systems, including the commonly seen "non-Earth projected coordinate system," can be categorized into the foregoing two types.

Geodetic coordinate: It is a coordinate that uses a reference spheroid as a datum in geodetic surveying. A ground point P is represented by geodetic longitude L, geodetic latitude B, and geodetic height H. A point on the reference spheroid is represented only by geodetic longitude and geodetic latitude. Geodetic longitude is the angle from the prime meridian plane to the meridian plane of a given point. Geodetic latitude is the angle from the equatorial plane to the perpendicular to the ellipsoid through a given point. Geodetic height is the distance between the ground point and the reference spheroid along the normal of a given point.

Kilometer grid: It is a grid consisting of two groups of parallel lines parallel to the projected coordinate axes. A vertical coordinate line and a horizontal coordinate line are separately drawn for every integer kilometer point in the grid. That is why the grid is referred to as a kilometer grid. The kilometer lines are also coordinate grid lines parallel to the axes of a rectangular coordinate system, therefore also referred to as a rectangular coordinate grid.

On a topographic map with a scale of 1:10,000 to 1:200,000, longitude and latitude lines are directly presented as sheet lines, and the corresponding degrees are labeled in the corners. To draw lines on the map to form a net during use, draw graduations (referred to as scale division lines in schematism) between the inner and outer map borders, and connect the corresponding graduations to form a graticule. On a topographic map with a scale of 1:250,000, in addition to the graduations provided on the inner map border for drawing lines to form a graticule, reticles are further provided on the map.

In China, on a topographic map with a scale of 1:500,000 to 1:1,000,000, the graticule is directly drawn on the map, and graduations are further provided on the inner map border for drawing more lines.

In the rectangular coordinate grid coordinate system, a projected line of the central longitude line is the X-axis, a projected line of the equator is the Y-axis, and the intersection of the X-axis and the Y-axis is the origin. In this way, the coordinate system has four quadrants. The Y-axis is positive to the north and negative to the south from the equator. The X-axis is positive to the east and negative to the west from the central longitude.

Although the kilometer grid can be regarded as a rectangular coordinate system, geodetic coordinates are spherical coordinates. Kilometer grids and graticules are commonly seen on maps. A graticule is habitually referred to as a geodetic coordinate system. In this case, the geodetic coordinate system is a planar coordinate system rather than a spherical coordinate system. It has the same projection (which is usually a Gaussian projection) as a kilometer grid.

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