An Overview of Geographic and Projected Coordinate Systems

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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