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I was googling coordinate related information all the day. Now I am confused with some concepts and terms. I hope some one can help me to make it clear.

  • Geographic coordinate system

    Geographic coordinate is used to describe the location of the earth in a three-dimension which will base on the ellipsoid and a datum. And I always thought that the geographic coordinate are always the latitude and longitude. Am I wrong?

  • Projected coordinate system

    It seems that the projected coordinate system will contains three points:

    1. The projection itself. It means how the earth will be translate to a two-dimension surface. For example the Cylindrical and Pseudocylindrical.

    2. The geographic coordinate system which this pcs working for.

    3. The Mathematics manner to translate the geographic coordinate to projection coordinate. BTW, is projection coordinate always a point inside the the Cartesian coordinate system? And is projection coordinate only fit for one kind of geographic coordinate system?

  • Coordinate reference system

    Now I have no idea about what a coordinate reference system is. Is the Coordinate reference system has anything to do with the projection?

BTW,is the geodetic latitude is measured on the surface of the referenced ellipsoid?

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The first two questions are duplicates of gis.stackexchange.com/questions/60622/…. –  whuber May 14 '13 at 17:20
    
There maybe some duplicates, but through the old post I got some answsers and I have some ideas. But I am not sure if I am right. So the first questions contains my own opinions. –  giser May 14 '13 at 23:48
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up vote 2 down vote accepted

I think, technically, this 'question' should be split into several questions! I going to try to answer your questions or clarify your statements out of order because I think it will make more sense.

A coordinate reference system, when used in the GIS field, is a generic term for a reference framework that's used to locate points (lines, polygons, etc). Geographic, vertical, projected and other terms are used to identify particular versions of a coordinate reference system. I believe ISO 19111 (International Standards Organization) uses the term 'coordinate system' for a different thing. Certainly, the EPSG Geodetic Parameter Dataset does in its schema, and it follows ISO 19111. So I'll use coordinate reference system for the rest of this answer. You might want to look at the Guidance Notes 7-1 and 7-2 from the EPSG website.

A geographic coordinate reference system is based upon a geodetic datum and an angular unit of measure. A geodetic datum is built upon an ellipsoid and a prime meridian. A 2D geographic CRS uses latitude and longitude values to location positions on the surface of the datum (aka the ellipsoid). A 3D geographic CRS has latitude and longitude and h (ellipsoidal height). A geographic CRS is often valid only in a particular area, particularly older ones. In that case, positions in this geographic CRS may not really fit the ellipsoid surface that well, due to inaccuracies in the original control network used to define the datum.

Geodetic latitude is the angle formed between the equatorial plane and a line that's perpendicular to the ellipsoid surface. That line will not cross the polar axis at the equatorial plan except at the equator, so it's not a geocentric angle (measured at the center of the ellipsoid).

A projected coordinate reference system is a 2D Cartesian system and contains a geographic CRS (usually 2D), a map projection and any parameter values needed by the projection, plus a linear unit of measure. You may also want to know what the axes directions, order and labels are. In the US, directions are usually easting,northing, and labeled X,Y. The map projection is just an identifier of an algorithm that is used to convert between latitude,longitude and X,Y (easting,northing) values.

A projected coordinate system can use the same map projection and parameter values but be based upon difference geographic CRS. A good example is a UTM zone. UTM zone 17N could be based upon NAD 1927, NAD 1983, NAD 1983 (CSRS), NAD 1983 (2011), etc.

Your first point under 'projected coordinate system' is a characteristic of a particular map projection. A map projection might be cylindrical, conformal, supports spheres only, etc.

I think that's enough for now!

Disclaimer: I'm on the subcommittee that maintains the EPSG Geodetic Parameter Dataset.

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In fact, I just read the '04-046r3_Topic_2_-_Spatial_referencing_by_coordinates' after which I feel more confused. So I want to make it clear it that: gcs with projection(with parameters) will generate a new pcs? For example, we have maps which use the CSCS2000 gcs, now if we want to use the Mercator projection, does it mean that we are creating a new projection coordinate systaem, since I have not found any existed pcs can meet my requirement? –  giser May 18 '13 at 0:55
    
Yes, that's correct. –  mkennedy May 19 '13 at 15:24
    
Thank you , I got it.:) –  giser May 19 '13 at 23:56
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