The GIS program must deal with three type of coordinates:

**Screen coordinates**, which are reported by the operating system as the mouse moves, and used to plot of bitmaps which are then displayed on the screen. This has an origin in the upper left corder, the standard for computer graphics.**Projected map coordinates**, in meters (perhaps stretched, depending on the projection). These have a cartesian references system. These are used by the GIS program to map to the screen, which is a simple operation between two Cartesian system which involves scaling and translation of the axes. These reference a particular datum and projection.**Geographic map coordinates**, in latitude/longitude. These reference only a datum.

This is the full data stream to do conversions. The map to data column must be done every time the user moves the mouse, to show the screen coordinates, or when the user clicks on the map or selects a rectangular region. The data to map coordiniates column must be done every time the program must display coordinates from a data file on the screen. Since a map can have millions of data points, anything that speeds up the process can have significant results.

Coordinates | Action, map to data coordinates (top to bottom) | Action, data coordinates to map (bottom to top) |

Screen Coordinates | Simple transformation (move origin, rescale) | |

Projected map coordinates, like UTM | Inverse projection equations (x,y to lat, long) | Simple transformation (move origin, rescale) |

Geographic map coordinates | Molodensky transformation (lat, long to lat, long) | Projection forward equations (lat,long to x,y) |

WGS84 geographic coordinates | Molodensky transformation (lat, long to lat, long) | Molodensky transformation (lat, long to lat, long) |

Second datum WGS geographic coordinates | Projection forward equations (lat,long to x,y) | Molodensky transformation (lat, long to lat, long) |

Second datum projected map coordinates, Like UTM | Inverse projection equations (x,y to lat, long) |

In the early days of GIS, many of the transformation equations were very expensive to use. Thus programs often requried that the data files used had the same projection as the map. Any required transformations would be done once, before analysis. The equatrions required require only simple arithmetic.

Coordinates | Action, map to data (top to bottom) | Action, data to map (bottom to top) |

Screen Coordinates | Simple transformation (move origin, rescale) | |

Projected map coordinates, like UTM | Simple transformation (move origin, rescale) |

This does not work with data in geographic coordinates, unless one uses a plate carrée projection which is not appropriate for large scale mapping. Many global data sets like ETOPO use geographic coordinates, as do most moderate scale DEMs like SRTM, ASTER, and MERIT, becasue they do not have the zone boundary problems in projections like the UTM. This required using the inverse or forward projection equations for every point.

Coordinates | Action, map to data (top to bottom) | Action, data to map (bottom to top) |

Screen Coordinates | Simple transformation (move origin, rescale) | |

Projected map coordinates, like UTM | Inverse projection equations (x,y to lat, long) | Simple transformation (move origin, rescale) |

Geographic map coordinates | Projection forward equations (lat,long to x,y) |

If you need to put data sets from a different projection on the map, say a SPCS system on a UTM map, the required actions would look like this:

Coordinates | Action, map to data (top to bottom) | Action, data to map (bottom to top) |

Screen Coordinates | Simple transformation (move origin, rescale) | |

Projected map coordinates, like UTM | Inverse projection equations (x,y to lat, long) | Simple transformation (move origin, rescale) |

Geographic map coordinates | Second projection forward equations (lat,long to x,y) | Projection forward equations (lat,long to x,y) |

Second projection projected map coordinates, Like SPCS | Second projection Inverse equations (x,y to lat, long) |

As computers got faster, the cost of performing the transformations grew less, and currently is essentially negligible. The requriment to reproject data before it could be used became a bother for users, and led to having to have copies of particular data sets in each projection a user wanted to use. To ease this burden, GIS programs began to allow "on the fly reprojection", when the the program would reproject as needed, and spare the user having to worry about the details.

Google Earth allows only geographic coordinates in WGS84, so in a sense they have returned to the old standard, but picked a single world wide projection.

It should be clear that the GIS program needs to know the datum and projection for every data set, which should be in the metadata. If it is not, the user must assign a projection, and that requires the the user know the information. You can find this several ways:

- Look at the metadata with the file. Unlike the WKT standard for the PRJ file, there are no standards for metadata (or the standards are so loose that the GIS programs cannot easily extract the desired or requird information), this cannot be automated.
- Go to the website where you got the data; there will often be information there.
- Look at the coordinates.
- If the data is geographic, the ranges should clearly indicate this (x in the range -180 to 180, y in the range -90 to 90).
- If the numbers are in the 100,000's or 1,000,000's, it is probably UTM, SPCS, or a similar system. Based on the source of the data and the region it covers, you may be able to guess the projection. You can try assigning that projection; you must then verify your guess. Simply hoping the data is UTM, becasue that is what you would use, does not guarantee success.

Assigning the projection is not the same as Reprojecting the data set. You can reproject to any projection you want, and should notice the time it takes to change the coordinates; you can correctly only assign a single projection, that used by the data creator.

There should be no data in this situation with datum and projection information, but unfortunately there often is.

*Last revision 11/20/2017*