# Coordinates in Projected Maps

Before proceeding with this Topic, please read the Coordinates topic and Projections Tutorial topic first.

In the Coordinates topic we saw how a drawing can be created on graph paper with a sequence of X,Y coordinates measured from the origin showing how to draw every object in the drawing. Drawings are just computer files filled with sequences of coordinates that are used to make the drawing in a "connect the dots" fashion.

To create a "flat" digital map, we use the same approach we did in drawing a plan of our office desk set in the Coordinates topic.

Recall the illustration of a cylindrical projection from the Projections Tutorial topic. It showed how a small part of the surface of the Earth could be "projected" onto a section of cylinder, which could then be unrolled into a flat sheet. If we want to save the X,Y locations of points on our flat sheet we can now measure them as though the flat sheet were graph paper to create a diagram of geographic features, just as we created a diagram of our desk set on a sheet of graph paper.

The above illustration shows a key concept that often proves confusing to GIS newcomers: although "unprojected' data about locations on the Earth are specified in degrees, all projected maps specify the coordinates of the objects on them with X,Y coordinates that are numbers representing meters, feet or other linear measures. These coordinates are computed relative to some origin established by the projection in use.

Computer files that contain projected maps therefore contain coordinates like

44030976,38403088

44030984,38403080

44030900,38403077

…and not longitude,latitude coordinate numbers such as

-110.3484, 44.2856

-110.3463, 44.2889

-110.3511, 44.2902

Latitude,longitude coordinates are normally in decimal degrees as shown above, while the coordinate numbers in projected files are most often meters in X and Y directions from some origin known to the projection. It is as if the green sheet in the illustration above were an enormous piece of graph paper on which the map is drawn "full size" and then measured off in meters.

In a well run GIS system the internal coordinates of projected maps may be hidden from the user because the GIS software will automatically translate the internal map drawing coordinates into Latitude/Longitude values on the fly. Manifold, for example, will show cursor position in a projected map view using Latitude and Longitude values. What is going on is that Manifold is automatically translating internal projected coordinates like 44030984,38403080 into the equivalent Longitude and Latitude values. Manifold allows "toggling" the status XY indicator between native units and lat/lon.

New GIS users are often fooled by the system's "translation on the fly" into thinking that their projected maps still contain coordinates in latitude/longitude degree form. This is not the case, since once a drawing is projected out of Latitude / Longitude into a different projection it will be in meters or other linear measure even though many Manifold dialogs will show the contents in degrees for the convenience of the user.

Projected Coordinates and Projection Parameters

The particular set of coordinate numbers in a projected file will make sense only if used within the projection parameters and projection within which they are intended to be interpreted. The projection parameters in use for a drawing may be seen at any time by viewing its coordinate properties. Click on the drawing in the project view to highlight it and then choose the Edit - Assign Projection dialog to open the properties dialog for that component. The coordinate properties tell Manifold how to interpret the data in that drawing. If these properties are changed, they simply change how Manifold uses the existing data. Changes in this dialog do not change the data itself.

For example, if we imported the following sequence of coordinate numbers…

44030976,38403088

44030984,38403080

44030900,38403077

…from an ESRI "shapefile" they would make no sense if the coordinates properties were set to use Latitude / Longitude with coordinates interpreted as degrees. If we knew these coordinates were created for use with some particular UTM zone projection parameters we could open the Edit - Assign Projection dialog and enter those UTM zone parameters. The drawing would then make sense within Manifold.

Note that there is nothing about the raw numbers that says how they should be interpreted. "Smart" GIS formats will always save the required projection information with the file containing the coordinate numbers. When importing drawings from such formats Manifold can automatically grab the required projection information and use it for that drawing's coordinate properties.

Legacy GIS formats do not save the necessary projection information with the files containing projected coordinates. This poses a big problem if one acquires a file full of projected coordinates without knowing what projection was used. ESRI's "shapefile" format is a classic legacy format that does not include projection information. It's best to use this and other legacy formats only for unprojected maps that require no elaborate projection parameters.

Changing Projections

Changing projections in a Manifold map is easy: we simply use the Edit - Assign Projection dialog to specify whatever projection we want and Manifold will automatically display all drawings and images in that map within that projection. There's no change to the native projections used by the drawings and the images since map windows in Manifold re-project their contents on the fly.

Because drawings are normally seen through map view within maps, it is not normally necessary to reproject them from whatever projection they were in when imported. Specifying the projection used by a map in map view does not change any data - it simply changes the way the data is seen in that particular map view. If desired, we can see the same drawings simultaneously through different map views using different projections in each map view.

The only time we might need to reproject a drawing is to speed up map view. Map view works much faster if the drawings it contains use the same projection requested of map view. This is especially true if many, large drawings and images are used in the map.

The X,Y coordinates in a projected drawing make sense only within the "grid" coordinate system used by that particular set of projection parameters. If we wish to change the projection within which the drawing exists we need to re-compute the numbers into their equivalents in the new projection.

Manifold does this via the Edit - Change Projection dialog. Specifying a projection with any optional parameters in this dialog will cause the coordinate numbers within the file to be changed into their equivalents in the new projection. The Edit - Assign Projection dialog will also be updated with the new interpretation.