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Projection Parameters

Every projection has at least one parameter that controls how it transforms geographic coordinates into planar coordinates. Some projections are rather fixed, and aside from the orientation vector and nominal scale factor, have no parameters that the user should vary, as to do so would violate the definition of the projection. For example, the Robinson projection has one standard parallel that is fixed by definition at 38º North and South; the Cassini and Wetch projections cannot be constructed in other than Normal aspect. In general, however, projections have several variable parameters. The following section discusses map projection parameters and provides guidance for setting them.

Projection Characteristics Maps Can Have

In addition to the name of the projection itself, the parameters that a map projection can have are

  • Aspect — Orientation of the projection on the display surface

  • Center or Origin — Latitude and longitude of the midpoint of the display

  • Scale Factor — Ratio of distance on the map to distance on the ground

  • Standard Parallel(s) — Chosen latitude(s) where scale distortion is zero

  • False Northing — Planar offset for coordinates on the vertical map axis

  • False Easting — Planar offset for coordinates on the horizontal map axis

  • Zone — Designated latitude-longitude quadrangle used to systematically partition the planet for certain classes of projections

While not all projections require all these parameters, there will always be a projection aspect, origin, and scale.

Other parameters are associated with the graphic expression of a projection, but do not define its mathematical outcome. These include

  • Map latitude and longitude limits

  • Frame latitude and longitude limits

However, as certain projections are unable to map an entire planet, or become very distorted over large regions, these limits are sometimes a necessary part of setting up a projection.

Determining Projection Parameters

In the following exercise, you define a map axes and examine default parameters for a cylindrical, a conic, and an azimuthal projection.

  1. Set up a default Mercator projection (which is cylindrical) and pass its handle to the getm function to query projection parameters:

    figure;
    h=axesm('Mapprojection','mercator','Grid','on','Frame','on',...
    'MlabelParallel',0,'PlabelMeridian',0,'mlabellocation',60,...
    'meridianlabel','on','parallellabel','on')

    The graticule and frame for the default map projection are shown below.

  2. Query the map axes handle using getm to inspect the properties that pertain to map projection parameters. The principal ones are aspect, origin, scalefactor, nparallels, mapparallels, falsenorthing, falseeasting, zone, maplatlimit, maplonlimit, rlatlimit, and flonlimit:

    getm(h,'aspect')
    
    ans =
         normal
    
    getm(h,'origin')
    
    ans =
         0     0     0
    
    getm(h,'scalefactor')
    
    ans =
         1
    
    getm(h,'nparallels')
    
    ans =
         1
    
    getm(h,'mapparallels')
    
    ans =
         0
    
    getm(h,'falsenorthing')
    
    ans =
         0
    
    getm(h,'falseeasting')
    
    ans =
         0
    
    getm(h,'zone')
    
    ans =
         []
    
    getm(h,'maplatlimit')
    
    ans =
       -86    86
    
    getm(h,'maplonlimit')
    
    ans =
      -180   180
    
    getm(h,'Flatlimit')
    
    ans =
       -86    86
    
    getm(h,'Flonlimit')
    
    ans =
      -180   180

    For more information on these and other map axes properties, see the reference page for axesm.

  3. Reset the projection type to equal-area conic ('eqaconic'). The figure is redrawn to reflect the change. Determine the parameters that the toolbox changes in response:

    setm(h,'Mapprojection', 'eqaconic')
    getm(h,'aspect')
    
    ans =
    normal
    
    getm(h,'origin')
    
    ans =
         0     0     0
    
    getm(h,'scalefactor')
    
    ans =
         1
    
    getm(h,'nparallels')
    
    ans =
         2
    
    getm(h,'mapparallels')
    
    ans =
        15    75
    
    getm(h,'falsenorthing')
    
    ans =
         0
    
    getm(h,'falseeasting')
    
    ans =
         0
    
    getm(h,'zone')
    
    ans =
         []
    
    getm(h,'maplatlimit')
    
    ans =
       -86    86
    
    getm(h,'maplonlimit')
    
    ans =
      -135   135
    
    getm(h,'Flatlimit')
    
    ans =
       -86    86
    
    getm(h,'Flonlimit')
    
    ans =
      -135   135

    The eqaconic projection has two standard parallels, at 15º and 75º. It also has reduced longitude limits (covering 270º rather than 360º). The resulting eqaconic graticule is shown below.

  4. Now set the projection type to Stereographic ('stereo') and examine the same properties as you did for the previous projections:

    setm(h,'Mapprojection','stereo')
    setm(gca,'MLabelParallel',0,'PLabelMeridian',0)
    getm(h,'aspect')
    
    ans =
    normal
    
    getm(h,'origin')
    
    ans =
         0     0     0
    
    getm(h,'scalefactor')
    
    ans =
         1
    
    getm(h,'nparallels')
    
    ans =
         0
    
    getm(h,'mapparallels')
    
    ans =
         []
    
    getm(h,'falsenorthing')
    
    ans =
         0
    
    getm(h,'falseeasting')
    
    ans =
         0
    
    getm(h,'zone')
    
    ans =
         []
    
    getm(h,'maplatlimit')
    
    ans =
       -90    90
    
    getm(h,'maplonlimit')
    
    ans =
      -180   180
    
    getm(h,'Flatlimit')
    
    ans =
       -Inf    90
    
    getm(h,'Flonlimit')
    
    ans =
      -180   180

    The stereographic projection, being azimuthal, does not have standard parallels, so none are indicated. The map limits do not change from the previous projection. The map figure is shown below.

Supported Map Projections lists and illustrates all supported Mapping Toolbox™ map projections, including suggestions for parameter usage.

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