3 Examples

Here are some examples of how GeoTIFF may be implemented at the Tag and GeoKey level, following the general "Cookbook" approach above.

We have an aerial photo which has been orthorectified and resampled to a UTM grid, zone 60, using WGS84 datum; the coordinates of the upper-left corner of the image is are given in easting/northing, as 350807.4m, 5316081.3m. The scanned map pixel scale is 100 meters/pixels (the actual dpi scanning ratio is irrelevant).

   
      ModelTiepointTag       = (0, 0, 0,  350807.4, 5316081.3, 0.0)
      ModelPixelScaleTag      = (100.0, 100.0, 0.0)
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey        =  1      (ModelTypeProjected)
            GTRasterTypeGeoKey       =  1      (RasterPixelIsArea)
            ProjectedCSTypeGeoKey    =  32660  (PCS_WGS84_UTM_zone_60N)
            PCSCitationGeoKey        =  "UTM Zone 60 N with WGS84"
            
   
   Notes:
   1) We did not need to specify the GCS lat-long, since the 
      PCS_WGS84_UTM_zone_60N codes implies particular 
      GCS and units already (WGS_84 and meters). The citation
      was added just for documentation.
 
   2)  The "GeoKeyDirectoryTag" is expressed using the "GeoKey" 
   structure defined above. At the TIFF level the tags look like
   this:
      GeoKeyDirectoryTag=(  1,     0,     2,       4,
                         1024,     0,     1,       1,
                         1025,     0,     1,       1,
                         3072,     0,     1,       32660,
                         3073, 34737,    25,       0 ) 
      GeoAsciiParamsTag(34737)=("UTM Zone 60 N with WGS84|")
      
   For the rest of these examples we will only show the GeoKey-level
   dump, with the understanding that the actual TIFF-level tag
   representation can be determined from the documentation.

3.1.2. Standard State Plane

We have a USGS State Plane Map of Texas, Central Zone, using NAD83, correctly oriented. The map resolution is 1000 meters/pixel, at origin. There is a grid intersection line in the image at pixel location (50,100), and corresponds to the projected coordinate system easting/northing of (949465.0, 3070309.1).

      
      ModelTiepointTag           = (  50,  100, 0, 949465.0, 3070309.1, 0)   
      ModelPixelScaleTag         = (1000, 1000, 0)
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey            =  1   (ModelTypeProjected)
            GTRasterTypeGeoKey           =  1   (RasterPixelIsArea)
            ProjectedCSTypeGeoKey        = 32139 (PCS_NAD83_Texas_Central)
    Notice that in this case, since the PCS is a standard code, we
    do not need to define the GCS, datum, etc, since those are implied
    by the PCS code. Also, since this is NAD83, meters are used rather
    than US Survey feet (as in NAD 27).

3.1.3. Lambert Conformal Conic Aeronautical Chart

We have a 500 x 500 scanned aeronautical chart of Seattle, WA, using Lambert Conformal Conic projection, correctly oriented. The central meridian is at 120 degrees west. The map resolution is 1000 meters/pixel, at origin, and uses NAD27 datum. The standard parallels of the projection are at 41d20m N and 48d40m N. The latitude of the origin is at 45 degrees North, and occurs in the image at the raster coordinates (80,100). The origin is given a false easting and northing of 200000m, 1500000m.

      
      ModelTiepointTag          = (  80,  100, 0,  200000,  1500000,  0)   
      ModelPixelScaleTag         = (1000, 1000, 0)
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey               =  1     (ModelTypeProjected)
            GTRasterTypeGeoKey              =  1     (RasterPixelIsArea)
            GeographicTypeGeoKey            =  4267  (GCS_NAD27)
            ProjectedCSTypeGeoKey           =  32767 (user-defined)
            ProjectionGeoKey                =  32767 (user-defined)
            ProjLinearUnitsGeoKey           =  9001     (Linear_Meter)
            ProjCoordTransGeoKey            =  8  (CT_LambertConfConic_2SP)
                 ProjStdParallel1GeoKey     =  41.333
                 ProjStdParallel2GeoKey     =  48.666
                 ProjCenterLongGeoKey       =-120.0
                 ProjNatOriginLatGeoKey     =  45.0
                 ProjFalseEastingGeoKey,    = 200000.0
                 ProjFalseNorthingGeoKey,   = 1500000.0
   Notice that the Tiepoint takes the false easting and northing into
   account when tying the raster point (50,100) to the projection origin.

3.1.4. DMA ADRG Raster Graphic Map

The U.S. Defense Mapping Agency produces ARC digitized raster graphics datasets by scanning maps and geometrically resampling them into an equirectangular projection, so that they may be directly indexed with WGS84 geographic coordinates. The scale for one map is 0.2 degrees per pixel horizontally, 0.1 degrees per pixel vertically. If stored in a GeoTIFF file it contains the following information:

      ModelTiepointTag=(0.0, 0.0, 0.0,  -120.0,       32.0,     0.0)
      ModelPixelScale = (0.2, 0.1, 0.0) 
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey          =  2   (ModelTypeGeographic)
            GTRasterTypeGeoKey         =  1   (RasterPixelIsArea)
            GeographicTypeGeoKey       =  4326 (GCS_WGS_84)

3.2 Less Common Examples

3.2.1. Unrectified Aerial photo, known tiepoints, in degrees.

We have an aerial photo, and know only the WGS84 GPS location of several points in the scene: the upper left corner is 120 degrees West, 32 degrees North, the lower-left corner is at 120 degrees West, 30 degrees 20 minutes North, and the lower-right hand corner of the image is at 116 degrees 40 minutes West, 30 degrees 20 minutes North. The photo is not geometrically corrected, however, and the complete projection is therefore not known.

   
    ModelTiepointTag=(   0.0,    0.0, 0.0,  -120.0,       32.0,     0.0,
                         0.0, 1000.0, 0.0,  -120.0,       30.33333, 0.0,
                      1000.0, 1000.0, 0.0,  -116.6666667, 30.33333, 0.0) 
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey          =   1 (ModelTypeGeographic)
            GTRasterTypeGeoKey         =   1 (RasterPixelIsArea)
            GeographicTypeGeoKey       = 4326 (GCS_WGS_84)
            
    Remark: Since we have not specified the ModelPixelScaleTag, clients
       reading this GeoTIFF file are not permitted to infer that there
       is a simple linear relationship between the raster data and the
       geographic model coordinate space. The only points that are know
       to be exact are the ones specified in the tiepoint tag.

3.2.2. Rotated Scanned Map

We have a scanned standard British National Grid, covering the 100km grid zone NZ. Consulting documentation for BNG we find that the southwest corner of the NZ zone has an easting,northing of 400000m, 500000m, relative to the BNG standard false origin. This scanned map has a resolution of 100 meter pixels, and was rotated 90 degrees to fit onto the scanner, so that the southwest corner is now the northwest corner. In this case we must use the ModelTransformation tag rather than the tiepoint/scale pair to map the raster data into model space:

   
      ModelTransformationTag  = (     0, 100.0,     0,   400000.0,
                                  100.0,     0,     0,   500000.0,
                                      0,     0,     0,          0,
                                      0,     0,     0,          1)
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey        =  1 ( ModelTypeProjected)
            GTRasterTypeGeoKey       =  1  (RasterPixelIsArea)
            ProjectedCSTypeGeoKey    =  27700 (PCS_British_National_Grid)
            PCSCitationGeoKey        =  "British National Grid, Zone NZ"

Remark: the matrix has 100.0 in the off-diagonals due to the 90 degree rotation; increasing I points north, and increasing J points east.

3.2.3. Digital Elevation Model

The DMA stores digital elevation models using an equirectangular projection, so that it may be indexed with WGS84 geographic coordinates. Since elevation postings are point-values, the pixels should not be considered as filling areas, but as point-values at grid vertices. To accommodate the base elevation of the Angeles Crest forest, the pixel value of 0 corresponds to an elevation of 1000 meters relative to WGS84 reference ellipsoid. The upper left corner is at 120 degrees West, 32 degrees North, and has a pixel scale of 0.2 degrees/pixel longitude, 0.1 degrees/pixel latitude.

      ModelTiepointTag=(0.0, 0.0, 0.0,  -120.0,       32.0,    1000.0)
      ModelPixelScale = (0.2, 0.1, 1.0) 
      GeoKeyDirectoryTag:
            GTModelTypeGeoKey          =  2     (ModelTypeGeographic)
            GTRasterTypeGeoKey         =  2     (RasterPixelIsPoint)
            GeographicTypeGeoKey       =  4326  (GCS_WGS_84)
            VerticalCSTypeGeoKey       =  5030  (VertCS_WGS_84_ellipsoid)
            VerticalCitationGeoKey     =  "WGS 84 Ellipsoid"
            VerticalUnitsGeoKey        =  9001     (Linear_Meter)

   Remarks: 
          1) Note the "RasterPixelIsPoint" raster space, indicating that
             the DEM posting of the first pixel is at the raster point
             (0,0,0), and therefore corresponds to 120W,32N exactly.
          2) The third value of the "PixelScale" is 1.0 to indicate
             that a single pixel-value unit corresponds to 1 meter,
             and the last tiepoint value indicates that base value
             zero indicates 1000m above the reference surface.