Eric M. Eliason
7/1/1997

This report discusses discrepancies in map projection parameters found in the PDS labels on the Mars MDIM, Magellan F-Map (Venus), and Clementine Base Map Mosaic (Earth's Moon) produced by the USGS Astrogeology Team. This report is important for individuals needing to know the precise definition of the map projection and cartographic parameters that describe the image map. There are differences in the cartographic parameters in each of the data products that effect the algorithms defining the relationship between line and sample position in the image array and the latitude and longitude position on the planet surface. Specifically, the LINE_PROJECTION_OFFSET and SAMPLE_PROJECTION_OFFSET parameters have inconsistent definitions among these data sets.

Additionally, as discussed below there are differences in the keywords names used to describe the map projection parameters on the PDS labels due to the evolution of PDS standards.

Data Products In Question

The Mars MDIM, Magellan F-Map, and Clementine Basemap Mosaic exist on CD media and are available for wide distribution to the NASA science community. These data sets contain global Mosaicked Digital Image Models (MDIM). The data sets are organized according to a "tiling" scheme that divides the planet into tiles (or quadrangles). Each tile represents a specific area on the planet. A tile is stored as a PDS-labeled image file. For more information on the data products, refer to the "volinfo.txt" file located in the document directory on the CD volume sets.

Cartographic Keywords in the PDS Labels

The "IMAGE_MAP_PROJECTION" object contained in a PDS label provides the cartographic parameters necessary to define any map projection. For the Sinusoidal Equal-Area Projection only a subset of the cartographic keywords are required and parameters not applicable will contain "N/A" in the fields. The list below shows a typical IMAGE_MAP_PROJECTION group of keywords. For precise definitions of the keywords, refer to the volinfo.txt file (located in the document directory) and the dsmap.cat file (located in the catalog directory.)

OBJECT                         = IMAGE_MAP_PROJECTION
  ^DATA_SET_MAP_PROJECTION     = "DSMAP.CAT"
  MAP_PROJECTION_TYPE          = SINUSOIDAL
  MAP_RESOLUTION               = 1408.1316 <PIXEL/DEGREE>
  MAP_SCALE                    = 0.075 <KM/PIXEL>
  MAXIMUM_LATITUDE             = 38.00000
  MINIMUM_LATITUDE             = 35.99000
  EASTERNMOST_LONGITUDE        = 146.01088
  WESTERNMOST_LONGITUDE        = 144.00000
  LINE_PROJECTION_OFFSET       = -53510.0039
  SAMPLE_PROJECTION_OFFSET     = -6837.0801
  A_AXIS_RADIUS                = 6051.00 <KM>
  B_AXIS_RADIUS                = 6051.00 <KM>
  C_AXIS_RADIUS                = 6051.00 <KM>
  FIRST_STANDARD_PARALLEL      = "N/A"
  SECOND_STANDARD_PARALLEL     = "N/A"
  POSITIVE_LONGITUDE_DIRECTION = EAST
  CENTER_LATITUDE              = 0.00000
  CENTER_LONGITUDE             = 150.00000
  REFERENCE_LATITUDE           = "N/A"
  REFERENCE_LONGITUDE          = "N/A"
  LINE_FIRST_PIXEL             = 1
  SAMPLE_FIRST_PIXEL           = 1
  LINE_LAST_PIXEL              = 2830
  SAMPLE_LAST_PIXEL            = 2410
  MAP_PROJECTION_ROTATION      = 0.00000
  VERTICAL_FRAMELET_OFFSET     = 1
  HORIZONTAL_FRAMELET_OFFSET   = 6
END_OBJECT                     = IMAGE_MAP_PROJECTION
END

Because of the change in PDS standards the IMAGE_MAP_PROJECTION group is different between the Mars MDIM products and the Magellan F-Map and Lunar MDIM products. The Mars MDIM products were created before the "final" cartographic projection keywords were defined and so they are different from the F-MAP and Lunar MDIM products. Here is a list of the differences in keyword names:

Mars MDIM Label                       F-MAP / Lunar MDIM Label

IMAGE_ID (in main label body)         changed to PRODUCT_ID
IMAGE_MAP_PROJECTION_CATALOG          changed to IMAGE_MAP_PROJECTION
DATA_SET_MAP_PROJECTION_CATALOG       changed to DATA_SET_MAP_PROJECTION
X_AXIS_FIRST_PIXEL                    changed to LINE_LAST_PIXEL
X_AXIS_LAST_PIXEL                     changed to LINE_LAST_PIXEL
Y_AXIS_FIRST_PIXEL                    changed to SAMPLE_FIRST_PIXEL
Y_AXIS_LAST_PIXEL                     changed to SAMPLE_LAST_PIXEL
X_AXIS_PROJECTION_OFFSET              changed to LINE_PROJECTION_OFFSET
Y_AXIS_PROJECTION_OFFSET              changed to SAMPLE_PROJECTION_OFFSET

The LINE_PROJECTION_OFFSET and SAMPLE_PROJECTION_OFFSET parameters have inconsistent definitions among the Clementine, F-Map and Mars MDIM data products. This section describes the differences.

For the Mars MDIM, the offset parameters (called X_AXIS_PROJECTION_OFFSET and Y_AXIS_PROJECTION_OFFSET) are used to define line and sample number as a function of latitude and longitude:

    line   = INT(X_AXIS_PROJECTION_OFFSET - LAT*MAP_RESOLUTION + 1.0)

    sample = INT(Y_AXIS_PROJECTION_OFFSET - (LON - CENTER_LONGITUDE)
             *MAP_RESOLUTION*COS(LAT) + 1.0)

Note that the addition of 1.0 is part of the equation. This means the X_AXIS_PROJECTION_OFFSET and Y_AXIS_PROJECTION_OFFSET are relative to line and sample 0,0 in the image array. Because the direction of positive longitude is to the west for Mars, there is a "-" after the Y_AXIS_PROJECTION_OFFSET in the equation.

For the F-MAP and Clementine basemap the equations are defined as:

    line   = INT(LINE_PROJECTION_OFFSET - LAT*MAP_RESOLUTION)

    sample = INT(SAMPLE_PROJECTION_OFFSET + (LON - CENTER_LONGITUDE)
             *MAP_RESOLUTION*COS(LAT))

Note that the addition of 1.0 is not part of the equation. This means that the offset parameters are relative to line and sample 1,1. Because the direction of positive longitude is to the east for Venus and the Moon, there is a "+" after the SAMPLE_PROJECTION_OFFSET term.

An additional discrepancy exists in the F-MAP volume set. The LINE_PROJECTION_OFFSET and SAMPLE_PROJECTION_OFFSET parameters are actually the negative of the value that they should be. A software patch has been included on the F-MAP CD-ROMs to correct the projection offset keywords. The name of the program is PATH and it is stored in the SOFTWARE directory on the F-MAP volumes.