PDS_VERSION_ID = PDS3 RECORD_TYPE = STREAM LABEL_REVISION_NOTE = "2006-08-23 GEO:JGW INITIAL." OBJECT = DATA_SET_MAP_PROJECTION DATA_SET_ID = "ARCB/NRAO-L-RTLS/GBT-4/5-70CM-V1.0" OBJECT = DATA_SET_MAP_PROJECTION_INFO MAP_PROJECTION_TYPE = "SINUSOIDAL" MAP_PROJECTION_DESC = " With the exception of the North and South Pole data (dsmap_polar.cat), the lunar radar maps in this archive are presented in a sinusoidal equal-area map projection. In this projection, parallels of latitude are straight lines, with constant distances between equal latitude intervals. Lines of constant longitude on either side of the projection meridian are curved since longitude intervals decrease with the cosine of latitude to account for their convergence toward the poles. This projection offers a number of advantages for storing and managing global digital data; in particular, it is computationally simple, and data are stored in a compact form. The sinusoidal equal-area projection is characterized by a projection longitude (CENTER_LONGITUDE), which is the center meridian of the projection, and a MAP_RESOLUTION, which is given in units of pixels/degree. With the exception of the South Pole data (see dsmap_polar.cat), the CENTER_LATITUDE for all lunar radar maps is the equator. The transformation from latitude and longitude to line and sample is given by the following equations. (1) line = LINE_PROJECTION_OFFSET - (lat*MAP_RESOLUTION) + 0.5 (2) sample = SAMPLE_PROJECTION_OFFSET + ((lon - CENTER_LONGITUDE)*MAP_RESOLUTION*cos(lat)) + 0.5 (3) MAP_RESOLUTION = (2*PI*1738)/(MAP_SCALE*360) Note that integral values of line and sample correspond to the center of a pixel. Lat and lon are the latitude and longitude of a given spot on the surface. The other parameters in these equations are the names of keywords in the PDS labels of each image. The definitions of the PDS keyword names are shown below. LINE_PROJECTION_OFFSET is the line number minus 0.5 on which the map projection origin occurs. The map projection origin is the intersection of the equator and the projection longitude. The value of LINE_PROJECTION_OFFSET is positive for images starting north of the equator and is negative for images starting south of the equator. SAMPLE_PROJECTION_OFFSET is the nearest sample number to the west of the projection longitude. The value of SAMPLE_PROJECTION_OFFSET is positive for images starting to the west of the projection longitude and is negative for images starting to the east of the projection longitude. CENTER_LONGITUDE is the value of the projection longitude, which is the longitude that passes through the center of the projection. MAP_SCALE is the pixel spacing on the planet. MAP_SCALE is 0.4 km/pixel for all lunar radar maps. ------------------------------------------------------------------------ Projection parameters as identified in the PDS labels were calculated as follows: LINE_PROJECTION_OFFSET (equation 1): For maps with MAXIMUM_LATITUDE at or south of the equator, lat = MAXIMUM_LATITUDE and line = 0.5. For maps with MAXIMUM_LATITUDE north of the equator, lat = MINIMUM_LATITUDE and line = (LINES + 0.5). SAMPLE_PROJECTION_OFFSET (equation 2): For maps with MAXIMUM_LATITUDE at or south of the equator, lat = MAXIMUM_LATITUDE. For maps with MAXIMUM_LATITUDE north of the equator and MINIMUM_LATITUDE at or north of the equator, lat = MINIMUM_LATITUDE. For maps with MAXIMUM_LATITUDE north of the equator and MINIMUM_LATITUDE south of the equator, lat = 0 degrees. For all maps, lon = WESTERNMOST_LONGITUDE and sample = 0.5. ------------------------------------------------------------------------ To account for imprecise MINIMUM_LATITUDE, MAXIMUM_LATITUDE, EASTERNMOST_LONGITUDE, and WESTERNMOST_LONGITUDE values, 'actual' values were calculated using the LINE_PROJECTION_OFFSET and SAMPLE_PROJECTION_OFFSET values calculated above and the values of MAP_SCALE (converted to MAP_RESOLUTION) and CENTER_LONGITUDE given in the PDS labels. For 'Actual' MINIMUM_LATITUDE calculations (equation 1), line = (LINES + 0.5). For 'Actual' MAXIMUM_LATITUDE calculations (equation 1), line = 0.5. For 'Actual' EASTERNMOST_LONGITUDE calculations (equation 2), sample = (LINE_SAMPLES + 0.5), and For maps with MAXIMUM_LATITUDE at or south of the equator, lat = MAXIMUM_LATITUDE. For maps with MAXIMUM_LATITUDE north of the equator and MINIMUM_LATITUDE at or north of the equator, lat = MINIMUM_LATITUDE. For maps with MAXIMUM_LATITUDE north of the equator and MINIMUM_LATITUDE south of the equator, lat = 0 degrees. For 'Actual' WESTERNMOST_LONGITUDE calculations (equation 2), sample = 0.5, and For maps with MAXIMUM_LATITUDE at or south of the equator, lat = MAXIMUM_LATITUDE. For maps with MAXIMUM_LATITUDE north of the equator and MINIMUM_LATITUDE at or north of the equator, lat = MINIMUM_LATITUDE. For maps with MAXIMUM_LATITUDE north of the equator and MINIMUM_LATITUDE south of the equator, lat = 0 degrees. These 'Actual' latitude and longitude values were entered in the PDS labels as MINIMUM_LATITUDE, MAXIMUM_LATITUDE, EASTERNMOST_LONGITUDE, AND WESTERNMOST_LONGITUDE. ------------------------------------------------------------------------ " ROTATIONAL_ELEMENT_DESC = "See DAVIESETAL1989." OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "DAVIESETAL1989" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "SNYDER1987" END_OBJECT = DS_MAP_PROJECTION_REF_INFO END_OBJECT = DATA_SET_MAP_PROJECTION_INFO END_OBJECT = DATA_SET_MAP_PROJECTION END