PDS_VERSION_ID = PDS3 LABEL_REVISION_NOTE = "2005-05-10, Bryan Stiles, Version 1.2" RECORD_TYPE = STREAM INSTRUMENT_HOST_ID = CO INSTRUMENT_ID = RADAR TARGET_NAME = TITAN OBJECT = DATA_SET_MAP_PROJECTION DATA_SET_ID = "CO-SSA-RADAR-5-BIDR-V1.0" OBJECT = DATA_SET_MAP_PROJECTION_INFO MAP_PROJECTION_TYPE = "OBLIQUE CYLINDRICAL" MAP_PROJECTION_DESC = " Because of the highly variable geometry of the Cassini spacecraft's encounters with Titan and the elongated shape of the Synthetic Aperture Radar (SAR) footprints, the standard Simple Cylindrical coordinate system would be extremely inefficient for representing individual basic images. Therefore, the Cassini Basic Image Data Record (BIDR) products are produced in an Oblique Cylindrical map projection. This type of projection is a Cartesian plot of the angular (longitude and latitude) coordinates of features, not with respect to the standard coordinate axes of the body, but with respect to a rotated set of axes. A separate oblique coordinate system is established for each Titan pass, placing the equator of the rotated coordinates along the ground track of that Cassini flyby and the rotated prime meridian through the point of closest approach. The Oblique Cylindrical projection is characterized by the 3x3 rotation matrix between the standard and oblique coordinate systems or the equivalent set of angles, which are interpretable as the (north) pole latitude, pole longitude, and pole rotation. Projection Definition --------------------- The following PDS keywords define an instance of an oblique cylindrical projection with respect to the standard IAU/IAG positive west longitude planetographic latitude coordinate system. The projection is defined both by a rotation matrix and the equivalent set of angles. OBLIQUE_PROJ_POLE_LATITUDE = fff.ffffff One of the three angles defining the oblique coordinate system used in the OBLIQUE CYLINDRICAL projection. This is the ordinary latitude of the pole (Z axis) of the oblique system. OBLIQUE_PROJ_POLE_LONGITUDE = fff.ffffff One of the three angles defining the oblique coordinate system used in the OBLIQUE CYLINDRICAL projection. This is the ordinary longitude of the pole (Z axis) of the oblique system. NOTE that the value given is positive-west, whereas the equivalent positive-east value is used in the equations that define the OBLIQUE_PROJ_POLE_ROTATION and the rotation matrix entries below. OBLIQUE_PROJ_POLE_ROTATION = fff.ffffff One of the three angles defining the oblique coordinate system used in the OBLIQUE CYLINDRICAL projection. This is a rotation around the polar (Z) axis of the oblique system that completes the transformation from standard to oblique coordinates. The value is positive east (obeys right hand rule) and is in the range 0 to 360 degrees. OBLIQUE_PROJ_X_AXIS_VECTOR = {ff.ffffffff, ff.ffffffff, ff.fffffffff} Unit vector in the direction of the X axis of the oblique coordinate system used in the OBLIQUE CYLINDRICAL projection, in terms of the X, Y, and Z axes of the standard body-fixed coordinate system. In each system, the X axis points from the body center toward longitude and latitude (0,0) in that system, the Z axis to (0,90), and the Y-axis completes a right-handed set. The OBLIQUE_PROJ_X/Y/Z_AXIS_VECTORS make up the rows of a rotation matrix that when multiplied on the left of a vector referenced to the standard coordinate system converts it into its equivalent in the oblique coordinate system. This rotation matrix is the product of successively applied rotations by OBLIQUE_PROJ_POLE_LONGITUDE around the Z axis, 90 - OBLIQUE_PROJ_POLE_LATITUDE around the once-rotated Y axis, and OBLIQUE_PROJ_POLE_ROTATION around the twice-rotated Z axis. OBLIQUE_PROJ_Y_AXIS_VECTOR = {ff.ffffffff, ff.ffffffff, ff.fffffffff} Unit vector in the direction of the Y axis of the oblique coordinate system used in the OBLIQUE CYLINDRICAL projection, in terms of the X, Y, and Z axes of the standard body-fixed coordinate system. In each system, the X axis points from the body center toward longitude and latitude (0,0) in that system, the Z axis to (0,90), and the Y-axis completes a right-handed set. The OBLIQUE_PROJ_X/Y/Z_AXIS_VECTORS make up the rows of a rotation matrix that when multiplied on the left of a vector referenced to the standard coordinate system converts it into its equivalent in the oblique coordinate system. This rotation matrix is the product of successively applied rotations by OBLIQUE_PROJ_POLE_LONGITUDE around the Z axis, 90 - OBLIQUE_PROJ_POLE_LATITUDE around the once-rotated Y axis, and OBLIQUE_PROJ_POLE_ROTATION around the twice-rotated Z axis. OBLIQUE_PROJ_Z_AXIS_VECTOR = {ff.ffffffff, ff.ffffffff, ff.fffffffff} Unit vector in the direction of the Z axis of the oblique coordinate system used in the OBLIQUE CYLINDRICAL projection, in terms of the X, Y, and Z axes of the standard body-fixed coordinate system. In each system, the X axis points from the body center toward longitude and latitude (0,0) in that system, the Z axis to (0,90), and the Y-axis completes a right-handed set. The OBLIQUE_PROJ_X/Y/Z_AXIS_VECTORS make up the rows of a rotation matrix that when multiplied on the left of a vector referenced to the standard coordinate system converts it into its equivalent in the oblique coordinate system. This rotation matrix is the product of successively applied rotations by OBLIQUE_PROJ_POLE_LONGITUDE around the Z axis, 90 - OBLIQUE_PROJ_POLE_LATITUDE around the once-rotated Y axis, and OBLIQUE_PROJ_POLE_ROTATION around the twice-rotated Z axis. Lat/Lon to Line/Sample Transformations ------------------------------------ The transformations between the oblique latitude and longitude and the line and sample coordinates of the data products are line = INT( LINE_PROJECTION_OFFSET + lon_a*MAP_RESOLUTION + 1) sample = INT(SAMPLE_PROJECTION_OFFSET + lat_a*MAP_RESOLUTION + 1) where lon_a and lat_a are the oblique cylindrical pole longitude and pole latitude measured in degrees, and lon_a is in positive-east coordinates. Integral values of line and sample correspond to the center of a pixel. LINE_PROJECTION_OFFSET, SAMPLE_PROJECTION_OFFSET, and MAP_RESOLUTION are defined below. LINE_PROJECTION_OFFSET is the line offset value of the map projection origin position from the line and sample (1,1), i.e., the upper left corner of the array. The value is positive when the origin is below the upper left pixel. (The map projection origin is the intersection of the equator and the projection center longitude; this location is stored as the values of the CENTER_LATITUDE and CENTER_LONGITUDE keywords. Both keywords are nominally zero valued.) SAMPLE_PROJECTION_OFFSET is the sample offset value of the map projection origin position from the line and sample (1,1), i.e., the upper left corner of the array. The value is positive when the origin is to the right of the upper left pixel. MAP_RESOLUTION identifies the digital scale of the map-projected image in units of pixels per degree. Definitions of other mapping parameters can be found in the Planetary Science Data Dictionary and the Cassini Radar Basic Image Data Records Software Interface Specification. " ROTATIONAL_ELEMENT_DESC = "See SEIDELMANNETAL2002" OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "SEIDELMANNETAL2002" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "SNYDER1987" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "BUGAYEVSKIY&SNYD1995" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "YANGETAL2000" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "GREELEY&BATSON1990" END_OBJECT = DS_MAP_PROJECTION_REF_INFO END_OBJECT = DATA_SET_MAP_PROJECTION_INFO END_OBJECT = DATA_SET_MAP_PROJECTION END