CCSD3ZF0000100000001NJPL3IF0PDSX00000001 PDS_VERSION_ID = PDS3 OBJECT = DATA_SET_MAP_PROJECTION DATA_SET_ID = 'MGN-V-RDRS-5-C-BIDR-V1.0' OBJECT = DATA_SET_MAP_PROJECTION_INFO MAP_PROJECTION_TYPE = SINUSOIDAL MAP_PROJECTION_DESC = " C-BIDR MAP PROJECTIONS ====================== C-BIDR data are present in sinusoidal map projections, using the Venus body-fixed coordinate system approved by the IAU in 1985 [DAVIESETAL1989]. Although the C-BIDR data files are formatted as a series of rectangular arrays of varying size, following the long, narrow image swath, the underlying organization is that of a single rectangular array of pixels, centered on the integral values of a two-dimensional Cartesian coordinate system. The relationship between Cartesian coordinates (x,y) and geographic coordinates (latitude,longitude) is mathematically defined by the particular map projection. In all C-BIDR images, the x-coordinate increases from left to right and the y-coordinate increases from bottom to top. Longitude on Venus conventionally increases toward the east [LYONS1988]. SINUSOIDAL MAP PROJECTION ========================= In the sinusoidal 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. Areas on the map are proportional to the same areas on the planet. Distances are correct along all parallels and the central meridian, but shapes are increasingly distorted away from the central meridian and near the poles [ALPHA&SNYDER1982; SNYDER1987]. The sinusoidal equal-area projection is characterized by a projection longitude and a scale. The projection longitude defines the center meridian (X=0) of the projection; the planet's equator is coincident with the line Y=0. The scale is given in units of pixels/degree along the projection equator, which can be converted to km/pixel using the planetary radius. The object IMAGE_MAP_PROJECTION in the IM2.LBL file provides the specific projection parameters for the Sinusoidal projection used with this data set. The most important parameters are: A_AXIS_RADIUS Planetary radius CENTER_LATITUDE Center latitude CENTER_LONGITUDE Center longitude MAP_SCALE Pixel scale (225 meters/pixel) LINE_PROJECTION_OFFSET Image pixel offset of Y=0 SAMPLE_PROJECTION_OFFSET Image pixel offset of X=0 (See the PDS Data Dictionary [PDSDD1992] for a more detailed description of these and other parameters.) The transformation from latitude and longitude (LAT,LON) in radians to Sinusoidal Cartesian coordinates (X,Y) is given by the following equations. SCALE = A_AXIS_RADIUS / MAP_SCALE X = SCALE * (LON - CENTER_LONGITUDE) * COS(LAT) Y = SCALE * LAT; The transformation between Cartesian coordinates (X,Y) and image pixel coordinates (SAMPLE,LINE) is LINE = 1 + LINE_PROJECTION_OFFSET - Y SAMPLE = 1 + SAMPLE_PROJECTION_OFFSET + X In the above definitions, integral values of LINE and SAMPLE correspond to the center of a C-BIDR pixel, and the top left image pixel has LINE=1 and SAMPLE=1. Note that while SAMPLE increases from left to right (the same as X), LINE increases from top to bottom (the reverse of Y). OBLIQUE SINUSOIDAL MAP PROJECTION ================================= In the oblique sinusoidal projection, parallels of latitude and meridians of longitude are, in general, curved lines. Areas on the map are proportional to the same areas on the planet. Distances are correct along the central meridian (which maps to a straight line), but shapes are increasingly distorted away from the central meridian [ALPHA&SNYDER1982; SNYDER1987]. The sinusoidal equal-area projection employed for Magellan polar image data is characterized by a projection longitude, a projection latitude, and a scale. The projection longitude defines the center meridian of the projection (X=0), i.e. the coordinate system has been rotated by this angle about the planet's rotation axis; the projection latitude defines a second rotation that has been made to the coordinate system about an axis perpendicular to the central meridian. The effect of these two rotations is to bring to the center of the projection (X=0,Y=0) that point on the planet whose coordinates are equal to the projection latitude and longitude. A general oblique sinusoidal projection is characterized by a third parameter, a further rotation about the radius vector to the projection center. However, for Magellan images, this angle is always zero. The mapping scale is given in units of pixels/degree at the projection origin, which can be converted to km/pixel using the planetary radius. The object IMAGE_MAP_PROJECTION in the IM1.LBL file provides the specific projection parameters for the oblique sinusoidal projection used with this data set. The most important parameters are: A_AXIS_RADIUS Planetary radius CENTER_LATITUDE Projection latitude CENTER_LONGITUDE Projection longitude MAP_SCALE Pixel scale (225 meters/pixel) LINE_PROJECTION_OFFSET Line index of map origin SAMPLE_PROJECTION_OFFSET Sample index of map origin (See the PDS Data Dictionary [PDSDD1992] for a more detailed description of these and other parameters.) The transformation from latitude and longitude (LAT,LON) in radians to Oblique Sinusoidal Cartesian coordinates (X,Y) is given by the following equations. SCALE = A_AXIS_RADIUS / MAP_SCALE PLAT = ASIN(SIN(LAT) * COS(CENTER_LATITUDE) - COS(LAT) * SIN(CENTER_LATITUDE) * COS(LON - CENTER_LONGITUDE)) PLON = ATAN2(COS(LAT) * SIN(LON - CENTER_LONGITUDE), SIN(LAT) * SIN(CENTER_LATITUDE) + COS(LAT) * COS(CENTER_LATITUDE) * COS(LON - CENTER_LONGITUDE)) Y = SCALE * PLON * COS(PLAT) X = SCALE * PLAT; The transformation between Cartesian coordinates (X,Y) and image pixel coordinates (SAMPLE,LINE) is LINE = 1 + LINE_PROJECTION_OFFSET + Y SAMPLE = 1 + SAMPLE_PROJECTION_OFFSET + X In the above definitions, integral values of LINE and SAMPLE correspond to the center of a C-BIDR pixel, and the top left image pixel has LINE=1 and SAMPLE=1." 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 OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "LYONS1988" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "PDSDD1992" END_OBJECT = DS_MAP_PROJECTION_REF_INFO OBJECT = DS_MAP_PROJECTION_REF_INFO REFERENCE_KEY_ID = "ALPHA&SNYDER1982" END_OBJECT = DS_MAP_PROJECTION_REF_INFO END_OBJECT = DATA_SET_MAP_PROJECTION_INFO END_OBJECT = DATA_SET_MAP_PROJECTION END