PDS_VERSION_ID = PDS3
LABEL_REVISION_NOTE = "
2009-03-15 original release;
2009-12-15 revised projection description - scale in meters
per pixel is exact; removed old text related to pixels per degree.
2013-11-12 kj:revised explanation for conversion from lat/lon to
line/sample.
2021-09-15 kj:revised transformation equation for longitude LON
"
RECORD_TYPE = STREAM
OBJECT = DATA_SET_MAP_PROJECTION
DATA_SET_ID = "LRO-L-LOLA-4-GDR-V1.0"
TARGET_NAME = MOON
OBJECT = DATA_SET_MAP_PROJECTION_INFO
MAP_PROJECTION_TYPE = "POLAR STEREOGRAPHIC"
MAP_PROJECTION_DESC = "
In this polar stereographic projection [SNYDER1987], the projection is
centered on the north or south pole. Lines of longitude extend
radially from the center and parallels of latitude are concentric
circles around the center. In the north, Longitude 0 extends straight
down from the center and Longitude 90 East extends to the right.
In the south, Longitude 0 extends straight up from the center, and
Longitude 90 East extends to the right. The LOLA Team adopts a spherical
geometry with a radius of 1737.4 km, with a spacing of an integral number
of meters per pixel at the pole. The projection MAP_SCALE keyword is exact.
MAP_RESOLUTION is the approximate number of pixels per degree of latitude
at the pole. The MAXIMUM or MINIMUM_LATITUDE keywords are approximately
the extent of the map coverage at the edge of the projected image, but
the corners extend further, i.e., the 60 degree map will extend to latitude
48.48755 degrees at the corners and to 59.996 degrees at the edges.
The transformation from line and sample coordinates to planetocentric
latitude and longitude is given by these equations.
X = (I - N/2 - 0.5)*MAP_SCALE
Y = (J - N/2 - 0.5)*MAP_SCALE
R = SQRT(X^2 + Y^2)
LON = ATAN2(X,-Y) * 180/PI
LAT = 90 - 180/PI * 2*ATAN(0.5 * R/1737400) (northern hemisphere)
LAT = -90 + 180/PI * 2*ATAN(0.5 * R/1737400) (southern hemisphere)
where
I = sample coordinate
J = line coordinate
X,Y = I,J converted to Cartesian coordinate system with 0,0 at center
MAP_SCALE = the map resolution in meters per pixel
N = the number of lines or samples per line in the image
(the images are square)
R = radius from center of map to pixel I,J in meters
LON = east longitude of pixel I,J in degrees
LAT = latitude of pixel I,J in degrees
Values for RES and N can be found in the image label as the
keywords MAP_RESOLUTION and LINES.
The transformation from latitude and longitude to SAMPLE and LINE
indices (I,J) is
R = 2*1737400*TAN((90-LAT) * PI/360)
X = R*SIN(LON*PI/180)
Y = R*COS(LON*PI/180)
I = NINT(X/MAP_SCALE + N/2 + 0.5)
J = NINT(Y/MAP_SCALE + N/2 + 0.5)
NINT is a Fortran intrinsic rounding function, identical to the C math.h
library function rint. In the case of half-integer values, the NINT
function rounds to the nearest even whole number.
"
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
END_OBJECT = DATA_SET_MAP_PROJECTION_INFO
END_OBJECT = DATA_SET_MAP_PROJECTION
END