PDS_VERSION_ID = PDS3
LABEL_REVISION_NOTE = "Eric Eliason, 2007-05-01"
RECORD_TYPE = STREAM
SPACECRAFT_NAME = "MARS RECONNAISSANCE ORBITER"
TARGET_NAME = "MARS"
OBJECT = DATA_SET_MAP_PROJECTION
DATA_SET_ID = "MRO-M-HIRISE-3-RDR-V1.1"
OBJECT = DATA_SET_MAP_PROJECTION_INFO
MAP_PROJECTION_TYPE = "EQUIRECTANGULAR"
MAP_PROJECTION_DESC = "
The EQUIRECTANGULAR projection is based on the formula for a
sphere. To eliminate confusion in the IMAGE_MAP_PROJECTION
object we have set all three values, A_AXIS_RADIUS, B_AXIS_RADIUS,
and C_AXIS_RADIUS to the same number. The value recorded in the
three radii is the local radius at the CENTER_LATITUDE on the
Mars ellipsoid. The ellipsoid is defined as, equatorial radius
of 3396.190000 km and polar radius of 3376.200000 kilometers.
Using the local radius of the ellipsoid implies that the MAP_SCALE
and MAP_RESOLUTION are true at the CENTER_LATITUDE.
The Equirectangular projection, used in observations whose center
latitude of the observation is in the range -65 to 65 degrees
latitude, is a simple projection providing a linear relationship
between the geographic coordinates of latitude and longitude and
the Cartesian space of the map. In continuous form, the equations
relating map coordinates (x, y) to geographic coordinates (Lat,
Lon) are:
x = R * (Lon - LonP) * COS(LatP)
y = R * Lat
where LonP is the center longitude of the map projection,
LatP is the center latitude of the projection at which scale
is given, and R the radius of the body at the center latitude.
The Re and Rp parameters refer to equitorial and polar radius
respectively.
R = Re * Rp / SQRT(a^2 + b^2)
a = Rp * COS(LatP)
b = Re * SIN(LatP)
The inverse formulas for Lat and Lon from x and y position in the
projection are:
Lat = (y / R) * (180 / pi)
Lon = LonP + (x / (R * COS(LatP))) * (180 / pi)
The Conversion from (x, y) map coordinates to image array
coordinates (sample, line) is standard for all map projections and
is:
x = (Sample - S0) * Scale
y = (L0 - Line) * Scale
where Scale is the map resolution in km/pixel (located at the
center planetocentric latitude of the projection). Line and
Sample are the coordinates of the image array, and line (L0)
and sample offsets (S0) are the respective image coordinate
displacements from pixel (1,1) to the origin of the projection
(x,y) = (0,0). Please note, pixel (1,1) is spatially located
in the upper-left corner of the image array.
The equations from (x, y) to (Sample, Line) are:
Sample = x / Scale + S0 + 1
Line = -y / Scale - L0 + 1
The equation from (Sample, Line) to (Lat, Lon) is:
Lat = (y / R) * (180 / Pi)
y = (1 - L0 - Line) * Scale
Lat = ((1 - L0 - Line) * Scale / R) * (180 / pi)
Lon = LonP + ((x / (R * COS(LatP))) * (180 / pi))
x = (Sample - S0 - 1) * Scale
Lon = LonP + (((Sample - S0 - 1) * Scale/ (R * COS(LatP))) * (180 / pi))
The keywords corresponding to the Equirectangular projection
parameters are located in the IMAGE_MAP_PROJECTION object found
in the PDS labels. The keywords for each equation parameter are
shown below:
LonP | CENTER_LONGITUDE
LatP | CENTER_LATITUDE
L0 | LINE_PROJECTION_OFFSET
S0 | SAMPLE_PROJECTION_OFFSET
Scale | MAP_SCALE
Re | A_AXIS_RADIUS
Rp | C_AXIS_RADIUS
"
END_OBJECT = DATA_SET_MAP_PROJECTION_INFO
OBJECT = DATA_SET_MAP_PROJECTION_INFO
MAP_PROJECTION_TYPE = "POLAR STEREOGRAPHIC"
MAP_PROJECTION_DESC = "
The Polar Stereographic projection, used in observations whose
center latitude of the observation is greater than 65 or less
than -65 degrees latitude, is ideally suited for observations
near the poles as shape and scale distortion are minimized. The
HiRISE RDR products with Polar Stereographic projection use the
ellipsoid form of the equations. However, most cartographic
processing software cannot support planetocentric coordinates for
this projection with the ellipsoid equation. The fallback is to
use the spherical equations. The error between the spherical and
ellipsoidal equations is highest at 60 and -60 degrees latitude
and is approximately 26 meters or about 100 HiRISE pixels. The
error is less than the accuracy of the camera pointing,
approximately 100m, and can be ignored.
In continuous form, the spherical equations relating map
coordinates (x, y) to planetocentric coordinates (Lat, Lon)
are:
North Polar Stereographic
x = 2 * Rp * TAN(Pi / 4 - Lat / 2) * SIN(Lon - LonP)
y = -2 * Rp * TAN(Pi / 4 - Lat / 2) * COS(Lon - LonP)
South Polar Stereographic
x = 2 * Rp * TAN(Pi / 4 + Lat / 2) * SIN(Lon - LonP)
y = 2 * Rp * TAN(Pi / 4 + Lat / 2) * COS(Lon - LonP)
Where LonP is the central longitude, LatP is the latitude of
true scale and is always 90 or -90, and Rp is the polar radius of
Mars or 3376.2 km.
The spherical inverse formulas for Lat and Lon from X and Y
position in the image array are:
Lat = ARCSIN[COS(C) * SIN(LatP) + y * SIN(C) * COS(LatP) / P]
North Polar Stereographic
Lon = LonP + ARCTAN[x / (-y)]
South Polar Stereographic
Lon = LonP + ARCTAN[x / y]
where:
P = SQRT(x^2 + y^2)
C = 2 * ARCTAN(P / 2 * Rp)
recall:
x = (Sample - S0 - 1) * Scale
y = (1 - L0 - Line) * Scale
The keywords corresponding to the equation parameters for the
Polar Stereographic projection are located in the
IMAGE_MAP_PROJECTION object found in the PDS labels. The
keywords for each equation parameter are shown below.
LonP | CENTER_LONGITUDE
LatP | CENTER_LATITUDE
L0 | LINE_PROJECTION_OFFSET
S0 | SAMPLE_PROJECTION_OFFSET
Scale | MAP_SCALE
Re | A_AXIS_RADIUS
Rp | C_AXIS_RADIUS
"
END_OBJECT = DATA_SET_MAP_PROJECTION_INFO
OBJECT = DS_MAP_PROJECTION_REF_INFO
REFERENCE_KEY_ID = "SNYDER1987"
END_OBJECT = DS_MAP_PROJECTION_REF_INFO
END_OBJECT = DATA_SET_MAP_PROJECTION
END