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