# Map Projection Info Map Projection Type = Simple Cylindrical for Ceres

## Description

This simple cylindrical map projection projection is neither equal-area nor
conformal.  The meridians and parallels are equidistant straight lines,
intersecting at right angles (See Snyder 1987, Ch 12. Equidistant
Cylindrical Projection, pp 90-91).                                           
                                                                              
In general the transformation from the cartographic coordinates X, Y to line
and sample in the PDS image is as follows:                 
                                                                        
sample = INT( X + SAMPLE_PROJECTION_OFFSET) + 1                         
line   = INT(-Y + LINE_PROJECTION_OFFSET) + 1                           
                                                                        
where                                                                   
      X = F1(latitude,longitude)                                        
      Y = F2(latitude,longitude)                                        
                                                                        
                                                                        
and F1(latitude,longitude) and F2(latitude,longitude) are the cartographic
formulas described detailed in (Snyder 1987)               
                                                                        
As an example, the transformation from latitude and longitude to the
cartographic coordinates for the Simple Cylindrical projection is given by the
following equations (Snyder 1987):                      
                                                                        
X =  (lon - CENTER_LONGITUDE)*MAP_RESOLUTION*cos(CENTER_LATITUDE)       
Y =  lat*MAP_RESOLUTION                                                 
(Note that CENTER_LATITUDE=0 and the formula above equals:              
                                                                        
X =  (lon - CENTER_LONGITUDE)*MAP_RESOLUTION                            
Y =  lat*MAP_RESOLUTION                                                 
)
                                                                        
Latitude and longitudes are given for the pixel centers while the map boundaries
 apply to the pixel edges. Thus the center of the pixel for sample 1 is one half
  of a pixel greater than the westernmost longitude and sample 8448 is one half
  pixel less than the easternmost longitude. Similarly for the lines, line 1 is
   half a pixel less than the maximum latitude and line 8448 is half a pixel
   greated than the minimum latitude.                                   

LINE_PROJECTION_OFFSET is the line number minus one on which the map projection
origin occurs. The map projection origin is the intersection of the equator and
the projection longitude. The value of LINE_PROJECTION_OFFSET is positive for
images starting north of the equator and is negative for images starting south
of the equator.                                   
                                                                        
SAMPLE_PROJECTION_OFFSET is the nearest sample number to the left of the
projection longitude. The value of SAMPLE_PROJECTION_OFFSET is positive for
images starting to the west of the projection longitude and is negative for
images starting to the east of the projection longitude.                
                                                                        
CENTER_LONGITUDE is the value of the projection longitude, which is the longitude
that passes through the center of the projection. 
                                                                        
MAP_RESOLUTION is measured in pixels/degree.                            
                                                                        
There are four PDS parameters that specify the latitude and longitude boundaries
of an image.  MAXIMUM_LATITUDE and MINIMUM_LATITUDE specify the latitude
boundaries of the image, and EASTERNMOST_LONGITUDE and WESTERNMOST_LONGITUDE
specify the longitudinal boundaries of the map.                                 
                                                                        
Definitions of other mapping parameters can be found in the PDS Data dictionary.

## References

IAU-WGCCRE-Coordinate-System-for-Vesta,
(http://astrogeology.usgs.gov/search/details/Docs/WGCCRE/IAU-WGCCRE-Coordinate-System-for-Vesta/pdf)

Snyder, John P., Map Projections -- A Working Manual,
    U. S. Geological Survey Professional Paper 1395, 383p., 1987.