Help for EFGISO

PURPOSE:
To create images of E F and G for the ISO (irregularly shaped object),
and an image of the object radius.
E F and G are used to compute the validity of conformal and authalic
map projections.
The planet models must conform to a standard grid and reside in a directory 
pointed to by the PATH keyword.

EXECUTION:
mapiso out=(E,F.G) planet=phobos nl=180 ns=360 

METHOD:
First the program reads the planet model file located in PATH.
This is an ascii table with west longitude, latitude, radius each 5 degrees.
All angles are planetocentric.

1> Construct a radius surface, which is a function of lat. and long.
   Two dimentional cubic spline interpolation is used here.
 
2> With the radius surface, the ISO can be constructed as
 
   X = r(lat, long) cos(lat)cos (long)
   Y = r(lat, long) cos(lat)sin (long)
   Z = r(lat, long) sin(lat)
 
3> From the cubic spline and the equations in (2), the partial derivatives 
can be calculated.
 
  X_lat, X_long, Y_lat, Y_long, Z_lat and Z_long.
 
4>
   E = (X_lat)(X_lat) + (Y_lat)(Y_lat) + (Z_lat)(Z_lat)
   F = (X_lat)(X_long) + (Y_lat)(Y_long) + (Z_lat)(Z_long)
   G = (X_long)(X_long) + (Y_long)(Y_long) + (Z_long)(Z_long)
 
To verify that the map projection is truly conformal or authalic the 
following constraint must be true, where:
EFG are measured on the ISO.
efg are mesured on the map projection of the ISO.

Conformal case:
E/e=G/g  and F/sqrt(EG)=f/sqrt(eg)
(note: f/sqrt(eg) is the cosine of the angle between meridians and latitudes)

Authalic case:
EG-FF=eg-ff and F/sqrt(EG)=f/sqrt(eg)
(note: ff is f*f)

HISTORY:
9-1-98  J Lorre. 
COGNIZANT PROGRAMMER:  Jean Lorre