In many cases, the three defining parameters discussed in paragraphs 2-5;a;1,2, and 3 above will not be available.  The user can compute the third parameter from two known parameters using the formulas below.     1.  To compute the semi-minor axis (b) use the formula b=a(1-f).       Example:  GRS-80 ellipsoid    Step 1:  determine f.     1/f = 298.257222101 so f = 1/298.257222101 f = 0.00335281068118    Step 2:  determine b.     b=a(1-f) b = 6378137 ( 1 - 0.00335281068118 ) b = 6356752.31414    *  NIMA published value for b is 6356752.3141.     2.  To compute flattening (1/f) use the formula             f=(a-b)/a.     Example:  GRS-80 ellipsoid    Step 1:  determine f.     f = ( a - b ) / a f = (6378137 - 6356752.3141) / 6378137 f = 0.00335281068751      Step 2:  determine 1/f.      Flattening = 1 / 0.00335281068751 1/f = 298.257221538    *  NIMA published value for 1/f is 298.257222101.     3.  These computations may provide a quantity that is slightly different than the accepted NIMA parameters.  This is generally due to rounding and is considered insignificant for many geodetic applications and for all artillery survey applications.   2-6  Reference Ellipsoid a.  The oblate ellipsoid is used in geodesy because it is a regularly shaped mathematical figure.  Unlike the geoid, there is no undulation.  If the geoid were regularly shaped, there would be no need for an ellipsoid, we would simply compute surveys referenced strictly to the geoid itself.  Since that is not the case, an ellipsoid is defined and then fixed to a specific location (usually located on the surface of the geoid) and orientation which makes it closely resemble the surface of the geoid; this is accomplished by establishing a Horizontal Datum which is discussed in detail in Section 3 of this chapter.  Once an ellipsoid is fixed by a specific datum it is referred to as a Reference Ellipsoid.   b.  Reference ellipsoids can be either local in extent or global.  If the ellipsoid resembles only a small region of the geoid, and it is fixed to a point on the surface of the earth, it is local.  If the ellipsoid is fixed to the center of mass of the earth and is designed to resemble the geoid as a whole, then it can be considered global and is considered an Earth-centered Earth-fixed (ECEF) ellipsoid.  See Figures 2-5 and 2-6. Figure 2-5    Local Reference Ellipsoid DRAFT 2-3 ELLIPSOID GEOID GEOID ELLIPSOID N Ellipsoid Geoid