[Proj] Spheroidal gnomonic projection

[Karney, Charles]

Noel,

Thanks for the E-mail.  Your method is same as given by Roy Williams,
Geometry of Navigation (Horwood, Chichester, 1998), pp 29-37.  (Google
books will allow you to "preview" these pages.)

Incidentally the "neatest" way to project from a point to a plane is via
homogeneous 4-vectors.  A point X is given by [x, y, z, 1]^t (possibly
multiplied by a constant).  A plane P is defined by P^t.X = 0.  The
operation which projects a point X from a center point C onto a plane P
is given by

   Y = M.X

where

   M = (C^t.P) I - C.P^t

The nice thing about 4-vectors is that you can deal with orthogonal
projections (from a point at infinity) easily.

I've measured deviations of straight lines in this projection from
geodesics and within 1000km of the center point the errors in the
initial/final azimuths are up to 108".  This is OK, but not great.

The "geodesic" version (which, I might add, also entails no intermediate
mappings, no truncations, and no approximations) gets this error down to
1.04".  With the conformal method (also free of approximations), the
error is 17".

--
Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

Tel: +1 609 734 2312
Fax: +1 609 734 2662