function [out1,out2,savepts] = gstereo(mstruct,in1,in2,object,direction,savepts)

%GSTEREO  Gall Stereographic Cylindrical Projection
%
%  This is a perspective projection from a point on the Equator
%  opposite a given meridian onto a cylinder secant at the 45 degree
%  parallels.  It is not equal area, equidistant, or conformal.
%  Scale is true along the standard parallels and constant between
%  two parallels equidistant from the Equator.  There is no distortion
%  along the standard parallels, but it increases moderately away from
%  these parallels, becoming severe at the poles.
%
%  This projection was presented by James Gall in 1855.  It is also
%  known simply as the Gall projection.  It is special form of the
%  Braun Perspective Cylindrical projection secant at 45 deg N and S.
%
%  This projection is available for the spherical geoid only.

%  Copyright 1996-2003 The MathWorks, Inc.
% $Revision: 1.10.4.1 $
%  Written by:  E. Byrns, E. Brown


if nargin == 1                  %  Set the default structure entries
	  mstruct.trimlat = angledim([ -90  90],'degrees',mstruct.angleunits);
      mstruct.trimlon = angledim([-180 180],'degrees',mstruct.angleunits);
	  mstruct.mapparallels = angledim(45,'degrees',mstruct.angleunits);
      mstruct.nparallels   = 0;
	  mstruct.fixedorient  = [];
	  out1 = mstruct;          return
elseif nargin ~= 5 & nargin ~= 6
      error('Incorrect number of arguments')
end

%  Extract the necessary projection data and convert to radians

units   = mstruct.angleunits;
geoid   = mstruct.geoid;
aspect  = mstruct.aspect;
origin  = angledim(mstruct.origin,units,'radians');
trimlat = angledim(mstruct.flatlimit,units,'radians');
trimlon = angledim(mstruct.flonlimit,units,'radians');
scalefactor = mstruct.scalefactor;
falseeasting = mstruct.falseeasting;
falsenorthing = mstruct.falsenorthing;


switch direction
case 'forward'

     lat       = angledim(in1,units,'radians');
     long      = angledim(in2,units,'radians');

     [lat,long] = rotatem(lat,long,origin,direction);   %  Rotate to new origin
     [lat,long,clipped] = clipdata(lat,long,object);    %  Clip at the date line
     [lat,long,trimmed] = trimdata(lat,trimlat,long,trimlon,object);

%  Construct the structure of altered points

     savepts.trimmed = trimmed;
     savepts.clipped = clipped;

%  Projection transformation

	 x = geoid(1) * long / sqrt(2);
     y = geoid(1) * ( 1 + sqrt(2)/2) * tan(lat/2);

%  Apply scale factor, false easting, northing

	x = x*scalefactor+falseeasting;
	y = y*scalefactor+falsenorthing;

%  Set the output variables

     switch  aspect
	    case 'normal',         out1 = x;      out2 = y;
	    case 'transverse',	   out1 = y;      out2 = -x;
        otherwise,             error('Unrecognized aspect string')
     end


case 'inverse'

     switch  aspect
	    case 'normal',         x = in1;    y = in2;
	    case 'transverse',	   x = -in2;   y = in1;
        otherwise,             error('Unrecognized aspect string')
     end

%  Apply scale factor, false easting, northing

	x = (x-falseeasting)/scalefactor;
	y = (y-falsenorthing)/scalefactor;

% Inverse projection

     lat  = 2* atan(y/(geoid(1)*(1+sqrt(2)/2)) );
	 long = sqrt(2) * x / geoid(1);


%  Undo trims and clips

     [lat,long] = undotrim(lat,long,savepts.trimmed,object);
     [lat,long] = undoclip(lat,long,savepts.clipped,object);

%  Rotate to Greenwich and transform to desired units

     [lat,long] = rotatem(lat,long,origin,direction);

     out1 = angledim(lat, 'radians', units);
     out2 = angledim(long,'radians', units);

otherwise
     error('Unrecognized direction string')
end

%  Some operations on NaNs produce NaN + NaNi.  However operations
%  outside the map may product complex results and we don't want
%  to destroy this indicator.

indx = find(isnan(out1) | isnan(out2));
out1(indx) = NaN;   out2(indx) = NaN;