function [x, y, azi, rk] = gnomonic_fwd(lat0, lon0, lat, lon, ellipsoid)
%GNOMONIC_FWD Forward ellipsoidal gnomonic projection
%
% [X, Y] = GNOMONIC_FWD(LAT0, LON0, LAT, LON)
% [X, Y, AZI, RK] = GNOMONIC_FWD(LAT0, LON0, LAT, LON, ELLIPSOID)
%
% performs the forward ellipsoidal gnomonic projection of points
% (LAT,LON) to (X,Y) using (LAT0,LON0) as the center of projection.
% These input arguments can be scalars or arrays of equal size. The
% ELLIPSOID vector is of the form [a, e], where a is the equatorial
% radius in meters, e is the eccentricity. If ellipsoid is omitted, the
% WGS84 ellipsoid (more precisely, the value returned by
% DEFAULTELLIPSOID) is used. GEODPROJ defines the projection and gives
% the restrictions on the allowed ranges of the arguments. The inverse
% projection is given by GNOMONIC_INV.
%
% AZI and RK give metric properties of the projection at (LAT,LON); AZI
% is the azimuth of the geodesic from the center of projection and RK is
% the reciprocal of the azimuthal scale. The scale in the radial
% direction is 1/RK^2.
%
% If the point lies "over the horizon", i.e., if RK <= 0, then NaNs are
% returned for X and Y (the correct values are returned for AZI and RK).
%
% LAT0, LON0, LAT, LON, AZI are in degrees. The projected coordinates X,
% Y are in meters (more precisely the units used for the equatorial
% radius). RK is dimensionless.
%
% The ellipsoidal gnomonic projection is an azimuthal projection about a
% center point. All geodesics through the center point are projected
% into straight lines with the correct azimuth relative to the center
% point. In addition all geodesics are pass close to the center point
% are very nearly straight. The projection is derived in Section 8 of
%
% C. F. F. Karney, Algorithms for geodesics,
% J. Geodesy 87, 43-55 (2013);
% http://dx.doi.org/10.1007/s00190-012-0578-z
% Addenda: http://geographiclib.sf.net/geod-addenda.html
%
% which also includes methods for solving the "intersection" and
% "interception" problems using the gnomonic projection.
%
% This routine depends on the MATLAB File Exchange package "Geodesics on
% an ellipsoid of revolution":
%
% http://www.mathworks.com/matlabcentral/fileexchange/39108
%
% See also GEODPROJ, GNOMONIC_INV, GEODDISTANCE, DEFAULTELLIPSOID.
% Copyright (c) Charles Karney (2012) <charles@karney.com>.
%
% This file was distributed with GeographicLib 1.29.
if nargin < 4, error('Too few input arguments'), end
if nargin < 5, ellipsoid = defaultellipsoid; end
try
[~] = lat0 + lon0 + lat + lon;
catch err
error('lat0, lon0, lat, lon have incompatible sizes')
end
[~, azi0, azi, ~, m, M] = geoddistance(lat0, lon0, lat, lon, ellipsoid);
rho = m ./ M;
azi0 = azi0 * (pi/180);
x = rho .* sin(azi0);
y = rho .* cos(azi0);
rk = M;
x(M <= 0) = NaN;
y(M <= 0) = NaN;
end