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Geodesic projections for an ellipsoid

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Geodesic projections for an ellipsoid

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07 Dec 2012 (Updated )

Four map projections based on geodesics

eqdazim_fwd(lat0, lon0, lat, lon, ellipsoid)
function [x, y, azi, rk] = eqdazim_fwd(lat0, lon0, lat, lon, ellipsoid)
%EQDAZIM_FWD  Forward azimuthal equidistant projection
%
%   [X, Y] = EQDAZIM_FWD(LAT0, LON0, LAT, LON)
%   [X, Y, AZI, RK] = EQDAZIM_FWD(LAT0, LON0, LAT, LON, ELLIPSOID)
%
%   performs the forward azimuthal equidistant 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 EQDAZIM_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.
%
%   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.
%
%   Section 14 of
%
%     C. F. F. Karney, Geodesics on an ellipsoid of revolution (2011),
%     http://arxiv.org/abs/1102.1215
%     Errata: http://geographiclib.sf.net/geod-addenda.html#geod-errata
%
%   describes how to use this projection in the determination of maritime
%   boundaries (finding the median line).
%
%   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, EQDAZIM_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

  [s, azi0, azi, ~, m, ~, ~, sig] = ...
      geoddistance(lat0, lon0, lat, lon, ellipsoid);
  azi0 = azi0 * (pi/180);
  x = s .* sin(azi0);
  y = s .* cos(azi0);
  rk = m ./ s;
  rk(sig <= 0.01 * sqrt(realmin)) = 1;
end

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