## Copyright (C) 2020 ## ## This program is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## -*- texinfo -*- ## @deftypefn {Functional File} {@var{lat}, @var{lon} =} gcxgc (@var{lat1}, @var{lon1}, @var{az1}, @var{lat2}, @var{lon2}, @var{az2}) ## @deftypefnx {Functional File} {@var{lat}, @var{lon} =} gcxgc (@var{lat1}, @var{lon1}, @var{az1}, @var{lat2}, @var{lon2}, @var{az2}, @var{angleUnit}) ## Determines the intersection points between two great circles ## ## Input: ## @itemize ## @item ## @var{lat1}, @var{lon1}, @var{az1}: latitude, longitude, and azimuth of ## great circle #1. These must be scalar values or vectors of equal length. ## @end item ## ## @item ## @var{lat2}, @var{lon2}, @var{az2}: latitude, longitude, and azimuth of ## great circle #2. These must be scalar values or vectors of equal length. ## @end item ## ## @item ## @var{angleUnit}: string for angular units ('degrees' or 'radians', ## case-insensitive, just the first character will do). Default is 'degrees'. ## @var{angleUnit} applies to all inputs and outputs. ## @end item ## @end itemize ## ## Output: ## If scalar values have been input, @var{lat} and @var{lon} are both 1x2 ## vectors. If vectors have been input @var{lat} and @var{lon} are Nx2 arrays ## where N is the number of great circle pairs. The results for multiple ## great circle pairs are concatenated vertically no matter the orientation of ## input vectors. ## ## Example: ## @example ## lat1 = 51.8853; ## lon1 = 0.2545; ## az1 = 108.55; ## lat2 = 49.0034; ## lon2 = 2.5735; ## az2 = 32.44; ## [newlat, newlon] = gcxgc (lat1, lon1, az1, lat2, lon2, az2) ## newlat = ## 50.908 -50.908 ## newlon = ## 4.5086 -175.4914 ## @end example ## @end deftypefn function [lat, lon] = gcxgc (varargin) if (nargin < 6) print_usage(); elseif (nargin == 6) angleUnit = "degrees"; else angleUnit = varargin{7}; endif if (! (all (cellfun ("isnumeric", varargin(1:6)) && ... all (cellfun ("isreal", varargin(1:6)))))) error ("gcxgc: numeric values expected for first six inputs"); endif isv = ! cellfun ("isscalar", varargin(1:6)); if (any (isv)) ## At least one of the location inputs is a vector. Check sizes numval = cellfun ("numel", varargin(isv)); if (any (diff (numval))) error ("gcxgc: all vector inputs must have same lengths"); endif ## Make sure all inputs are column vectors of same length for ii=1:6 if (isv(ii)) varargin(ii) = {varargin{ii}(:)}; else varargin(ii) = {(repmat (varargin{ii}, numval(1), 1))}; endif endfor endif if (! ischar (angleUnit)) error ("gcxgc: character value expected for 'angleUnit'"); elseif (strncmpi (angleUnit, "degrees", min (length (angleUnit), 7))) vect = deg2rad ([varargin{:}]); if (vect(:, 1) > pi / 2 || vect(:, 1) < - pi / 2 ||... vect(:, 4) > pi / 2 || vect(:, 4) < - pi / 2 ||... vect(:, 2) > pi || vect(:, 2) < -pi || ... vect(:, 5) > pi || vect(:, 5) < -pi) error("gcxgc: values out of expected range lat [-90, 90] and long [-180, 180]") endif elseif (strncmpi (angleUnit, "radians", min (length (angleUnit), 7))) vect = [varargin{:}]; if (vect(:, 1) > pi / 2 || vect(:, 1) < - pi / 2 ||... vect(:, 4) > pi / 2 || vect(:, 4) < - pi / 2 ||... vect(:, 2) > pi || vect(:, 2) < -pi || ... vect(:, 5) > pi || vect(:, 5) < -pi) error("gcxgc: values out of expected range lat [-pi/2, pi/2] and long [-pi, pi]") endif else error ("gcxgc: illegal input for 'angleUnit'"); endif #Algorithm from Michael Geyer #EARTH-REFERENCED AIRCRAFT NAVIGATION AND SURVEILLANCE ANALYSIS" pg 111 & 123 c1 = lla2xyz (vect(:, 1), vect(:, 2), vect(:, 3)); c2 = lla2xyz (vect(:, 4), vect(:, 5), vect(:, 6)); N = cross (c1, c2); lat3 = atan2 (N(3), hypot (N(1), N(2))); del_su = vect(:,5) - vect(:,2); phi_su = atan2 ((cos (vect(:,4)) .* sin (del_su)), ... (sin (vect(:, 4)) .* cos (vect(:, 1)) .- ... cos (vect(:, 4)) .* sin (vect(:, 1)) .* cos(del_su))); phi_us = atan2 ((cos (vect(:,1)) .* sin (-del_su)), ... (sin (vect(:, 1)) .* cos (vect(:, 4)) .- ... cos (vect(:, 1)) .* sin (vect(:, 4)) .* cos(-del_su))); beta_u = min ([abs(phi_su .- vect(:,3)), abs(phi_su .- vect(:,3) .+ 2 * pi), abs(phi_su .- vect(:,3) .- 2*pi)]); beta_s = min ([abs(phi_us .- vect(:,6)), abs(phi_us .- vect(:,6) .+ 2 * pi), abs(phi_us .- vect(:,6) .- 2*pi)]); if (sind (rad2deg (vect(:,3))) == 0 && sind (rad2deg (vect(:,6))) == 0) #Note: use sind because sin (pi) != 0 lon3 =0; elseif ( beta_u == beta_s || beta_u + beta_s >= pi || beta_u + beta_s <= 0) warning("gcxgc: Non-unique intersection.\n") lat3 = NaN; lon3 = NaN; elseif ((phi_su + beta_u == vect(:, 3)) || (phi_su - beta_u == vect(:, 3)) || (phi_us - beta_s == vect(:, 6)) || (phi_us + beta_s == vect(:, 6))) lon3 = atan2(N(2), N(1)); endif [alat3 alon3] = antipode (lat3, lon3, "r"); lat = [lat3 alat3]; lon = [lon3 alon3]; if (strncmpi (angleUnit, "degrees", length (angleUnit))) lat = rad2deg (lat); lon = rad2deg (lon); endif endfunction function [C] = lla2xyz (lat, long, az) C(:,1) = cos (lat) ^ 2 .* sin (long) .* cos (az) .- sin (lat) .* ... (sin (az) .* cos (long) .- sin (lat) .* cos (az) .* sin (long)); C(:,2) = -cos (lat) ^ 2 .* cos (long) .* cos (az) .- sin (lat) .* ... (sin (az) .* sin (long) .+ sin (lat) .* cos (az) .* cos (long)); C(:,3) = cos (lat) .* sin (az); endfunction %!test %! [lat3, lon3] = gcxgc ( 51.8853, 0.2545, 108.55, 49.0034, 2.5735, 32.44); %! assert (degrees2dms (lat3(1)), [50 54 27], 10-3) %! assert (degrees2dms (lon3(1)), [04 30 31], 10-3) %!test %! [lat3, lon3] = gcxgc (20, -5, 45, 30, 5, 15); %! assert (lat3(1), 28.0620, 10-3) %! assert (lon3(1), 4.4121, 10-3) %!test %! [lat3, lon3] = gcxgc (0, 0, 90, 0, 180, 80); %! assert (lat3(1), 0, 10-3) %! assert (lon3(1), 180, 10-3) %!warning [lat3, lon3] = gcxgc (0, 0, 45, 0, 180, -45); %!warning [lat3, lon3] = gcxgc (45, 45, 90, -45, -135, 90); %!error gcxgc ("s", 0, 100, 10, 30, 0); %!error gcxgc (3i, 0, 100, 10, 30, 0); %!error gcxgc (50, "s", 100, 10, 30, 0); %!error gcxgc (50, 2i, 10, 10, 30, 0); %!error gcxgc (50, 0, "s", 10, 30, 0); %!error gcxgc (50, 0, 100i, 10, 30, 0); %!error gcxgc (50, 0, 100, "s", 30, 0); %!error gcxgc (50, 0, 100, 10i, 30, 0); %!error gcxgc (50, 0, 100, 10, "s", 0); %!error gcxgc (50, 0, 100, 10, 30i, 0); %!error gcxgc (50, 0, 100, 10, 30, "s"); %!error gcxgc (50, 0, 100, 10, 30, 2i); %!error gcxgc (50, 0, 100, 10, 30, 0, "f"); %!error gcxgc (50, 0, 100, 10, 30, 0, "degreef"); %!error gcxgc (190, 0, 90, -90.000001, 180, 80);