## Copyright (C) 2020 The Octave Project Developers ## ## 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 {} {@var{lat}, @var{lon} =} gcxgc (@var{lat1}, @var{lon1}, @var{r1}, @var{lat2}, @var{lon2}, @var{r2}) ## @deftypefnx {} {@var{lat}, @var{lon} =} gcxgc (@var{lat1}, @var{lon1}, @var{r1}, @var{lat2}, @var{lon2}, @var{r2}, @var{angleUnit}) ## Determines the intersection points between two small circles. ## ## Input: ## @itemize ## @item ## @var{lat1}, @var{lon1}, @var{r1}: latitude, longitude, and range of ## small circle #1. These must be scalar values or vectors of equal length. ## @end item ## ## @item ## @var{lat2}, @var{lon2}, @var{r2}: latitude, longitude, and range of ## small 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 ## @item ## @var{lat} and @var{lon} are both 1x2 vectors ## @end item ## ## Example: ## @example ## lat1 = 37.67; ## lon1 = -90.2; ## rng1 = 1.79; ## lat2 = 36.11; ## lon2 = -90.95; ## rng2 = 2.42; ## [newlat, newlon] = scxsc (lat1, lon1, rng1, lat2, lon2, rng2) ## newlat = ## 36.964 38.260 ## newlon = ## -88.132 -92.343 ## @end example ## @seealso{gcxgc, gcxsc, gc2sc} ## @end deftypefn function [lat, lon] = scxsc (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 ("scxsc: 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 nv = numval(1); ## 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 else nv = 1; endif vect = [varargin{1:6}]; if (! ischar (angleUnit)) error ("scxsc: character value expected for 'angleUnit'"); elseif (strncmpi (angleUnit, "degrees", min (length (angleUnit), 7))) ## Latitude must be within (-90, 90) if (any (abs (vect(:, [1 4])) >= 90)) error("scxsc: azimuth value(s) out of acceptable range (-90, 90)") endif vect = deg2rad (vect); elseif (strncmpi (angleUnit, "radians", min (length (angleUnit), 7))) ## Latitude must be within (-pi/2, pi/2) as azimuth isn't defined there if (any (abs (vect(:, [1 4])) >= pi / 2)) error("scxsc: azimuth value(s) out of acceptable range (-pi/2, pi/2)") endif else error ("scxsc: illegal input for 'angleUnit'"); endif c1 = geoc2cart (vect(:,1), vect(:,2)); c2 = geoc2cart (vect(:,4), vect(:,5)); ## Algorithm insight comes from ## https://gis.stackexchange.com/questions/48937/calculating-intersection-of-two-circles q = dot (c1, c2, 2); q2 = q .^ 2; #TODO VECTORIZE len = size(q2); [lat lon]=deal (zeros (len,2)); for i=1:size(q2) A = abs (vect(i,1)) - abs (vect(i,4)); #TODO find a better method B = abs (vect(i,2)) - abs (vect(i,5)); if (q2(i) == 1-eps) #Note being exactly == 1 happens rarely but .9999999 does lat(i,:) = NaN; lon(i,:) = NaN; warning("Octave: coinciding-small-circles\n\ scxsc: no solution circle centers are either the same or antipodal.\n") elseif (abs (A) <= 10e-15 && abs (B) <= 10e-15) lat(i,:) = NaN; lon(i,:) = NaN; warning("Octave: coinciding-small-circles\n\ scxsc: no solution circle centers are either the same or antipodal.\n") endif endfor n = cross (c1, c2); n2 = dot(n, n, 2); if (n2 == 1) error("Octave: coinciding-small-circles\n\ scxsc: no solution circle centers are either the same or antipodal.\n") endif r1 = vect(:,3); r2 = vect(:,6); a = (cos (r1) .- q .* cos (r2)) ./ (1 .- q2); b = (cos (r2) .- q .* cos (r1)) ./ (1 .- q2); x0 = a .* c1 .+ b .* c2; x02 = dot(x0, x0, 2); if (x02 > 1) error("scxsc: circles do not intersect\n") endif t = sqrt ((1 .- x02) ./ n2); p1 = x0 .+ (t .* n); p2 = x0 .- (t .* n); #TODO Vectorize for i=1:len if (lat(i,1) == 0) lat(i,1) = atan2(p1(i,3), hypot(p1(i,1),p1(i,2))); lon(i,1) = atan2 (p1(i,2), p1(i,1)); lat(i,2) = atan2 (p2(i,3), hypot(p2(i,1),p2(i,2))); lon(i,2) = atan2 (p2(i,2), p2(i,1)); #lat(i,:) = [lat1 lat2]; #lon(i,:) = [lon1 lon2]; if (strncmpi (angleUnit, "degrees", length (angleUnit))) lat(i) = rad2deg (lat(i)); lon(i) = rad2deg (lon(i)); endif else lat(i); lon(i); endif endfor endfunction function [c] = geoc2cart(lat, lon) c(:,1) = cos (lon) .* cos (lat); c(:,2) = sin (lon) .* cos (lat); c(:,3) = sin (lat); endfunction %!test %! R1 = rad2deg (107.5 / earthRadius ("NM")); #Convert NM to deg %! R2 = rad2deg (145 / earthRadius ("NM")); %! [lat, lon] = scxsc (37.673442, -90.234036, R1, 36.109997, -90.953669, R2); %! assert (lat(1), 36.988778646, 1e-6); %! assert (lon(1), -88.15335362, 1e-6); %!test %! [a, b, c] = gc2sc (45, [0:45:360], 45); %! [d, e, f] = gc2sc (-45, -135, -45); %! [g, h] = scxsc (a, b, c, d, e, f); %! assert (g(2,1), NaN) %! assert (g(6,1), NaN) %! assert ([g(9,1) h(9,1)], [-57.997936587 -102.76438968], 1e-6) %!error scxsc (45, 90, 1, -30, 60, 1) %!error scxsc ("s", 0, 100, 10, 30, 0) %!error scxsc (3i, 0, 100, 10, 30, 0) %!error scxsc (50, "s", 100, 10, 30, 0) %!error scxsc (50, 2i, 10, 10, 30, 0) %!error scxsc (50, 0, "s", 10, 30, 0) %!error scxsc (50, 0, 100i, 10, 30, 0) %!error scxsc (50, 0, 100, "s", 30, 0) %!error scxsc (50, 0, 100, 10i, 30, 0) %!error scxsc (50, 0, 100, 10, "s", 0) %!error scxsc (50, 0, 100, 10, 30i, 0) %!error scxsc (50, 0, 100, 10, 30, "s") %!error scxsc (50, 0, 100, 10, 30, 2i) %!error scxsc (50, 0, 100, 10, 30, 0, "f") %!error scxsc (50, 0, 100, 10, 30, 0, "degreef") %!error scxsc (190, 0, 90, -90.000001, 180, 80); %!error scxsc (190, 0, -90.001, -90.000001, 180, 80); %!error scxsc (pi/1.999, 0, pi/2, pi/2.0001, 2, 2*pi/3, "r");