--- /dev/null
+%% Copyright (c) 2012 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% 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
+%% 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 <http://www.gnu.org/licenses/>.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {[@var{tangent},@var{inner}] = } beltproblem (@var{c}, @var{r})
+%% Finds the four lines tangent to two circles with given centers and radii.
+%%
+%% The function solves the belt problem in 2D for circles with center @var{c} and
+%% radii @var{r}.
+%%
+%% @strong{INPUT}
+%% @table @var
+%% @item c
+%% 2-by-2 matrix containig coordinates of the centers of the circles; one row per circle.
+%% @item r
+%% 2-by-1 vector with the radii of the circles.
+%%@end table
+%%
+%% @strong{OUPUT}
+%% @table @var
+%% @item tangent
+%% 4-by-4 matrix with the points of tangency. Each row describes a segment(edge).
+%% @item inner
+%% 4-by-2 vector with the point of intersection of the inner tangents (crossed belts)
+%% with the segment that joins the centers of the two circles. If
+%% the i-th edge is not an inner tangent then @code{inner(i,:)=[NaN,NaN]}.
+%% @end table
+%%
+%% Example:
+%%
+%% @example
+%% c = [0 0;1 3];
+%% r = [1 0.5];
+%% [T inner] = beltproblem(c,r)
+%% @result{} T =
+%% -0.68516 0.72839 1.34258 2.63581
+%% 0.98516 0.17161 0.50742 2.91419
+%% 0.98675 -0.16225 1.49338 2.91888
+%% -0.88675 0.46225 0.55663 3.23112
+%%
+%% @result{} inner =
+%% 0.66667 2.00000
+%% 0.66667 2.00000
+%% NaN NaN
+%% NaN NaN
+%%
+%% @end example
+%%
+%% @seealso{edges2d}
+%% @end deftypefn
+
+function [edgeTan inner] = beltproblem(c,r)
+
+ x0 = [c(1,1) c(1,2) c(2,1) c(2,2)];
+ r0 = r([1 1 2 2]);
+
+ middleEdge = createEdge(c(1,:),c(2,:));
+
+ ind0 = [1 0 1 0; 0 1 1 0; 1 1 1 0; -1 0 1 0; 0 -1 1 0; -1 -1 1 0;...
+ 1 0 0 1; 0 1 0 1; 1 1 0 1; -1 0 0 1; 0 -1 0 1; -1 -1 0 1;...
+ 1 0 1 1; 0 1 1 1; 1 1 1 1; -1 0 1 1; 0 -1 1 1; -1 -1 1 1;...
+ 1 0 -1 0; 0 1 -1 0; 1 1 -1 0; -1 0 -1 0; 0 -1 -1 0; -1 -1 -1 0;...
+ 1 0 0 -1; 0 1 0 -1; 1 1 0 -1; -1 0 0 -1; 0 -1 0 -1; -1 -1 0 -1;...
+ 1 0 -1 -1; 0 1 -1 -1; 1 1 -1 -1; -1 0 -1 -1; 0 -1 -1 -1; -1 -1 -1 -1];
+ nInit = size(ind0,1);
+ ir = randperm(nInit);
+ edgeTan = zeros(4,4);
+ inner = zeros(4,2);
+ nSol = 0;
+ i=1;
+
+ %% Solve for 2 different lines
+ while nSol<4 && i<nInit
+ ind = find(ind0(ir(i),:)~=0);
+ x = x0;
+ x(ind)=x(ind)+r0(ind);
+ [sol f0 nev]= fsolve(@(x)belt(x,c,r),x);
+ if nev~=1
+ perror('fsolve',nev)
+ end
+
+ for j=1:4
+ notequal(j) = all(abs(edgeTan(j,:)-sol) > 1e-6);
+ end
+ if all(notequal)
+ nSol = nSol+1;
+ edgeTan(nSol,:) = createEdge(sol(1:2),sol(3:4));
+ % Find innerTangent
+ inner(nSol,:) = intersectEdges(middleEdge,edgeTan(nSol,:));
+ end
+
+ i = i+1;
+ end
+
+endfunction
+
+function res = belt(x,c,r)
+ res = zeros(4,1);
+
+ res(1,1) = (x(3:4) - c(2,1:2))*(x(3:4) - x(1:2))';
+ res(2,1) = (x(1:2) - c(1,1:2))*(x(3:4) - x(1:2))';
+ res(3,1) = sumsq(x(1:2) - c(1,1:2)) - r(1)^2;
+ res(4,1) = sumsq(x(3:4) - c(2,1:2)) - r(2)^2;
+
+end
+
+%!demo
+%! c = [0 0;1 3];
+%! r = [1 0.5];
+%! [T inner] = beltproblem(c,r)
+%!
+%! figure(1)
+%! clf
+%! h = drawEdge(T);
+%! set(h(find(~isnan(inner(:,1)))),'color','r');
+%! set(h,'linewidth',2);
+%! hold on
+%! drawCircle([c(1,:) r(1); c(2,:) r(2)],'linewidth',2);
+%! axis tight
+%! axis equal
+%!
+%! % -------------------------------------------------------------------
+%! % The circles with the tangents edges are plotted. The solution with
+%! % crossed belts (inner tangets) is shown in red.
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff