using union of polyshape, just different order
WARNING: code not fully tested and NOT commented not fully optimized. But it looks like about 3.5 time faster on TMW server with this specific example.
load('borders2.mat');
warning('off','MATLAB:polyshape:repairedBySimplify')
tic
n = length(a);
Q = polyshape(zeros(0,2));
for k=1:n
Q=union(polyshape(a{k}),Q);
end
toc
% plot(Q)
tic
A = cellfun(@(a) polyshape(a), a, 'unif', 0);
a = cellfun(@(P) P.Vertices, A, 'unif', 0);
m = length(A);
while (m > 1)
xy = cat(1,a{:});
n = cellfun('size', a, 1);
id = repelem((1:m)',n);
[~, ~, J] = unique(xy,'rows');
isbrd = accumarray(J,1) == 2;
isbrd = isbrd(J);
idbdr = id(isbrd);
[~,is] = sortrows(xy(isbrd,:));
idbdr = reshape(idbdr(is),2,[]).';
idbdr = sortrows(idbdr);
b = [true; any(diff(idbdr,1,1),2); true];
lp = diff(find(b));
b(end) = false;
idpair = idbdr(b,:);
lt = sum(n(idpair),2);
r = lp ./ (lt-2*lp);
[~,imax] = max(r);
p = idpair(imax,:);
P = union(A{p(1)}, A{p(2)});
A{p(1)} = P;
A(p(2)) = [];
a{p(1)} = P.Vertices;
a(p(2)) = [];
m = length(A);
end
Q = A{1};
toc
close all
plot(Q)
