function xyOut = solver(a, xyIn, wts)
% Comment: Ken is my hero.
p = (xyIn(:,1)+1j*xyIn(:,2))';
[u,v]=find(triu(a,1));
pairs=[u v];
k1=0.1;
k2_relax=100;
iters_relax=300;
npoints=length(p);
allpairs=nchoosek(1:npoints,2);
ix1=sub2ind([npoints npoints],allpairs(:,1),allpairs(:,2));
ix2=sub2ind([npoints npoints],allpairs(:,2),allpairs(:,1));
f2=zeros(npoints);
w0=max(xyIn(:,1))-min(xyIn(:,1));
h0=max(xyIn(:,2))-min(xyIn(:,2));
for i=1:iters_relax
forces=k1*(p(pairs(:,1))-p(pairs(:,2)));
f1=sparse([pairs(:,1);pairs(:,2)],[pairs(:,2);pairs(:,1)],[forces -forces]);
v=p(allpairs(:,1))-p(allpairs(:,2));
forces=v*k2_relax./abs(v);
f2([ix1;ix2])=[-forces forces];
p=p+sum(f1)+sum(f2)+((rand(1,npoints)-1/2)+1j*(rand(1,npoints)-1/2))*(1-i/iters_relax);
end
xyReal = [real(p)' imag(p)'];
r = 1;
w1=max(xyReal(:,1))-min(xyReal(:,1));
h1=max(xyReal(:,2))-min(xyReal(:,2));
while 1
xyOut(:,1) = round((r*w0/w1)*xyReal(:,1));
xyOut(:,2) = round((r*h0/h1)*xyReal(:,2));
if (npoints == length(unique(xyOut,'rows')))
break
end
r=r+1;
end
end
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