try13

function xyOut = solver(a, xyIn, wts)

N=size(xyIn,1);

D=min(N,mindist(a,N));
E=D-repmat(mean(D,1),[size(D,1),1])-repmat(mean(D,1)',[1,size(D,2)])+mean(D(:));
[xyOut0,nill]=svd(E);
xyOut0=xyOut0(:,1:2); 

xyOut = xyOut0;
% xyOut=N*xyOut0+randn(size(xyOut0))/1e3;
for ncut=1:2
    M=a+eye(size(a)); 
    Mbeta=(((0.9)*eye(N)+0.1*bsxfun(@rdivide,M,sum(M,2)))^10);
    for n1=1:120
        xyOut=Mbeta*xyOut;
        mxyOut=mean(xyOut,1);
        [c1,d1,c2]=svd(cov(xyOut,1));
        xyOut=(xyOut-mxyOut(ones(N,1),:))*c1*diag(1./sqrt(.1+diag(d1)))*c2'; %sqrtm(pinv(.1*eye(2)+cxyOut));
    end
    [i,j]=find(a>0.01); 
    dd=sum((xyOut(i,:)-xyOut(j,:)).^2,2);
    k=find(dd>4*mean(dd));
    if isempty(k), break; end
    a(i(k)+N*(j(k)-1))=0.01;
end
xyOut0=xyOut;

xyOut0=sqrt(N)*detrend(xyOut0,'constant')*diag(1./max(eps,std(xyOut0,1,1)));
% K=10;
k=5;
[sxyOut0,idxequal]=sortrows(round(10*xyOut0)/10);
idxequal=idxequal(all(~diff(sxyOut0,1,1),2));
xyOut=round(xyOut0);
while size(unique(xyOut,'rows'),1)~=N
    k=k*1.1;
    xyOut=xyOut0*k;
    xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/10)*k;
    xyOut=round(xyOut);
end
if N<30 % small map knot lines
 xyOut=2*xyOut+(randi(3,size(xyOut))-2);
end
%xyOut=bsxfun(@plus,xyOut,round(median(xyIn,1)-median(xyOut,1)));
dxy = round(wts*(xyOut-xyIn)./sum(wts)); % Howe's
xyOut = bsxfun(@minus,xyOut,dxy);

end

function D=mindist(C,N)

X=logical(speye(N));
D=inf(N);

D(X)=0;
for n=1:N,
    X=((C*X)>0)&(D>n);
    if ~any(X(:)),break;end
    D(X)=n;
end

end