n1wd1

function xy = solver(kd,bx)

p0=bx([1 3]);
npts = length(kd);
dela=ones(1000,1);
dela(500)=400;
dela=fft(dela);
if npts>78,
xy = zeros(npts,2);
xy(:,2) = (bx(3) + bx(4))/2;
xy(:,1) = linspace(bx(1), bx(2), npts)';
return
end
nones=ones(npts,1);
if any(kd(:)>0)
  dx=bx(2)-bx(1);
  dy=bx(4)-bx(3);
D=dx+dy;
d=D/20;
while max(2,ceil(dx/d))*max(2,ceil(dy/d))<200
	d=d/2;
end
x=0:d:dx;
if x(end)<dx
	x(end+1)=dx;
end
y=0:d:dy;
if y(end)<dy
	y(end+1)=dy;
end
[x,y]=meshgrid(x,y);
x=x(:).';
y=y(:).';
k = length(x);
  [dum,p]=sort(-max(kd));
  kd=kd(p,p);
  M=9;
  N0=min(M,npts);
  xy = zeros(npts,2);
  xy(1:N0,:) = solverl(kd(1:N0,1:N0),dx,dy);
  for N=M+1:npts
    xy(N,:) = solver2(kd(1:N,1:N),N,x,y,xy(1:N,:),k,d,dx,dy);
  end
  for N=1:N0
    xy(N,:) = solver2(kd,N,x,y,xy,k,d,dx,dy);
  end
  i0=0;
  for N=1:N0
    x1=xy(:,1);
    y1=xy(:,2);
    [XY1,XY2] = meshgrid(x1,y1);
    dist = sqrt((XY1 - XY1').^2 + (XY2 - XY2').^2); 
    
    % Calculate strain matrix
    strainMatrix = dist - kd;
    strainMatrix(kd < 0) = 0;
    [m,i]=max(sum(abs(strainMatrix)));
    if i==i0, break; else, i0=i; end
    xy(i,:) = solver2(kd,i,x,y,xy,k,d,dx,dy);
  end
  [v,w]=sort(p);
  xy=xy(w,:);
  xy=xy+p0(nones,:);
else
  xy = p0(nones,:);
end


function xy = solverl(kd,dx,dy)
npts = length(kd);
[I,J,v] = find(triu(kd)>0);
k = 1000; % change k according to memory capacity.
x = rand(npts,k)*dx+i*rand(npts,k)*dy;
[tv,id] = min(sum(abs(abs(x(I,:)-x(J,:))-...
	repmat(kd((J-1)*npts+I),1,k))));
xy=[real(x(:,id)) imag(x(:,id))];


function xy = solver2(kd,N,x,y,xy0,k,d,dx,dy)
[I,dm1,dm2] = find(kd(:,N)>0); nn=length(I);
nnones=ones(1,nn);
kones=ones(1,k);
[tv,id] = min(sum(abs(sqrt((xy0(I,kones)-x(nnones,:)).^2+...
	(xy0(I,kones+1)-y(nnones,:)).^2)-kd(I,N+kones-1))));
x=max(0,x(id)-d):d/5:min(dx,x(id)+d);
y=max(0,y(id)-d):d/5:min(dy,y(id)+d);
[x,y]=meshgrid(x,y);
x=x(:).';
y=y(:).';
k = length(x);
nnones=ones(1,nn);
kones=ones(1,k);
[tv,id] = min(sum(abs(sqrt((xy0(I,kones)-x(nnones,:)).^2+...
	(xy0(I,kones+1)-y(nnones,:)).^2)-kd(I,N+kones-1))));
xy=[x(id) y(id)];