Cheeeese

function xyOut = solver(a, xyIn, wts)
% In code we trust

N = length(a);
tmp = pdist(xyIn);
W = max(tmp(:))*sum(wts);
nbin = 10;
xtra = 10;

diag(sum(a));
[V,~] = eig(ans-a, ans);

for ss=1:3
    [c{ss} c{ss+3}] = solver_1(a, ss+1, N, V+rand(size(V))/25);
end
c{7} = solver_2(xyIn, N, V(:,2:3),0);

[p1,p2] = find(triu(a,1));
[pickr,pickc] = find(tril(true(nnz(triu(a,1))),-1));
parfor ss=1:7
    NN(ss) = gradeIt(p1,p2,pickr,pickc,c{ss});
end

[~, best] = min(NN);
tmp = c{best};
xy = bsxfun(@minus, tmp, round(wts*(tmp-xyIn)./sum(wts)));

% --- Slipknot

m1 = min(xy,[], 1);
m2 = max(xy,[], 1);
xbin = unique(round(linspace(m1(1)-xtra, m2(1)+xtra, nbin)));
ybin = unique(round(linspace(m1(2)-xtra, m2(2)+xtra, nbin)));
[Y, X] = meshgrid(ybin, xbin);

for i = 1:N
    
    D = sqrt((xy(i,1)-X).^2 + (xy(i,2)-Y).^2);
    nei = find(a(i,:));
    I = p1~=i & p2~=i;
    v = funknots(xy, xy(i,1), xy(i,2), nei, p1(I), p2(I));
    
    if v
        
        K = funknots(xy, X, Y, nei, p1(I), p2(I));
        M = K+D*wts(i)/W;
        [m, mi] = min(M(:));
        if m<v
            x0 = X(mi);
            y0 = Y(mi);
            if ismember([x0 y0], xy, 'rows')
                for gs = 1:N
                    [X_, Y_] = meshgrid(x0+(-gs:gs), y0+(-gs:gs));
                    xy_ = [X_(:) Y_(:)];
                    xy_(ismember(xy_, xy, 'rows'),:) = NaN;
                    if any(~isnan(xy_(:,1)))
                        tmp = (x0-xy_(:,1)).^2+(y0-xy_(:,2)).^2;
                        tmp(isnan(tmp)) = Inf;
                        [~,mi] = min(tmp);
                        x0 = xy_(mi,1);
                        y0 = xy_(mi,2);
                        break;
                    end
                end
            end
            xy(i,:) = [x0 y0];
        end
    end
end

xyOut = xy;

end

function [xyOut xyOut1] = solver_1(a, ss, N, V)
randn('seed',ss);
xyOut=V(:,2:3);
sN=sqrt(N);
for ncut=1:2
    Mbeta=((1-ss/15)*eye(N)+(ss/15)*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
    for n1=1:(117+ss)
        xyOut=Mbeta*xyOut;
        xc = bsxfun(@minus,xyOut,sum(xyOut)/N);
        [c1,D]=svd(xc');
        xyOut=xc*c1*diag(sN./(.1+D([1 4])))*c1';
    end
    [i,j]=find(a>0.002+ss*5.1e-4);
    sum((xyOut(i,:)-xyOut(j,:)).^2,2);
    k=find(ans>(3.15 + ss*0.102)*mean(ans));
    if isempty(k), break; end
    a(i(k)+N*(j(k)-1))=0.002+ss*5.1e-4;
end

xyOutH=xyOut;
single_idx = find(sum(a)==1);
[singles_link, ~] = find(a(:,single_idx)==1);
xyOut(single_idx,:)=xyOut(singles_link,:);

for zsingle=1:2
    xyOut0=sqrt(N)*detrend(xyOut,'constant')*diag(1./std(xyOut,1,1));
    k=5;
    [sxyOut0,idxequal]=sortrows(round(15*xyOut0));
    idxequal=idxequal(all(~diff(sxyOut0,1,1),2));
    xyOut=round(xyOut0);
    while size(unique(xyOut,'rows'),1)~=N
        k=k*(1.0+ss*0.055);
        xyOut=xyOut0*k;
        xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/(9+ss))*k;
        xyOut=round(xyOut);
    end
    if zsingle==1
        xyOut1=xyOut;
        xyOut=xyOutH;
    end
end
end

function xyOut = solver_2(xyIn, N, V,xyOut)
mult    = norm(max(xyIn)-min(xyIn))/norm(max(V)-min(V));
while size(unique(xyOut,'rows'),1)<N
    xyOut       = round(V*mult);
    [~,i]       = unique(xyOut,'rows');
    m           = setdiff(1:N,i);
    xyOut(m,:)  = xyOut(m,:) + randi([-1 1],length(m),2);
    mult        = mult*1.5;
end
end

function ans = gradeIt(p1i,p2i,pickr,pickc,XYnew)
X = [XYnew(p1i,:) XYnew(p2i,:)];
x1 = X(pickr,:);
x3 = X(pickc,:);
sum(areIntersecting(x1(:,1),x1(:,2),x1(:,3),x1(:,4),x3(:,1),x3(:,2),x3(:,3),x3(:,4)));
end

function ans = areIntersecting(x1,y1,x2,y2,x3,y3,x4,y4)
a = x1.*y2 - y1.*x2;
b = x3.*y4 - y3.*x4;
Px_n = a.*(x3 - x4) - b.*(x1 - x2);
Py_n = a.*(y3 - y4) - b.*(y1 - y2);
Pxy_d = (x1 - x2).*(y3 - y4) - (y1 - y2).*(x3 - x4);
isPointBetween(x1, x2, Px_n, Pxy_d) & ...
    isPointBetween(y1, y2, Py_n, Pxy_d) & ...
    isPointBetween(x3, x4, Px_n, Pxy_d) & ...
    isPointBetween(y3, y4, Py_n, Pxy_d);
end

function ans = isPointBetween(pt1, pt2, num, den)
(pt1.*den - num).*(num - pt2.*den) >= 0;
end

function K = funknots(xy, X, Y, Lb, Lc, Ld)
% Knots for nuts

bx = permute(xy(Lb,1), [2 3 1]);
by = permute(xy(Lb,2), [2 3 1]);
cx = permute(xy(Lc,1), [2 3 4 1]);
cy = permute(xy(Lc,2), [2 3 4 1]);
dx = permute(xy(Ld,1), [2 3 4 1]);
dy = permute(xy(Ld,2), [2 3 4 1]);
ax_cx = bsxfun(@minus, X, cx);
ay_cy = bsxfun(@minus, Y, cy);
bx_ax = bsxfun(@minus, bx, X);
by_ay = bsxfun(@minus, by, Y);
dx_cx = bsxfun(@minus, dx, cx);
dy_cy = bsxfun(@minus, dy, cy);
nr = bsxfun(@minus, bsxfun(@times,ay_cy,dx_cx), bsxfun(@times,ax_cx,dy_cy));
ns = bsxfun(@minus, bsxfun(@times,ay_cy,bx_ax), bsxfun(@times,ax_cx,by_ay));
dn = bsxfun(@minus, bsxfun(@times,bx_ax,dy_cy), bsxfun(@times,by_ay,dx_cx));

r = bsxfun(@rdivide, nr, dn);
s = bsxfun(@rdivide, ns, dn);
K = sum(sum(r>=0 & r<1 & s>=0 & s<=1, 3), 4);
end

function D = pdist(X)
N = size(X,1);
D = NaN(N*(N-1)/2,1);
for i = 1:N-1
    D((i-1)*(N-i/2)+1:i*(N-(i+1)/2)) = (X(i,1)-X(i+1:end,1)).^2 + (X(i,1)-X(i+1:end,1)).^2;
end
D = sqrt(D);
end