Sorting 2D matrix and retaining nodes in triangle groups

I am trying to optimize a script (below) that finds the bounding boxes to functional values of all lower left triangles in a 2D space. The code goes through all the triangles and then sorts the nodes in ascending order based on the functional values. This seems inefficient.

Is there some way that I could sort the functional values before the loops but still retain the nodes in the triangle groups? Or some other smart way to speed things up?

clear;

x = (1:600)';
y = (1:500);
z = 2 * x.^2 + y;

zGrid = linspace(min(z, [], 'all') - 1, max(z, [], 'all') + 1, 200);

for iX = 1:length(x) - 1
    for iY = 1:length(y) - 1
        % Node indices
        xIndices = [iX, iX, iX + 1];
        yIndices = [iY, iY + 1, iY];
        
        % Node values
        xTmp = x(xIndices);
        yTmp = y(yIndices);
        zTmp = z(sub2ind(size(z), xIndices, yIndices));
        
        % Node sorted according to z
        [zSorted, indicesSorted] = sort(zTmp);
        xSorted = xTmp(indicesSorted);
        ySorted = yTmp(indicesSorted);
        
        % Get bounding box on zGrid
        iMin = find(zGrid <= zSorted(1), 1, 'last');
        iMax = find(zGrid(iMin:end) >= zSorted(end), 1, 'first') + (iMin - 1);
    end
end

Answer 1

[Fredrik P]

See answer on Stack Overflow.