plot multiple 2d contour plots in one 3d figure [Matlab]

Question

I would like to know how to plot multiple, 2D contour plots spaced apart in the z-axis, in a 3D figure like this:

Answer 1

NOTE: The first part of this answer was meant for HG1 graphics. See the second part if you're working with MATLAB R2014b and up (HG2).

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HG1:

The contour function internally creates a number of patch objects, and returns them as a combined hggroup object. So we could set the ZData of all patches by shifting in the Z-dimensions to the desired level (by default contour is shown at z=0).

Here is an example:

[X,Y,Z] = peaks;
surf(X, Y, Z), hold on       % plot surface

[~,h] = contour(X,Y,Z,20);   % plot contour at the bottom
set_contour_z_level(h, -9)
[~,h] = contour(X,Y,Z,20);   % plot contour at the top
set_contour_z_level(h, +9)

hold off
view(3); axis vis3d; grid on

Here is the code for the set_contour_z_level function used above:

function set_contour_z_level(h, zlevel)
    % check that we got the correct kind of graphics handle
    assert(isa(handle(h), 'specgraph.contourgroup'), ...
        'Expecting a handle returned by contour/contour3');
    assert(isscalar(zlevel));

    % handle encapsulates a bunch of child patch objects
    % with ZData set to empty matrix
    hh = get(h, 'Children');
    for i=1:numel(hh)
        ZData = get(hh(i), 'XData');   % get matrix shape
        ZData(:) = zlevel;             % fill it with constant Z value
        set(hh(i), 'ZData',ZData);     % update patch
    end
end

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HG2:

The above solution doesn't work anymore starting with R2014b. In HG2, contour objects no longer have any graphic objects as children (Why Is the Children Property Empty for Some Objects?).

Fortunately there is an easy fix, with a hidden property of contours called ContourZLevel. You can learn more undocumented customizations of contours plots here and here.

So the previous example simply becomes:

[X,Y,Z] = peaks;
surf(X, Y, Z), hold on       % plot surface

[~,h] = contour(X,Y,Z,20);   % plot contour at the bottom
h.ContourZLevel = -9;
[~,h] = contour(X,Y,Z,20);   % plot contour at the top
h.ContourZLevel = +9;

hold off
view(3); axis vis3d; grid on

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Another solution that works in all versions would be to "parent" the contour to a hgtransform object, and transform that using a simple z-translation. Something like this:

t = hgtransform('Parent',gca);
[~,h] = contour(X,Y,Z,20, 'Parent',t);
set(t, 'Matrix',makehgtform('translate',[0 0 9]));