MATLAB: The exact size and position of the axis box in the case of `axis equal`? - matlab

Question

How to know the exact size and position of the axis box (without axis labels and numbers)? For example, if I use
figure
contourf(x,y,u,100,'linestyle','none')
axis equal
set(gca,'position',[0.1,0.1,0.7,0.8]) %normalized units
The size of the axis frame/box is varyed in the case of the figure window resizing (or using axis equal), but the value of get(gca,'position') remains unchanged. For example:
figure
Z = peaks(20);
contourf(Z,10)
set(gca,'Units','pixels')
get(gca,'position')
axis equal
get(gca,'position')
ans =
0.1300 0.1100 0.7750 0.8150
after axis equal, the axis box is changed, but get(gca,'position') gives the same coordinates:
ans =
0.1300 0.1100 0.7750 0.8150
I need these to align the colorbar to the axis box (with fixed gap between them) in the case of axis equal.

Answer 1

When you call axis equal, the axis box aspect ratio is fixed and the Position property is treated as a maximum size. When you resize the figure window, the axis box will remain centered in the Position rectangle, but in order to maintain the same aspect ratio as before, it may not take up the entire Position rectangle.
If you want it to take up the entire Position rectangle, you can call axis equal again. (this may depend on your MATLAB version; it worked for me in R2015b).
This is also discussed in a bit more detail on MATLAB Central.
To answer your original question, it's a bit complicated. You'd have to get the plot box aspect ratio (using pbaspect() or the axes PlotBoxAspectRatio property) and figure it out:
ah = gca();
% Get the axes Position rectangle in units of pixels
old_units = get(ah,'Units');
set(ah,'Units','pixels');
pos = get(ah,'Position');
set(ah,'Units',old_units);
% Figure the PlotBox and axes Position aspect ratios
pos_aspectRatio = pos(3) / pos(4);
box_aspect = pbaspect(ah);
box_aspectRatio = box_aspect(1) / box_aspect(2);
if (box_aspectRatio > pos_aspectRatio)
% PlotBox is wider than the Position rectangle
box_height = pos(3) / box_aspectRatio;
box_dy = (pos(4)-box_height) / 2;
box_position = [pos(1), pos(2)+box_dy, pos(3), box_height];
else
% PlotBox is taller than the Position rectangle
box_width = pos(4) * box_aspectRatio;
box_dx = (pos(3)-box_width) / 2;
box_position = [pos(1)+box_dx, pos(2), box_width, pos(4)];
end
Note that this will give you the box position in pixels; if you want it in the normalized units that are the axes default, you'll need to normalize it:
fig_pos = get(get(ah,'Parent'),'Position');
box_position = box_position ./ fig_pos([3 4 3 4]);