This is the What's New image:

If the user sets limits afterwards, that will also break the equal aspect ratios

Oh, I see now: the aspect ratio will be set for the current view. Makes perfect sense!

There appears to be connection between setting the box aspect to (1, 1, 1) and the new dimensions being (delta, delta, delta). Hacking it might preserve the limits … If I understand set_box_aspect correctly,

v_internals = np.array((self.xaxis.get_view_interval(),
                        self.yaxis.get_view_interval(),
                        self.zaxis.get_view_interval()))
deltas = np.ptp(v_intervals, axis=1)
self.set_box_aspect(deltas)

should do the trick. (Unable to test this right now, so I'll let somebody else decide which approach is better.)

@tfpf I actually quite like the result with your idea there:

v_intervals = np.vstack((self.xaxis.get_view_interval(),
                         self.yaxis.get_view_interval(),
                         self.zaxis.get_view_interval()))
deltas = np.ptp(v_intervals, axis=1)
self.set_box_aspect(deltas)

# One liner for an existing axes3d `ax`:
# ax.set_box_aspect(np.ptp(np.array([a.get_view_interval() for a in (ax.xaxis, ax.yaxis, ax.zaxis)]), axis=1))

I had another idea for how this could look like too, similar to the original idea except it keeps the current (here the default 4:4:3) box aspect ratio:

v_intervals = np.vstack((self.xaxis.get_view_interval(),
                         self.yaxis.get_view_interval(),
                         self.zaxis.get_view_interval()))
mean = np.mean(v_intervals, axis=1)
delta = np.max(np.ptp(v_intervals, axis=1))
deltas = delta * self._box_aspect / min(self._box_aspect)

self.set_xlim3d(mean[0] - deltas[0] / 2., mean[0] + deltas[0] / 2.)
self.set_ylim3d(mean[1] - deltas[1] / 2., mean[1] + deltas[1] / 2.)
self.set_zlim3d(mean[2] - deltas[2] / 2., mean[2] + deltas[2] / 2.)

If I had to choose one I think I would choose the last, since the user can precede it with a set_box_aspect((1, 1, 1)) and get the same result as the first. But would welcome input on this. I don't believe matlab has prior art for 3D plots here that we can copy.

So to summarize, here are the three options I see:

1. Set the box aspect to (1, 1, 1), change axes limits to show equal data aspects
2. Set the box aspect to be tight around the data, change axes limits to show equal data aspects
3. Keep the box aspect to the present value, change axes limits to show equal data aspects

I would vote 3 since it encompasses 1 and keeps clear separation between the functions that change the box aspect and the data aspect. Will make the change to 3 unless there are any objections.

Perhaps 2 could be set_box_aspect('tight') or something similar? I'm not too familiar with the 2D analogue for this.

For the PR cleanliness check, I'm not sure how to squash the image commits while making sure @patquem keeps credit for the work in their initial commit.

Edit: I'll just keep them as the author on the squashed commit.

I would vote 3 since it encompasses 1, and perhaps 2 could be another keyword? Will make that change unless there are any objections.

This is a nice idea. Could use the adjustable keyword argument—how about:

if adjustable == 'datalim': change the limits, keeping the box aspect the same
if adjustable == 'box': change the box aspect, keeping the limits the same

which would make it more closely resemble the behaviour of 2D axes.

I am not too familiar with this part of the codebase, though. Perhaps somebody else could also provide their suggestions.

I think matching that adjustable keyword is a good idea for API consistency. It looks like a decent bit of effort to build that scaffolding which I don't really have time to do at the moment, so I would say that we keep this as-is and put that in a separate PR. In other words, just doing the adjustable == 'datalim' behavior right now.

Nice discussion, which probably shows why it wasn't implemented earlier: there are lots of definitions of "equal" here...

One thing that struck me, that of course doesn't have to be part of this, is that maybe one would also like to add something like "equalyxy", "equalxz" and "equalyz" to set two out of three axes equal?

@oscargus good idea, wasn't too hard to add!
Here's the what's new image, setting the aspect after a set_box_aspect((3, 4, 5)):

Updated to maximally fill the available space (it was shrunk before), and changed the what's new plotted cuboid to side lengths (1, 1, 5) to exaggerate what's happening:

Huh, gallery updates must have gotten lost in a rebase, added back in

As discussed in the dev call yesterday, this is now a blocker for #23449.

🎉 I'm very excited this is going in!