I've attached requested output

I now have the arrowshaft and the angle that the arrowheads make with the arrowshaft correct, but I still can't figure out the algorithm that Matlab is using for the size of the arrowhead.  New test code for Matlab is:

hq = quiver ([5 5 5 5 5], [5 5 5 5 5], [1 2 3 1 0], [0 1 3 4 5]);
saveas (gcf, 'tstquiver4a.png');
set (hq, 'maxheadsize', 0.4);
saveas (gcf, 'tstquiver4b.png');

Actually, a better test case to run would be

quiver ([5 6 8], [5 5 5], [10 10 10], [0 0 0]);
saveas (gcf, 'tstquiver3.png');

Thanks.  It looks like Octave is correctly calculating the length of the arrowshaft, but the arrowhead is too big.  At least that points towards which part of the algorithm in _quiver_.m needs modification.

Could someone with Matlab try this code?

quiver ([5 6], [5 6], [1 1], [1 1])
saveas (gcf, 'tstquiver2.png')

According to the documentation for AutoScale

Scale the arrow length to fit within the grid-defined coordinate data and scale arrows so that they do not overlap. The quiver function then applies the AutoScaleFactor to the arrow length.

The idea I'm trying to check is whether AutoScale has a specific case for a single arrow (for which there is no grid).

@Rik:

>> version

ans =

    '9.3.0.713579 (R2017b)'

>> quiver (5,5,1,1);
>> saveas (gcf, 'tstquiver.png')

Changing category back to "Need Info".

@Clark: Can you start Matlab without any user customizations and see if you get the same size figure?

@Dmitri: It could also be the case that Matlab has special logic for weird corner cases such as this one.

Marking as confirmed.  The attached jpg from Matlab shows a much smaller arrowhead.

Using a simple

quiver(5, 5, 1, 1)

produces an arrow whose head is too large.