Bug summary

Calling get_extents on a BufferRegion returns the values as unsigned ints so if the region was outside of the canvas, they are incorrect.
The y-axis increases downwards.

Code for reproduction

import matplotlib.pyplot as plt
from matplotlib.transforms import Bbox
import struct

fig = plt.figure()
canvas = fig.canvas
w,h = canvas.get_width_height()
br = canvas.copy_from_bbox(Bbox.from_extents(-10,h-1,10,h+1))
ext = br.get_extents()
print(ext,struct.unpack('iiii',struct.pack('IIII',*ext)))

Actual outcome

(4294967286, 4294967295, 10, 1) (-10, -1, 10, 1)

Expected outcome

(-10, -1, 10, 1)

Additional information

I think the problem comes from this:
https://github.com/matplotlib/matplotlib/blob/main/src/_backend_agg_wrapper.cpp#L77

static PyObject *PyBufferRegion_get_extents(PyBufferRegion *self, PyObject *args)
{
    agg::rect_i rect = self->x->get_rect();

    return Py_BuildValue("IIII", rect.x1, rect.y1, rect.x2, rect.y2);
}

Replacing 'IIII' with 'iiii' would solve it

Operating system

Windows 10

Matplotlib Version

3.5.2

Matplotlib Backend

TkAgg

Python version

3.10.4

Jupyter version

No response

Installation

pip