Why matplotlib circle/patchCollection's point of rotation get changed

To rotate it, it seems to be specified with .rotate_deg_around(x,y,degree). This example is rotated 90 degrees at xy=0.5.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.collections
import matplotlib as mpl
 
num = 5
sizes = 0.01, 0.01, 0.01, 0.01, 0.01
xy = (.5,.7),(.5,.6),(.5,.5),(.5,.4),(.5,.3)

print(xy)
 
 # Note that the patches won't be added to the axes, instead a collection will
patches = [plt.Circle(center, size) for center, size in zip(xy, sizes)]
patches2 = [plt.Circle(center, size) for center, size in zip(xy, sizes)]
 
fig, ax = plt.subplots(1,1)
 
coll = matplotlib.collections.PatchCollection(patches, facecolors='none')
coll2 = matplotlib.collections.PatchCollection(patches2, facecolors='None')
ax.add_collection(coll)
ax.add_collection(coll2)
coords = [0.5,0.5]
# t2 = mpl.transforms.Affine2D().rotate_deg(12.5) + ax.transData
# t2 = mpl.transforms.Affine2D().rotate_deg(2.5) + ax.transData
t2 = mpl.transforms.Affine2D().rotate_deg_around(coords[0], coords[1], 90) + ax.transData
coll2.set_transform(t2)

plt.show()

If you don't specify a center of rotation, the rotation will be around (0,0). To rotate around a certain point, you can first subtract its coordinates, do the rotation and then add these coordinates again.

The following example shows the difference:

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.collections
import matplotlib as mpl

sizes = [0.01, 0.01, 0.01, 0.01, 0.01]
xy = [(.5, .7), (.5, .6), (.5, .5), (.5, .4), (.5, .3)]
xc, yc = xy[-1]  # (.5, .3)

fig, axes = plt.subplots(ncols=2, figsize=(12, 4))
for ax in axes:
    patches = [plt.Circle(center, size) for center, size in zip(xy, sizes)]
    coll = matplotlib.collections.PatchCollection(patches, facecolors='none')
    ax.add_collection(coll)
    cmap = plt.get_cmap('rainbow')
    for angle in np.arange(12.5, 360, 12.5):
        patches2 = [plt.Circle(center, size) for center, size in zip(xy, sizes)]
        coll2 = matplotlib.collections.PatchCollection(patches2, facecolors=cmap(angle / 360))
        if ax == axes[0]:
            t2 = mpl.transforms.Affine2D().rotate_deg(angle) + ax.transData
            ax.set_title('rotation around (0, 0)')
        else:
            t2 = mpl.transforms.Affine2D().translate(-xc, -yc).rotate_deg(angle).translate(xc, yc) + ax.transData
            ax.set_title(f'rotation around {xc, yc}')
        coll2.set_transform(t2)
        ax.add_collection(coll2)
    ax.autoscale()
plt.show()