Rotate object around point other than the center without bpy.ops [duplicate]

Question

I'm trying to build upon this answer to rotate an object around an arbitrary point.

I get that if I do:

rot_mat = Matrix.Rotation(-pi / 4, 4, 'Z')
orig_loc, orig_rot, orig_scale = obj.matrix_world.decompose()

orig_loc_mat = Matrix.Translation(orig_loc)
orig_rot_mat = orig_rot.to_matrix().to_4x4()
orig_scale_mat = Matrix.Scale(orig_scale[0],4,(1,0,0)) * Matrix.Scale(orig_scale[1],4,(0,1,0)) * Matrix.Scale(orig_scale[2],4,(0,0,1))

obj.matrix_world = rot_mat @ orig_rot_mat @ orig_scale_mat 

instead of

obj.matrix_world = orig_loc_mat @ rot_mat @ orig_rot_mat @ orig_scale_mat 

I will have my object rotated correctly and centered on 0.0.

So I guess I need to perform some transform on orig_loc_mat so that the location is also moved.

What's the transform I need to do?

Answer 1

If you rotate around the center (i.e.: location) of the object, the process is:

1. translate the object to location (0, 0, 0)
2. rotate the object
3. translate it back to the original location

which is what this does:

 obj.matrix_world = orig_loc_mat @ rot_mat @ orig_rot_mat @ orig_scale_mat 

In order to rotate around an arbitrary point the process is:

1. translate the object to location (0, 0, 0)
2. rotate the object
3. rotate the location
4. translate it back to the new location

where rotating the location is the same as rotating any object, so what you do is:

# get the rotation matrix (deg is negated - bpy goes clockwise, mathutils counter-clockwise
rot_matrix = mathutils.Matrix.Rotation(math.radians(-deg), 4, axis.upper())

# decompose the world matrix
orig_loc, orig_rot, orig_scale = obj.matrix_world.decompose()
orig_rot_matrix =   orig_rot.to_matrix().to_4x4()
orig_scale_matrix = mathutils.Matrix.Scale(orig_scale[0],4,(1,0,0)) @ mathutils.Matrix.Scale(orig_scale[1],4,(0,1,0)) @ mathutils.Matrix.Scale(orig_scale[2],4,(0,0,1))

# this does the job
#                       1. translate to center
#         2. rotate     |
#         |             |                  3. translate back
#         |             |                  |
new_loc = rot_matrix @ (orig_loc - center) + center)

# make a matrix out of the new location 
new_loc_matrix = mathutils.Matrix.Translation(new_loc)

# all together now
obj.matrix_world = new_loc_matrix @ rot_matrix @ orig_rot_matrix @ orig_scale_matrix 

I pieced this together from answers on rotating without bpy.opy and on rotation around a cursor, so I was clearly standing on the shoulders of giants. Summing things up here in hope it's useful for someone else.