How to get global rotation of a bone with respect to global planes of axis via python?

Question

I'm simply trying to find the global rotation of a bone in pose mode using python

i.e. what angle a bone makes with the global axis?

The closest I've come is:

for pb in context.selected_pose_bones_from_active_object:
    
    
    pb_world_matrix=armature.matrix_world @ pb.matrix
    loc, rot, scale = pb_world_matrix.decompose()
    rot= rot.to_euler();
    
    print(pb.name,"x=",math.degrees(rot.x),"y=",math.degrees(rot.y),"z=",math.degrees(rot.z))

Edit:
let me explain what I mean with an example:

As you can see in the gif above, initially the angles are:

x_glob= 0deg
y_glob= 0deg
z_glob= 0deg

then I first rotate it by 38deg on global y orientation then I rotate by 41.3deg on global x orientation so the final output should be:

x_glob= 41.3deg
y_glob= 38deg
z_glob= 0deg

I think a better way of looking at the problem is finding the angle made with the planes of global axis (I couldn't find the wording to phrase it till now)

Answer 1

I had a little look into it but I'm not an expert. Discovered you can get the matrix world of the selected bone using pb_mw = pb.matrix. Then using pb_mw.to_euler() you can obtain the euler rotation from the matrix. The only catch seemed to be that a bone at rest position in the interface (x,y,z rotation at 0 degrees in the UI) is actually at 90 degrees on the x axis in the world matrix. Happy for further input on this.

import bpy
from math import degrees

context = bpy.context

for pb in context.selected_pose_bones_from_active_object:
    
    pb_mw = pb.matrix
    pb_rot = pb_mw.to_euler()
    
    print(f"pb matrix world: {pb_mw}")
    print(f"x rotation: {degrees(pb_rot.x) - 90}")
    print(f"y rotation: {degrees(pb_rot.y)}")
    print(f"z rotation: {degrees(pb_rot.z)}")

# Test on empty  
# empty = bpy.data.objects["Empty"]
# empty.matrix_world = pb_mw

Edit: related answer here... Get bone rotation in pose mode using Python

Answer 2

You can't do this.

Why? It is because you have converted rotation from quaternions to Euler angles. That's basically means, that you have dozens of variants to have the same rotation using Eulers. Let me show the example:

Here are 2 figures rotated same way, but, first one has rotation 90,90,0:

second 180, 90, 90

As you see, you can't get initial transforms of the object.

Using rot.to_euler(); gives you one of the variants. But you may get something different, that you have expected.

Of course, you have some initial rotation values, but it's hard to convert them to global without using a transform matrix. And when you put values in the matrix, there is no way to return them back unchanged.

Answer 3

I think I've found a solution

import bpy
from bpy import context
import math
from mathutils import Matrix,Vector

unit_x=Vector((1.0,0.0,0.0))
unit_y=Vector((0.0,1.0,0.0))
unit_z=Vector((0.0,0.0,1.0))

for pb in context.selected_pose_bones_from_active_object:
    
    axis, roll = pb.bone.AxisRollFromMatrix(pb.matrix.to_3x3(), axis=pb.y_axis)

    x_angle=Vector((pb.vector.x,0,pb.vector.z)).angle(unit_x) #angle made with x plane
    y_angle=Vector((0,pb.vector.y,pb.vector.z)).angle(unit_y) #angle made with y plane
    z_angle=Vector((pb.vector.x,0,pb.vector.z)).angle(unit_z) #angle made with z plane
    
    print("angle with plane x:",math.degrees(x_angle))
    print("angle with plane y:",math.degrees(y_angle))
    print("angle with plane z:",math.degrees(z_angle))
    print("self roll:",math.degrees(roll))

added a little roll bonus in there