Blender中各种Matrix之间的关系

0. bpy_types

• bpy_types.Object

>>> type(bpy.data.objects['Armature'])
<class 'bpy_types.Object'>

• bpy.types.Armature

>>> type(bpy.data.armatures['Armature'])
<class 'bpy.types.Armature'>
>>> type(bpy.data.objects['Armature'].data)
<class 'bpy.types.Armature'>

• bpy.types.Pose <- bpy.types.Object.pose

>>> type(bpy.data.objects['Armature'].pose)
<class 'bpy.types.Pose'>

• bpy_types.PoseBone <- bpy.types.Pose.bones[0]

>>> type(bpy.data.objects['Armature'].pose.bones[0])
<class 'bpy_types.PoseBone'>

• bpy_types.Bone <- bpy.types.Armature.bones[0]
• bpy_types.Bone <- bpy.types.PoseBone.bone

>>> type(bpy.data.armatures['Armature'].bones[0])
<class 'bpy_types.Bone'>
>>> type(bpy.data.objects['Armature'].data.bones[0])
<class 'bpy_types.Bone'>
>>> type(bpy.data.objects['Armature'].pose.bones[0].bone)
<class 'bpy_types.Bone'>

1. Matrix

How can I manually calculate bpy.types.PoseBone.matrix using Blender's Python API? - Blender Stack Exchange

scripting - bpy.types.Bone.matrix vs matrix_local - Blender Stack Exchange

Blender Manual - Space types

均为4×4矩阵。

• Bone.matrix_local：bone在ARMATURE SPACE中的无pose矩阵；等价于在Rest Position状态下的 PoseBone.matrix。

>>> bpy.data.objects['Armature'].data.bones["Bone"].matrix_local \
... == bpy.data.objects['Armature'].pose.bones["Bone"].matrix
True

• Bone.matrix: 在Rest Position下，从bone的BONE SPACE变换到父骨骼的BONE SPACE的变换矩阵(3x3)，但不包含translation。

  矩阵的各个列分别等于 Bone.x_axis, Bone.y_axis, Bone.z_axis，表示骨骼的 x/y/z 轴在父骨骼的BONE SPACE中的位置。

>>> bone = bpy.data.objects['Armature'].data.bones["Bone"]
>>> bone.matrix \
... == (bone.parent.matrix_local.inverted() @ bone.matrix_local).to_3x3()
True

• PoseBone.matrix_basis：bone在BONE SPACE中的局部变换矩阵，不受父骨骼影响。

>>> bpy.data.objects['Armature'].pose.bones["Bone"].matrix_basis.translation \
... == bpy.data.objects['Armature'].pose.bones["Bone"].matrix_basis.to_translation() \
... == bpy.data.objects['Armature'].pose.bones["Bone"].location
True

>>> bpy.data.objects['Armature'].pose.bones["Bone"].matrix_basis.to_quaternion() \
... == bpy.data.objects['Armature'].pose.bones["Bone"].rotation_quaternion
True

>>> bpy.data.objects['Armature'].pose.bones["Bone"].matrix_basis.to_scale() \
... == bpy.data.objects['Armature'].pose.bones["Bone"].scale
True

• PoseBone.matrix：bone在ARMATURE SPACE中的pose矩阵。

  子骨骼的matrix_basis在与父骨骼的matrix复合可得到子骨骼在在POSE SPACE (ARMATURE SPACE带上pose参数) 中的变换矩阵。

>>> posebone = bpy.data.objects['Armature'].pose.bones["Bone"]
>>> posebone.parent.matrix @ posebone.matrix_basis \
... == posebone.matrix
# bone无parent时
>>> posebone.bone.matrix_local @ posebone.matrix_basis \
... == posebone.matrix

• PoseBone.matrix_channel: （只读）在ARMATURE SPACE中，使bone从REST POSE状态直接变换到POSE SPACE的矩阵

>>> posebone = bpy.data.objects['Armature'].pose.bones["Bone"]
>>> posebone.matrix_channel @ posebone.bone.matrix_local == posebone.matrix

• Object.matrix_world：object在WORLD SPACE中的变换矩阵。

矩阵间的变换关系

def matrix_armature(armature_ob, bone_name):
    local = armature_ob.data.bones[bone_name].matrix_local
    basis = armature_ob.pose.bones[bone_name].matrix_basis

    parent = armature_ob.pose.bones[bone_name].parent
    if parent is None:
        return local @ basis
    else:
        parent_local = armature_ob.data.bones[parent.name].matrix_local
        return matrix_armature(armature_ob, parent.name) @ (parent_local.inverted() @ local) @ basis

思路：从 BONE SPACE 逐级变换到父骨骼的 BONE SPACE，最终到达根骨骼的 BONE SPACE 即为 ARMATURE SPACE。

• basis：当前骨骼在自己的bone space中的变换矩阵。
• local @ basis：当所有祖先骨骼都在rest position状态下时，当前骨骼在armature space中的变换矩阵。
• (parent_local.inverted() @ local) W basis：父骨骼在rest position状态下时，当前骨骼在父骨骼的bone space中的变换矩阵。
• parent_basis @ (parent_local.inverted() @ local) @ basis：当前骨骼在父骨骼的bone space中的变换矩阵。
• parent_local @ parent_basis @ (parent_local.inverted() @ local) @ basis：考虑了父骨骼的pose后，父骨骼以上骨骼都在rest position状态下时，在当前骨骼在armature space中的变换矩阵。

只考虑旋转的话，可以用另一种变换方式：利用Bone.matrix和PoseBone.matrix_basis

def rotation_armature(armature_ob, bone_name):
    bone_mat = armature_ob.data.bones[bone_name].matrix
    rot_mat = armature_ob.pose.bones[bone_name].rotation_quaternion.to_matrix()

    parent = armature_ob.pose.bones[bone_name].parent
    if parent is None:
        return bone_mat @ rot_mat
    else:
        return rotation_armature(armature_ob, parent.name) @ bone_mat @ rot_mat