Question Add Displacement Matrix To Existing Matrix In Compute Shader

Hello, I am trying to implement animation layers with GPU Instancing and in order to do so, rather than baking the positions and rotations of each bone into a texture, except the root bone, I want to bake the translation and the rotation (from the parent bone to the current bone) into the texture.

I believe I have this part down. Rather than:

boneMatrices[index] = boneTransform.localToWorldMatrix * bindPoses[boneIndex];

I am doing:

Code (CSharp):

1. Matrix4x4 displacement = Matrix4x4.TRS(boneTransform.position - parentBoneTransform.position, Quaternion.Inverse(parentBoneTransform.rotation) * boneTransform.rotation, Vector3.one);
2.                         boneMatrices[index] = displacement;

Now, after passing these "displacement" matrices into a compute shader, I would like to "add" the displacement for each bone to the resulting matrix of its parent bone.

To be more descriptive, I am setting the root bone's matrix normally (position and rotation). But, for each child bone down the hierarchy, I wish to use said child's parent bone matrix (float4x4) as a base, and "add" the displacement of said child bone (float4x4) to calculate the final position and rotation of the child bone.

I did this simple test in C# that seems to confirm that this can work as the resulting transforms r1-r4 matched the original transforms t1-t4:

Code (CSharp):

1. Matrix4x4 t1Matrix = Matrix4x4.TRS(t1.position, t1.rotation, t1.lossyScale);
2.         Matrix4x4 t2Displacement = Matrix4x4.TRS(t2.position - t1.position, Quaternion.Inverse(t1.rotation) * t2.rotation, Vector3.one);
3.         Matrix4x4 t3Displacement = Matrix4x4.TRS(t3.position - t2.position, Quaternion.Inverse(t2.rotation) * t3.rotation, Vector3.one);
4.         Matrix4x4 t4Displacement = Matrix4x4.TRS(t4.position - t3.position, Quaternion.Inverse(t3.rotation) * t4.rotation, Vector3.one);
5.  
6.         r1.SetPositionAndRotation(t1Matrix.GetColumn(3), t1Matrix.rotation);
7.  
8.         r2.SetPositionAndRotation(r1.position + (Vector3)t2Displacement.GetColumn(3), r1.rotation * t2Displacement.rotation);
9.  
10.         r3.SetPositionAndRotation(r2.position + (Vector3)t3Displacement.GetColumn(3), r2.rotation * t3Displacement.rotation);
11.  
12.         r4.SetPositionAndRotation(r3.position + (Vector3)t4Displacement.GetColumn(3), r3.rotation * t4Displacement.rotation);

But I am unsure of how to do this inside a compute shader and with matrices.

Please let me know if any more info would help. Any help would be appreciated. Thanks.