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bone matrix difficulties

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I can get a transformation for a bone either in global space matrix, or global space location, rotation and scale vectors. I need to assign it to a bone which can have parents, so I need to recalculate the rotation and location (and scale) in respect to the parent bone transforms.

The API I use is the Blender API and I can get the transforms of the parent bone relative to their own parent, if any.

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