# Velocity Matrix

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If I have the derivative of the derivative of the position, scale, and rotation of the transformation of a bone, is there anyway i can turn that into a matrix in which when a vector is multiplied by that matrix returns the velocity of that point? Basically I want to use this to turn my keyframe bone animation into a velocity texture used in my deferred rendering engine.

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Euler's theorem states that given a velocity v of a point p on a rigid body you can find the velocity v' of any other point p' like this:

v' = v + cross( omega, r )

Here omega is the angular velocity and r is the vector from p to p'. I don't know exactly what you need, but you could write the cross product as matrix multiplication.

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