# C.20.2.1.1 Frame of Reference Transformation Matrix

The Frame of Reference Transformation Matrix (3006,00C6) A M B describes how to transform a point ( B x, B y, B z) with respect to RCS B into ( A x, A y, A z) with respect to RCS A according to the equation below.

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The Matrix Registration is expressible as multiple matrices, each in a separate item of the Matrix Sequence (0070,030A). The equation below specifies the order of the matrix multiplication where M 1 , M 2 and M 3 are the first, second and third items in the sequence.

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Registration often involves two or more RCS, each with a corresponding Frame of Reference Transformation Matrix. For example, another Frame of Reference Transformation Matrix A M C can describe how to transform a point ( C x, C y, C z ) with respect to RCS C into ( A x, A y, A z ) with respect to RCS A . It is straightforward to find the Frame of Reference Transformation Matrix B M C that describes how to transform the point ( C x, C y, C z ) with respect to RCS C into the point ( B x, B y, B z ) with respect to RCS B. The solution is to invert A M B and multiply by A M C , as shown below:

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