Principal Axes of a Volume 

To determine the orientation of a volume segment in space, you can calculate the second central moments of its density distribution and derive the corresponding eigenvectors. Here is a short script to compute central moments and volume orientation.

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Define a function that calculates the moments of an array.

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Convert the volume into a data array with its indices aligned to the graphics coordinates.

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Compute the first- and second-order moments of the tooth density.

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Compute the principal axes of the central moments matrix.

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Display the principal axes of the tooth.

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