Methods are described that use measured pole figures directly to calculate pole figures, inverse pole figures, and the crystal orientation matrix; this latter is a frequency distribution of the Euler rotations, which relate the crystal orientations in a polycrystalline aggregate to a standard crystallographic orientation. It is demonstrated that if data from crystal forms with different crystallographic multiplicities are to be compared the appropriate multiplicity factor must be applied to the data in the measured pole figures.These techniques are applied to computer-simulated fabrics and the data obtained are compared with data derived via the orientation distribution function. It is concluded that the data derived directly from the measured pole figures more closely represent the actual data. In the case of inverse pole figures the procedures based on the orientation distribution function yield results that are of doubtful geological significance.

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