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The relationship between the orientation distribution function (ODF) and the polefigure is based on the geometry of projection lines in the orientation space.  The paper presents an analytical description of the projection lines and theirtransformations by symmetry operations. Using simple algebraical rules someproperties of the projection lines as well as some properties of the associatedprojection lines (coupled due to the centrosymmetry of the pole figure) have beenderived.

Properties of Projection Lines in the Space of the Orientation Distribution Function